v | k | b | a | groups | characteristic polynomial | generating sets | matrix | download | WL-closure |
---|---|---|---|---|---|---|---|---|---|
48 | 11 | 3 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; D48; C2x(C3:C8); (C3xQ8):C2; C3:Q16{2}; C3x(C8:C2); C3xQ16; GL(2,3); C2xSL(2,3); (C12xC2):C2{2}; Q8xS3; (C4xS3):C2; C6xQ8 | (x – 11) (x + 5) (x – 1)2 (x + 1)2 (x – 3)20 (x + 3)22 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 11 | 4 | 2 | C8xS3; D48; C2x(C3:C8); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C2x(C3:C4)):C2{1}; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3xD16; C2xD24; D8xS3; C2x((C6xC2):C2); C6xD8 | (x – 11) (x – 5)2 (x + 1)6 (x – 3)13 (x + 3)14 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 11 | 4 | 2 | C8xS3; D48; C2x(C3:C8); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C2x(C3:C4)):C2{1}; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3xD16; C2xD24; D8xS3; C2x((C6xC2):C2); C6xD8 | (x – 11) (x – 5)2 (x – 1)6 (x – 3)7 (x + 3)20 (x2 – 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 11 | 4 | 2 | C8xS3; D48; C2x(C3:C8); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C2x(C3:C4)):C2{1}; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3xD16; C2xD24; D8xS3; C2x((C6xC2):C2); C6xD8 | (x – 11) (x – 5)2 (x – 1)6 (x – 3)11 (x + 3)16 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 12 | 4 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 12) (x + 4) (x – 2)2 (x + 6)2 (x – 4)6 (x + 2)12 (x2 – 8)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 12 | 4 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 12) (x – 4)2 (x + 6)2 (x + 2)4 (x + 4)5 (x – 2)10 (x2 – 8)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 12 | 4 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 12) (x – 4)2 (x + 6)2 (x + 2)4 (x + 4)5 (x – 2)10 (x2 – 8)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 12 | 4 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 12) (x – 4)2 (x + 6)2 (x + 2)4 (x + 4)5 (x – 2)10 (x2 – 8)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 13 | 4 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 13) (x – 5)2 (x + 5)2 (x + 1)4 (x + 3)5 (x – 3)10 (x2 + 2x – 7)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 13 | 4 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 13) (x – 5)2 (x + 5)2 (x + 1)4 (x + 3)5 (x – 3)10 (x2 + 2x – 7)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 13 | 4 | 2 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 13) (x – 5)2 (x + 5)2 (x + 1)4 (x + 3)5 (x – 3)10 (x2 + 2x – 7)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 13 | 4 | 2 | C2x(C3:C8); (C3xD8):C2; C2xD24 | (x – 13) (x – 5)2 (x + 5)2 (x + 1)4 (x – 3)6 (x + 3)9 (x2 – 2x – 7)6 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 13 | 4 | 2 | C2x(C3:C8); (C3xD8):C2; C2xD24 | (x – 13) (x – 1)4 (x + 5)4 (x + 3)7 (x – 3)8 (x2 – 2x – 7)6 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 13 | 4 | 2 | C2x(C3:C8); (C3xD8):C2; C2xD24 | (x – 13) (x – 1)4 (x + 5)4 (x + 3)7 (x – 3)8 (x2 – 2x – 7)6 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 15 | 6 | 4 | C2x(C3:C8); (C3xD8):C2; C2xD24 | (x – 15) (x + 1) (x – 5)5 (x – 3)10 (x + 3)19 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 15 | 6 | 4 | C2x(C3:C8); (C3xD8):C2; C2xD24 | (x – 15) (x + 1) (x – 5)5 (x – 3)6 (x + 3)23 (x2 – 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 15 | 6 | 4 | C2x(C3:C8); (C3xD8):C2; C2xD24 | (x – 15) (x + 1) (x – 5)2 (x + 5)3 (x + 3)14 (x – 3)15 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 25 | 24 | 2 | C3:C16; C48; C8xS3; C24:C2{1}; C24:C2{2}; D48; C3:Q16{1}; C2x(C3:C8); (C3:C8):C2{1}; C4x(C3:C4); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C3:C8):C2{2}; (C3xQ8):C2; C3:Q16{2}; (C2x(C3:C4)):C2{1}; C12xC4; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3x(C8:C2); C3xD16; C3xQD16; C3xQ16; C2.S4=SL(2,3).C2; GL(2,3); A4:C4; C4xA4; C2xSL(2,3); SL(2,3):C2; C2x(C3:Q8); C2xC4xS3; C2xD24; (C12xC2):C2{2}; D8xS3; (C2x(C3:C4)):C2{2}; Q8xS3; (C4xS3):C2; C2xC2x(C3:C4); C2x((C6xC2):C2); C12xC2xC2; C6xD8; C6xQ8; C3x((C4xC2):C2){2}; C2xS4; C2xC2xA4; C2xC2xC2xS3; C6xC2xC2xC2 | (x – 25) (x + 23) (x – 1)22 (x + 1)24 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 33 | 24 | 22 | C2x(C3:C8); (C3xD8):C2; C2xD24 | (x – 33) (x – 1) (x + 5)2 (x – 5)3 (x – 3)10 (x + 3)19 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 33 | 32 | 18 | C3:C16; C48; (C4xC4):C3; C8xS3; C24:C2{1}; C24:C2{2}; D48; C3:Q16{1}; C2x(C3:C8); (C3:C8):C2{1}; C4x(C3:C4); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C3:C8):C2{2}; (C3xQ8):C2; C3:Q16{2}; (C2x(C3:C4)):C2{1}; C12xC4; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3x(C8:C2); C3xD16; C3xQD16; C3xQ16; C2.S4=SL(2,3).C2; GL(2,3); A4:C4; C4xA4; C2xSL(2,3); SL(2,3):C2; C2x(C3:Q8); C2xC4xS3; C2xD24; (C12xC2):C2{2}; D8xS3; (C2x(C3:C4)):C2{2}; Q8xS3; (C4xS3):C2; C2xC2x(C3:C4); C2x((C6xC2):C2); C12xC2xC2; C6xD8; C6xQ8; C3x((C4xC2):C2){2}; C2xS4; C2xC2xA4; (C2xC2xC2xC2):C3; C2xC2xC2xS3; C6xC2xC2xC2 | (x – 33) (x + 15)2 (x – 1)21 (x + 1)24 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 35 | 26 | 24 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 35) (x – 5)2 (x + 5)2 (x – 1)4 (x – 3)5 (x + 3)10 (x2 + 2x – 7)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 35 | 26 | 24 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 35) (x – 5)2 (x + 5)2 (x – 1)4 (x – 3)5 (x + 3)10 (x2 + 2x – 7)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 35 | 26 | 24 | C8xS3; C24:C2{1}; C24:C2{2}; C2x(C3:C8); (C3xD8):C2; (C3:C8):C2{2}; C3:Q16{2}; C3x(C8:C2); C3xD16; C3xQD16; C2xD24; (C12xC2):C2{2}; D8xS3; (C4xS3):C2; C3x((C4xC2):C2){2} | (x – 35) (x – 5)2 (x + 5)2 (x – 1)4 (x – 3)5 (x + 3)10 (x2 + 2x – 7)12 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 37 | 29 | 28 | C8xS3; C24:C2{1}; C24:C2{2}; D48; C2x(C3:C8); (C3xQ8):C2; C3:Q16{2}; C3x(C8:C2); C3xQ16; GL(2,3); C2xSL(2,3); (C12xC2):C2{2}; Q8xS3; (C4xS3):C2; C6xQ8 | (x – 37) (x – 5) (x – 1)2 (x + 1)2 (x – 3)14 (x + 3)28 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 37 | 29 | 28 | C8xS3; C2x(C3:C8); (C3:C8):C2{2}; (C3xQ8):C2; C3xQD16; GL(2,3); C2xSL(2,3); Q8xS3; C6xQ8 | (x – 37) (x + 5) (x – 1)4 (x – 3)15 (x + 3)27 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 37 | 30 | 28 | C8xS3; D48; C2x(C3:C8); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C2x(C3:C4)):C2{1}; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3xD16; C2xD24; D8xS3; C2x((C6xC2):C2); C6xD8 | (x – 37) (x + 5)2 (x – 1)6 (x – 3)10 (x + 3)17 (x2 + 2x – 7)6 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 37 | 36 | 26 | C3:C16; C48; (C4xC4):C3; C8xS3; C24:C2{1}; C24:C2{2}; D48; C3:Q16{1}; C2x(C3:C8); (C3:C8):C2{1}; C4x(C3:C4); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C3:C8):C2{2}; (C3xQ8):C2; C3:Q16{2}; (C2x(C3:C4)):C2{1}; C12xC4; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3x(C8:C2); C3xD16; C3xQD16; C3xQ16; C2.S4=SL(2,3).C2; GL(2,3); A4:C4; C4xA4; C2xSL(2,3); SL(2,3):C2; C2x(C3:Q8); C2xC4xS3; C2xD24; (C12xC2):C2{2}; D8xS3; (C2x(C3:C4)):C2{2}; Q8xS3; (C4xS3):C2; C2xC2x(C3:C4); C2x((C6xC2):C2); C12xC2xC2; C6xD8; C6xQ8; C3x((C4xC2):C2){2}; C2xS4; C2xC2xA4; (C2xC2xC2xC2):C3; C2xC2xC2xS3; C6xC2xC2xC2 | (x – 37) (x + 11)3 (x – 1)20 (x + 1)24 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 41 | 40 | 34 | C3:C16; C48; (C4xC4):C3; C8xS3; C24:C2{1}; C24:C2{2}; D48; C3:Q16{1}; C2x(C3:C8); (C3:C8):C2{1}; C4x(C3:C4); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C3:C8):C2{2}; (C3xQ8):C2; C3:Q16{2}; (C2x(C3:C4)):C2{1}; C12xC4; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3x(C8:C2); C3xD16; C3xQD16; C3xQ16; C2.S4=SL(2,3).C2; GL(2,3); A4:C4; C4xA4; C2xSL(2,3); SL(2,3):C2; C2x(C3:Q8); C2xC4xS3; C2xD24; (C12xC2):C2{2}; D8xS3; (C2x(C3:C4)):C2{2}; Q8xS3; (C4xS3):C2; C2xC2x(C3:C4); C2x((C6xC2):C2); C12xC2xC2; C6xD8; C6xQ8; C3x((C4xC2):C2){2}; C2xS4; C2xC2xA4; (C2xC2xC2xC2):C3; C2xC2xC2xS3; C6xC2xC2xC2 | (x – 41) (x + 7)5 (x – 1)18 (x + 1)24 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 43 | 42 | 38 | C3:C16; C48; C8xS3; C24:C2{1}; C24:C2{2}; D48; C3:Q16{1}; C2x(C3:C8); (C3:C8):C2{1}; C4x(C3:C4); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C3:C8):C2{2}; (C3xQ8):C2; C3:Q16{2}; (C2x(C3:C4)):C2{1}; C12xC4; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3x(C8:C2); C3xD16; C3xQD16; C3xQ16; C2.S4=SL(2,3).C2; GL(2,3); A4:C4; C4xA4; C2xSL(2,3); SL(2,3):C2; C2x(C3:Q8); C2xC4xS3; C2xD24; (C12xC2):C2{2}; D8xS3; (C2x(C3:C4)):C2{2}; Q8xS3; (C4xS3):C2; C2xC2x(C3:C4); C2x((C6xC2):C2); C12xC2xC2; C6xD8; C6xQ8; C3x((C4xC2):C2){2}; C2xS4; C2xC2xA4; C2xC2xC2xS3; C6xC2xC2xC2 | (x – 43) (x + 5)7 (x – 1)16 (x + 1)24 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 44 | 42 | 40 | (C4xC4):C3; C8xS3; C24:C2{1}; C24:C2{2}; D48; C2x(C3:C8); (C3:C8):C2{1}; C4x(C3:C4); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C3:C8):C2{2}; (C3xQ8):C2; (C2x(C3:C4)):C2{1}; C12xC4; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3x(C8:C2); C3xD16; C3xQD16; GL(2,3); A4:C4; C4xA4; C2xSL(2,3); SL(2,3):C2; C2x(C3:Q8); C2xC4xS3; C2xD24; (C12xC2):C2{2}; D8xS3; (C2x(C3:C4)):C2{2}; Q8xS3; (C4xS3):C2; C2xC2x(C3:C4); C2x((C6xC2):C2); C12xC2xC2; C6xD8; C6xQ8; C3x((C4xC2):C2){2}; C2xS4; C2xC2xA4; (C2xC2xC2xC2):C3; C2xC2xC2xS3; C6xC2xC2xC2 | (x – 44) (x + 4)5 (x – 2)6 x18 (x + 2)18 | view download | raw gap magma sage | raw gap magma sage | view download |
48 | 45 | 44 | 42 | C3:C16; C48; (C4xC4):C3; C8xS3; C24:C2{1}; C24:C2{2}; D48; C3:Q16{1}; C2x(C3:C8); (C3:C8):C2{1}; C4x(C3:C4); (C3:C4):C4; C12:C4; (C12xC2):C2{1}; (C3xD8):C2; (C3:C8):C2{2}; (C3xQ8):C2; C3:Q16{2}; (C2x(C3:C4)):C2{1}; C12xC4; C3x((C4xC2):C2){1}; C3x(C4:C4); C24xC2; C3x(C8:C2); C3xD16; C3xQD16; C3xQ16; C2.S4=SL(2,3).C2; GL(2,3); A4:C4; C4xA4; C2xSL(2,3); SL(2,3):C2; C2x(C3:Q8); C2xC4xS3; C2xD24; (C12xC2):C2{2}; D8xS3; (C2x(C3:C4)):C2{2}; Q8xS3; (C4xS3):C2; C2xC2x(C3:C4); C2x((C6xC2):C2); C12xC2xC2; C6xD8; C6xQ8; C3x((C4xC2):C2){2}; C2xS4; C2xC2xA4; (C2xC2xC2xC2):C3; C2xC2xC2xS3; C6xC2xC2xC2 | (x – 45) (x + 3)11 (x – 1)12 (x + 1)24 | view download | raw gap magma sage | raw gap magma sage | view download |