v | k | b | a | groups | characteristic polynomial | generating sets | matrix | download | WL-closure |
---|---|---|---|---|---|---|---|---|---|
32 | 10 | 4 | 2 | C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C16:C2; QD32; (C4xC4):C2{2}; C4xD8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C8xC2xC2; C2x(C8:C2); C2xD16; C2xQD16; (C2xD8):C2{1}; C2xC2xD8 | (x – 10) (x + 6) (x – 2)6 (x + 2)8 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 10 | 4 | 2 | (C8xC2):C2{2}; C8:C4{2}; C16:C2; QD32; C2xD16 | (x – 10) (x + 6) (x – 2)6 (x + 2)8 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 10 | 4 | 2 | C16xC2; C16:C2; D32; QD32; C2xD16; C2xQD16; C2xQ16; (C8xC2):C2{4} | (x – 10) (x – 4) (x – 2) (x + 4) x2 (x + 2)10 (x2 – 4x – 4)2 (x2 – 8)6 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 11 | 4 | 3 | C4.D8=C4.(C4xC2); C16:C2 | (x – 11) (x – 1)2 (x – 3)3 (x + 3)6 (x2 + 2x – 7)2 (x2 – 7)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 12 | 8 | 4 | C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C16:C2; QD32; (C4xC4):C2{2}; C4xD8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C8xC2xC2; C2x(C8:C2); C2xD16; C2xQD16; (C2xD8):C2{1}; C2xC2xD8 | (x – 12) (x – 4)2 (x + 4)5 x8 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 12 | 8 | 4 | (C8xC2):C2{2}; C8:C4{2}; C16:C2; QD32; C2xD16 | (x – 12) (x – 4)2 (x + 4)5 x8 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 12 | 8 | 4 | (C8xC2):C2{2}; C8:C4{2}; C16:C2; QD32; C2xD16 | (x – 12) (x – 4)2 (x + 4)5 x8 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 16 | 8 | 4 | (C8xC2):C2{2}; C8:C4{2}; C16:C2; QD32; C2xD16 | (x – 16) (x – 4)2 (x + 4)6 x7 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 16 | 8 | 4 | (C8xC2):C2{2}; C8:C4{2}; C16:C2; QD32; C2xD16 | (x – 16) (x – 4)2 (x + 4)6 x7 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 17 | 16 | 2 | C32; (C4xC2):C4; C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; (C8:C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C4.D8=C4.(C4xC2); C16xC2; C16:C2; D32; QD32; Q32; C4xC4xC2; C2x((C4xC2):C2){1}; C2x(C4:C4); (C4xC4):C2{2}; C4xD8; C4xQ8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C2xQ8):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C4:Q8; C8xC2xC2; C2x(C8:C2); (C8xC2):C2{3}; C2xD16; C2xQD16; C2xQ16; (C8xC2):C2{4}; (C2xD8):C2{1}; (C2xQ8):C2{2}; C4xC2xC2xC2; C2xC2xD8; C2xC2xQ8; C2x((C4xC2):C2){2}; (C2xD8):C2{2}; (C2xQ8):C2{3}; C2xC2xC2xC2xC2 | (x – 17) (x + 15) (x – 1)14 (x + 1)16 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 20 | 16 | 12 | C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C16:C2; QD32; (C4xC4):C2{2}; C4xD8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C8xC2xC2; C2x(C8:C2); C2xD16; C2xQD16; (C2xD8):C2{1}; C2xC2xD8 | (x – 20) (x – 4) (x + 4)6 x8 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 20 | 16 | 12 | (C8xC2):C2{2}; C8:C4{2}; C16:C2; QD32; C2xD16 | (x – 20) (x – 4) (x + 4)6 x8 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 22 | 16 | 14 | C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C16:C2; QD32; (C4xC4):C2{2}; C4xD8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C8xC2xC2; C2x(C8:C2); C2xD16; C2xQD16; (C2xD8):C2{1}; C2xC2xD8 | (x – 22) (x – 6) (x + 2)14 (x2 – 8)8 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 22 | 16 | 14 | C16xC2; C16:C2; D32; QD32; C2xD16; C2xQD16; C2xQ16; (C8xC2):C2{4} | (x – 22) (x – 4) (x + 4) (x – 2)2 x2 (x + 2)9 (x2 + 4x – 4)2 (x2 – 8)6 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 25 | 24 | 18 | C32; (C4xC2):C4; C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; (C8:C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C4.D8=C4.(C4xC2); C16xC2; C16:C2; D32; QD32; Q32; C4xC4xC2; C2x((C4xC2):C2){1}; C2x(C4:C4); (C4xC4):C2{2}; C4xD8; C4xQ8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C2xQ8):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C4:Q8; C8xC2xC2; C2x(C8:C2); (C8xC2):C2{3}; C2xD16; C2xQD16; C2xQ16; (C8xC2):C2{4}; (C2xD8):C2{1}; (C2xQ8):C2{2}; C4xC2xC2xC2; C2xC2xD8; C2xC2xQ8; C2x((C4xC2):C2){2}; (C2xD8):C2{2}; (C2xQ8):C2{3}; C2xC2xC2xC2xC2 | (x – 25) (x + 7)3 (x – 1)12 (x + 1)16 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 28 | 26 | 24 | (C4xC2):C4; C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; (C8:C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C4.D8=C4.(C4xC2); C16xC2; C16:C2; D32; QD32; C4xC4xC2; C2x((C4xC2):C2){1}; C2x(C4:C4); (C4xC4):C2{2}; C4xD8; C4xQ8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C2xQ8):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C4:Q8; C8xC2xC2; C2x(C8:C2); (C8xC2):C2{3}; C2xD16; C2xQD16; C2xQ16; (C8xC2):C2{4}; (C2xD8):C2{1}; (C2xQ8):C2{2}; C4xC2xC2xC2; C2xC2xD8; C2xC2xQ8; C2x((C4xC2):C2){2}; (C2xD8):C2{2}; (C2xQ8):C2{3}; C2xC2xC2xC2xC2 | (x – 28) (x + 4)3 (x – 2)4 x12 (x + 2)12 | view download | raw gap magma sage | raw gap magma sage | view download |
32 | 29 | 28 | 26 | C32; (C4xC2):C4; C8xC4; C8:C4{1}; (C8xC2):C2{1}; ((C4xC2):C2):C2; (C8:C2):C2; C2.((C4xC2):C2)=(C2xC2).(C4xC2); (C8xC2):C2{2}; Q8:C4; (C4xC4):C2{1}; C4:C8; C8:C4{2}; C8:C4{3}; C4.D8=C4.(C4xC2); C16xC2; C16:C2; D32; QD32; Q32; C4xC4xC2; C2x((C4xC2):C2){1}; C2x(C4:C4); (C4xC4):C2{2}; C4xD8; C4xQ8; (C2xC2xC2xC2):C2; (C4xC2xC2):C2{1}; (C2xQ8):C2{1}; (C4xC2xC2):C2{2}; (C4xC4):C2{3}; (C2xC2).(C2xC2xC2); (C4xC4):C2{4}; (C4xC4):C2{5}; C4:Q8; C8xC2xC2; C2x(C8:C2); (C8xC2):C2{3}; C2xD16; C2xQD16; C2xQ16; (C8xC2):C2{4}; (C2xD8):C2{1}; (C2xQ8):C2{2}; C4xC2xC2xC2; C2xC2xD8; C2xC2xQ8; C2x((C4xC2):C2){2}; (C2xD8):C2{2}; (C2xQ8):C2{3}; C2xC2xC2xC2xC2 | (x – 29) (x + 3)7 (x – 1)8 (x + 1)16 | view download | raw gap magma sage | raw gap magma sage | view download |