v | k | b | a | groups | characteristic polynomial | generating sets | matrix | download | WL-closure |
---|---|---|---|---|---|---|---|---|---|
24 | 8 | 4 | 2 | C4xS3; D24; C2x(C3:C4); (C6xC2):C2; C12xC2; C3xD8; S4; C2xA4; C2xC2xS3; C6xC2xC2 | (x – 8) (x – 4)3 (x – 2)5 (x + 2)15 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 8 | 4 | 2 | C2xA4 | (x – 8) (x – 4) (x – 2)5 (x + 2)5 (x2 + 2x – 4)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 8 | 4 | 2 | C2xA4 | (x – 8) (x – 4) (x – 2)5 (x + 2)5 (x2 + 2x – 4)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 8 | 4 | 2 | C2xA4 | (x – 8) (x + 4) (x – 2)4 (x + 2)6 (x2 – 2x – 4)3 (x2 + 2x – 4)3 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 9 | 4 | 2 | (C6xC2):C2; S4; C2xA4 | (x – 9) (x + 5) (x – 3)2 (x – 1)2 (x + 1)3 (x + 3)3 (x2 – 5)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 9 | 4 | 2 | C2xA4 | (x – 9) (x + 3)2 (x – 1)3 (x3 + x2 – 9x – 1)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 9 | 4 | 2 | C2xA4 | (x – 9) (x + 3)2 (x + 1)3 (x3 – x2 – 9x + 1)3 (x3 + x2 – 9x – 1)3 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 11 | 6 | 4 | C2xA4 | (x – 11) (x + 1)2 (x + 3)3 (x3 – x2 – 9x + 1)3 (x3 + x2 – 9x – 1)3 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 13 | 8 | 6 | C2xA4 | (x – 13) (x – 1)2 (x + 3)3 (x3 + x2 – 9x – 1)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 13 | 12 | 2 | C3:C8; C24; C3:Q8; C4xS3; D24; C2x(C3:C4); (C6xC2):C2; C12xC2; C3xD8; C3xQ8; S4; C2xA4; C2xC2xS3; C6xC2xC2 | (x – 13) (x + 11) (x – 1)10 (x + 1)12 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 15 | 10 | 8 | D24; (C6xC2):C2; C3xD8; S4; C2xA4 | (x – 15) (x – 5) (x + 1)5 (x + 3)5 (x2 – 5)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 15 | 10 | 8 | C2xA4 | (x – 15) (x + 5) (x – 1)5 (x + 3)5 (x2 – 5)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 15 | 10 | 8 | C2xA4 | (x – 15) (x + 5) (x – 1)5 (x + 3)5 (x2 – 5)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 16 | 12 | 10 | C4xS3; D24; C2x(C3:C4); (C6xC2):C2; C12xC2; C3xD8; S4; C2xA4; C2xC2xS3; C6xC2xC2 | (x – 16) (x + 4)3 (x – 2)9 (x + 2)11 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 16 | 12 | 10 | C2xA4 | (x – 16) (x + 4) (x – 2)5 (x + 2)5 (x2 + 2x – 4)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 16 | 12 | 10 | C2xA4 | (x – 16) (x + 4) (x – 2)5 (x + 2)5 (x2 + 2x – 4)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 16 | 12 | 10 | C2xA4 | (x – 16) (x – 4) (x + 2)10 (x2 – 2x – 4)3 (x2 + 2x – 4)3 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 17 | 12 | 10 | D24; (C6xC2):C2; C3xD8; S4; C2xA4 | (x – 17) (x – 3) (x + 1)5 (x + 3)5 (x2 – 5)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 17 | 16 | 10 | C3:C8; C24; SL(2,3); C3:Q8; C4xS3; D24; C2x(C3:C4); (C6xC2):C2; C12xC2; C3xD8; C3xQ8; S4; C2xA4; C2xC2xS3; C6xC2xC2 | (x – 17) (x + 7)2 (x – 1)9 (x + 1)12 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 18 | 14 | 12 | D24; (C6xC2):C2; C3xD8; S4; C2xA4 | (x – 18) (x – 4) x5 (x + 2)5 (x2 + 2x – 4)6 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 19 | 18 | 14 | C3:C8; C24; SL(2,3); C3:Q8; C4xS3; D24; C2x(C3:C4); (C6xC2):C2; C12xC2; C3xD8; C3xQ8; S4; C2xA4; C2xC2xS3; C6xC2xC2 | (x – 19) (x + 5)3 (x – 1)8 (x + 1)12 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 20 | 18 | 16 | C4xS3; D24; C2x(C3:C4); (C6xC2):C2; C12xC2; C3xD8; S4; C2xA4; C2xC2xS3; C6xC2xC2 | (x – 20) (x + 4)2 (x – 2)3 x9 (x + 2)9 | view download | raw gap magma sage | raw gap magma sage | view download |
24 | 21 | 20 | 18 | C3:C8; C24; SL(2,3); C3:Q8; C4xS3; D24; C2x(C3:C4); (C6xC2):C2; C12xC2; C3xD8; C3xQ8; S4; C2xA4; C2xC2xS3; C6xC2xC2 | (x – 21) (x + 3)5 (x – 1)6 (x + 1)12 | view download | raw gap magma sage | raw gap magma sage | view download |