Finite Group DatabasebetaFinite Group Databasebeta| order | 11520 |
| isoclinism | isoclinic class of #72209666 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C25 ⋊ A6 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | #72209614 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C25 | A6 |
| LCS | G | |
| UCS | C1 ◁ C2 | |
410 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(3,6)(5,9)(8,11)(10,12);(1,2,3)(4,7,8)(5,6,9)(10,11,12);(2,5,6)(7,10,11);(1,4)(3,8)(6,11)(9,12);(2,7)(5,10)(6,11)(9,12);(1,4)(3,8)(5,10)(6,11);(2,7)(3,8)(5,10)(9,12);(1,4)(2,7)(3,8)(5,10)(6,11)(9,12)23 conjugacy classes — view the full character table.
| maximal quotient of | #72209929, #72209933, #72209937, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((3,6)(5,9)(8,11)(10,12), (1,2,3)(4,7,8)(5,6,9)(10,11,12), (2,5,6)(7,10,11), (1,4)(3,8)(6,11)(9,12), (2,7)(5,10)(6,11)(9,12), (1,4)(3,8)(5,10)(6,11), (2,7)(3,8)(5,10)(9,12), (1,4)(2,7)(3,8)(5,10)(6,11)(9,12));