Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C24×C4 ⋊ A5 |
| derived | #14515300 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2 | #14515297 |
| commutator, hypocenter | #14515300 | C2 |
| Frattini, cosocle | C25 | C2×A5 |
| Fitting | C24×C4 | A5 |
| LCS | G ▷ #14515300 | |
| UCS | C1 ◁ C2 | |
437 conjugacy classes of subgroups; only the 6 normal subgroups are shown.
This group has 437 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,11)(2,24)(3,13,10,23)(4,6,12,14)(5,15)(7,20)(8,21)(9,18)(16,19)(17,22);(1,7,4,5,18,12)(2,17,10,8,16,3)(6,22,21,14,19,24)(9,23,15,20,13,11)26 conjugacy classes — view the full character table.
| maximal subgroup of | #72239833 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,11)(2,24)(3,13,10,23)(4,6,12,14)(5,15)(7,20)(8,21)(9,18)(16,19)(17,22), (1,7,4,5,18,12)(2,17,10,8,16,3)(6,22,21,14,19,24)(9,23,15,20,13,11));