Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C24×C4 ⋊ A5 |
| derived | #11757162 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14515297 |
| commutator, hypocenter | #11757162 | C4 |
| Frattini, socle, cosocle | C25 | C2×A5 |
| Fitting | C24×C4 | A5 |
| prime radical | C2×#11757162 | C2 |
| LCS | G ▷ #11757162 | |
| UCS | C1 ◁ C2 | |
491 conjugacy classes of subgroups; only the 8 normal subgroups are shown.
This group has 491 conjugacy classes of subgroups — too many to draw. Only its 8 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) = 60 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,4,2,3)(5,19,7,18,15,13,23,11,20,12)(6,17,22,8,21,14,10,16,9,24);(5,6,12)(7,15,13)(8,14,22)(9,11,16)(10,18,20)(19,24,21)36 conjugacy classes — view the full character table.
| maximal subgroup of | #72239373, #72239411 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,4,2,3)(5,19,7,18,15,13,23,11,20,12)(6,17,22,8,21,14,10,16,9,24), (5,6,12)(7,15,13)(8,14,22)(9,11,16)(10,18,20)(19,24,21));