Finite Group DatabasebetaFinite Group Databasebeta| order | 5760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | A5×GL(2,ℤ/4) |
| Fitting | C24 ⋊ D3×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×S4×A5 |
| commutator | C2×A4×A5 | C22 |
| Fitting | C24 | D3×A5 |
| socle | C23×A5 | C2×D3 |
| cosocle | C2×A4 | C22×A5 |
| hypercenter | C22 | S4×A5 |
| hypocenter | A4×A5 | D4 |
| LCS | G ▷ C2×A4×A5 ▷ A4×A5 | |
| UCS | C1 ◁ C2 ◁ C22 | |
1320 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,3)(2,4)(6,7)(10,13,12);(1,2)(5,7,8)(9,10,13,12,11)70 conjugacy classes — view the full character table.
| maximal subgroup of | A5×#11757163 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,3)(2,4)(6,7)(10,13,12), (1,2)(5,7,8)(9,10,13,12,11));