Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | A4×D9⋊A4 |
| Fitting, derived | C24×C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C24×C9 | C2×C32 |
| Frattini | C3 | D3×A42 |
| socle | C24×C3 | C32×D3 |
| LCS | G ▷ C24×C9 | |
| UCS | C1 | |
414 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,4)(2,3)(5,8,6)(10,12)(11,15)(13,16)(14,17);(2,4,3)(6,7,8)(9,17,12,11,10,14,15,13,16)64 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,4)(2,3)(5,8,6)(10,12)(11,15)(13,16)(14,17), (2,4,3)(6,7,8)(9,17,12,11,10,14,15,13,16));