Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | A42×Dic5 |
| derived | C24×C5 ⋊ C32×C4 |
| Hall | C24×Dic5 ⋊ C32 |
| Sylow | C5 ⋊ C4×A42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×A42 |
| commutator, hypocenter | C24×C5 | C32×C4 |
| Fitting, socle, cosocle | C25×C5 | C2×C32 |
| prime radical | C2×C5×A42 | C2 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C2 | |
406 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 55 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) = 180 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,4)(2,3)(5,8,6)(9,10,11,12)(14,15)(16,17);(2,3,4)(6,8,7)(13,14,16,17,15)128 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)(9,10,11,12)(14,15)(16,17), (2,3,4)(6,8,7)(13,14,16,17,15));