Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | C22×D3×#1044 |
| Fitting, socle | C22×C3×C52 ⋊ C2×C4 |
| derived, Hall | C3×C52 ⋊ C23×C4 |
| Sylow | C52 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C23×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#1044 |
| commutator, hypocenter | C3×C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C2×C4 |
| prime radical | C22×D3×C5⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C24 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
1212 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 208 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) = 120 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2,3)(4,5,8,6,7)(9,10,11,13,12)(16,17);(2,3);(14,15);(5,6,7,8)(10,11,12,13)120 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((1,2,3)(4,5,8,6,7)(9,10,11,13,12)(16,17), (2,3), (14,15), (5,6,7,8)(10,11,12,13));