Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D52×D12 |
| Fitting | C3×C4×C52 ⋊ C23 |
| Hall | C3×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C22×D12 |
| Sylow | C3 ⋊ D4×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D52 |
| commutator, socle, cosocle | C2×C3×C52 | C24 |
| Fitting | C3×C4×C52 | C23 |
| hypercenter | C4 | D3×D52 |
| hypocenter | C3×C52 | C22×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 ◁ C4 | |
1052 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×D52, D12×D5⋊AGL(1,𝔽5), #72259959, … |
| maximal normal subgroup of | D3×D4×D52, D12×D5⋊AGL(1,𝔽5), #72259959, … |
Past the SmallGroups library coverage — no SmallGroups id.