Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3⋊D3×#6038 |
| Hall | C32×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C2×D4×C3⋊D3 |
| Sylow | C32 ⋊ C22×#6038 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D52×C3⋊D3 |
| commutator, cosocle | C2×C32×C52 | C24 |
| Frattini | C2 | C2×D52×C3⋊D3 |
| Fitting, socle | C22×C32×C52 | C23 |
| hypocenter | C32×C52 | C22×D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C22 | |
3636 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
348 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊D3×#87886 |
| maximal normal subgroup of | C2×C3⋊D3×#87886 |
Past the SmallGroups library coverage — no SmallGroups id.