Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#10588640 |
| Fitting | C22×C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D9 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini | C23×C3 | C23×D3 |
| Fitting | C22×C9×C22⋊C4 | C2 |
| socle | C24×C3 | C22×D3 |
| hypercenter | C22×C22⋊C4 | D9 |
| hypocenter | C9 | C2×#392 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
2718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | #72268791, #72268867, C2×D9×#392, … |
| maximal normal subgroup of | #72268791, #72268867, C2×D9×#392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42095);