Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D9×#575 |
| Fitting | C9×#575 ⋊ C2 |
| Sylow | C9 ⋊ C2×#575 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D9 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C9×#575 | C2 |
| socle | C2×C3 | C22×D3×D4 |
| hypercenter | #575 | D9 |
| hypocenter | C9 | C2×#575 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
2226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3585, D9×#3068, D9×#2956, … |
| maximal normal subgroup of | D9×#3585, D9×#3068, D9×#2956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152735);