Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D288 |
| Fitting | C2×C9×C32 ⋊ C2 |
| Sylow | C9 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D144 |
| commutator, cosocle | C9×C16 | C23 |
| Frattini | C3×C16 | C22×D3 |
| Fitting | C2×C9×C32 | C2 |
| socle | C22×C3 | D48 |
| hypercenter | C2×C32 | D9 |
| hypocenter | C9 | C2×D32 |
| LCS | G ▷ C9×C16 ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34510);