Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#10589836 |
| Fitting | C2×C9×C4⋊Q8 ⋊ C2 |
| Sylow | C9 ⋊ C2×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini | C22×C3 | C24×D3 |
| Fitting | C2×C9×C4⋊Q8 | C2 |
| socle | C23×C3 | C23×D3 |
| hypercenter | C2×C4⋊Q8 | D9 |
| hypocenter | C9 | C2×#555 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
1860 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137322);