Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10595438 |
| Fitting | C22×C32×Q8 ⋊ C22 |
| Sylow | C32 ⋊ C2×#538 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D32 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C22×C32×Q8 | C22 |
| socle | C23×C32 | C24 |
| hypercenter | C22×Q8 | D32 |
| hypocenter | C32 | C2×#538 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
2833 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135364);