Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#10595450 |
| Sylow | C32 ⋊ C2×#578 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#626 |
| commutator, cosocle | C32×C4 | C25 |
| Frattini | C4 | C23×D32 |
| Fitting | C2×C32×#41 | C22 |
| socle | C22×C32 | C22×D4 |
| hypercenter | C2×#41 | D32 |
| hypocenter | C32 | C2×#578 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
3213 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152958);