Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#64308 |
| Fitting | C23×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D32 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C24×D32 |
| Fitting | C23×C32×C4 | C22 |
| socle | C23×C32 | C24 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
13801 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#10596675, #72252264, #72252265 |
| maximal normal subgroup of | C22×#10596675, #72252264, #72252265 |
| maximal quotient of | #72252267 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153237);