Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | D32×M32 |
| Fitting | C32×M32 ⋊ C22 |
| Sylow | C32 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D32 |
| commutator, socle | C2×C32 | C23×C8 |
| Fitting | C32×M32 | C22 |
| prime radical | C22×D32 | C8 |
| cosocle | C32×C8 | C24 |
| hypercenter | M32 | D32 |
| hypocenter | C32 | C22×M32 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C8 ◁ M32 | |
845 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#347, D32×#365, #72222733, … |
| maximal normal subgroup of | D32×#347, D32×#365, #72222733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133375);