Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | D32×#124 |
| Fitting | C32×#124 ⋊ C22 |
| Sylow | C32 ⋊ C22×#124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#124 | C22 |
| prime radical | C2×D32×D4 | C2 |
| hypercenter | #124 | D32 |
| hypocenter | C32 | C22×#124 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #124 | |
3925 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#532, D32×#496 |
| maximal normal subgroup of | D32×#532, D32×#496 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134506);