Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D32×#121 |
| Fitting | C32×#121 ⋊ C22 |
| Sylow | C32 ⋊ C22×#121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#121 | C22 |
| hypercenter | #121 | D32 |
| hypocenter | C32 | C22×#121 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #121 | |
5269 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#532, D32×D42 |
| maximal normal subgroup of | D32×#532, D32×D42 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134293);