Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C2×#10595278 |
| Fitting | C22×C32×D4 ⋊ C22 |
| Sylow | C32 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D32 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C22×C32×D4 | C22 |
| socle | C23×C32 | C24 |
| hypercenter | C22×D4 | D32 |
| hypocenter | C32 | C22×#120 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
9769 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72214860, C2×#11902326, C2×#11902357, … |
| maximal normal subgroup of | #72214860, C2×#11902326, C2×#11902357, … |
| maximal quotient of | C2×#11864777, #72214664, #72214743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134263);