Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C3×C4 |
| direct product | C2×#10596003 |
| Fitting | C2×C32×#117 ⋊ C2 |
| Sylow | C32 ⋊ C2×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×C3⋊D3 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C24×C3⋊D3 |
| Fitting | C2×C32×#117 | C2 |
| socle | C23×C32 | C24 |
| hypercenter | C2×#117 | C3⋊D3 |
| hypocenter | C32 | C2×#555 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
3720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137314);