Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C3 |
| direct product | C3⋊D3×#585 |
| Fitting | C32×#585 ⋊ C2 |
| Sylow | C32 ⋊ C2×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C24×C3⋊D3 |
| commutator, socle, cosocle | C2×C32 | C26 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C32×#585 | C2 |
| hypercenter | #585 | C3⋊D3 |
| hypocenter | C32 | C2×#585 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ #585 | |
17868 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153259);