Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#2845⋊C3 |
| unambiguous semidirect product | #2845⋊C32 |
| unambiguous semidirect product | (C3×#2845)⋊C3 |
| Fitting | C3×#2845 ⋊ C3 |
| derived, Sylow | #2845 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #564⋊C3 |
| commutator, cosocle, hypocenter | #2845 | C32 |
| Frattini | C23 | C3×C22⋊A4 |
| Fitting | C3×#2845 | C3 |
| socle | C23×C3 | C22⋊A4 |
| LCS | G ▷ #2845 | |
| UCS | C1 ◁ C2×C3 | |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153671);