Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C42 |
| direct product | C3×#73290 |
| Fitting | C3×#2811 ⋊ C3 |
| derived, Sylow | #2811 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #5464 |
| commutator, cosocle, hypocenter | #2811 | C32 |
| Frattini | C23 | C3×C22⋊A4 |
| Fitting | C3×#2811 | C3 |
| socle | C23×C3 | C22⋊A4 |
| LCS | G ▷ #2811 | |
| UCS | C1 ◁ C2×C3 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153661);