Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C28×C3 |
| direct product | C3×C22⋊(C22⋊SL(2,𝔽3)) |
| unambiguous semidirect product | (C22×C3)⋊(C22⋊SL(2,𝔽3)) |
| Fitting | C24×C3×Q8 ⋊ C3 |
| derived, Sylow | C24×Q8 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C24×Q8 | C32 |
| Frattini | C2 | C3×C22⋊(C22⋊A4) |
| Fitting | C24×C3×Q8 | C3 |
| socle | C25×C3 | A4 |
| LCS | G ▷ C24×Q8 | |
| UCS | C1 ◁ C2×C3 | |
2360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153919);