Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3×#5945 |
| Fitting | C2×C3×#585 ⋊ C3 |
| Sylow | C2×#585 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | C22×A4 |
| commutator, cosocle, hypocenter | Q8 | C24×C32 |
| Frattini | C2 | C24×C3×A4 |
| Fitting | C2×C3×#585 | C3 |
| socle | C22×C3 | C23×A4 |
| hypercenter | C2×C3×#41 | A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C2×C3×#41 | |
2780 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153891);