Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C214 |
| direct product | C3×#87572 |
| Fitting | C32×#585 ⋊ C2 |
| Sylow | C32 ⋊ 2−1+6 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C25×D3 |
| commutator, cosocle | C2×C3 | C26×C3 |
| Frattini | C2 | C25×C3×D3 |
| Fitting | C32×#585 | C2 |
| socle | C2×C32 | C26 |
| hypercenter | C3×#585 | D3 |
| hypocenter | C3 | C3×2−1+6 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C3 ◁ C3×#585 | |
11997 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
297 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153302);