Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#86235 |
| Fitting | C32×#532 ⋊ C2 |
| Sylow | C32 ⋊ #3449 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | C23×D3 |
| commutator, cosocle | C22×C3 | C25×C3 |
| Frattini | C22 | C24×C3×D3 |
| Fitting | C32×#532 | C2 |
| socle | C22×C32 | C25 |
| hypercenter | C3×#532 | D3 |
| hypocenter | C3 | C3×#3449 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C3×#532 | |
3267 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135186);