Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
| direct product | C3⋊D3×#532 |
| Fitting | C32×#532 ⋊ C2 |
| Sylow | C32 ⋊ C2×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Frattini | C22 | C24×C3⋊D3 |
| Fitting | C32×#532 | C2 |
| hypercenter | #532 | C3⋊D3 |
| hypocenter | C32 | C2×#532 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
5184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3151, C3⋊D3×#3498, C3⋊D3×#3184, … |
| maximal normal subgroup of | C3⋊D3×#3151, C3⋊D3×#3498, C3⋊D3×#3184, … |
| maximal quotient of | C3⋊D3×#3184, C4×C3⋊D3×#127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134747);