Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211×C3 |
| direct product | C2×C3⋊D3×#120 |
| Fitting | C2×C32×#120 ⋊ C2 |
| Sylow | C32 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×C3⋊D3 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C24×C3⋊D3 |
| Fitting | C2×C32×#120 | C2 |
| socle | C23×C32 | C24 |
| hypercenter | C2×#120 | C3⋊D3 |
| hypocenter | C32 | C22×#120 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
13632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3484, C3⋊D3×#1889, C3⋊D3×#2846, … |
| maximal normal subgroup of | C3⋊D3×#3484, C3⋊D3×#1889, C3⋊D3×#2846, … |
| maximal quotient of | C3⋊D3×#2846, C22×C3⋊D3×#120, C2×C3⋊D3×#453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134250);