Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×C3⋊D3×#99 |
| Fitting | C2×C32×#99 ⋊ C2 |
| Sylow | C32 ⋊ C22×#99 |
3336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#1889, C3⋊D3×#1781, C2×C3⋊D3×B(4,𝔽2), … |
| maximal normal subgroup of | C3⋊D3×#1889, C3⋊D3×#1781, C2×C3⋊D3×B(4,𝔽2), … |
| maximal quotient of | C3⋊D3×#1781 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91494);