Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#10592940 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ C2×#453 |
2532 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#453, #72214920, C2×C3⋊(C3⋊#5935), … |
| maximal normal subgroup of | C2×C3⋊D3×#453, #72214920, C2×C3×#10592940, … |
| maximal quotient of | C2×C3×#10592940 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98775);