Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C4 |
| direct product | C3×#81783 |
| Fitting | C32×#493 ⋊ C2 |
| Sylow | C32 ⋊ #3151 |
1393 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#3151, D3×#81783, #72243471, … |
| maximal normal subgroup of | C3×D3×#3151, D3×#81783, #72243471, … |
| maximal quotient of | #72244694, C3×#10784427, C3×#10784429 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108479);