Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C3×#82624 |
| Fitting | C2×C32×#121 ⋊ C2 |
| Sylow | C32 ⋊ #3006 |
1825 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72252264, #72252269, C3×#10943884 |
| maximal normal subgroup of | #72252264, #72252269, C3×#10943884 |
| maximal quotient of | C3×#10767815 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98122);