Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#10594684 |
| Fitting | C22×C32×C8 ⋊ C22 |
| Sylow | C32 ⋊ C22×#135 |
3177 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11918798, #72222722, #72222726, … |
| maximal normal subgroup of | C2×#11918798, #72222722, #72222726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152626);