Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D32×D8 |
| Fitting | C2×C32×D8 ⋊ C22 |
| Sylow | C32 ⋊ C23×D8 |
4121 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#442, #72222718, C2×#11918798, … |
| maximal normal subgroup of | D32×#442, #72222718, C2×#11918798, … |
| maximal quotient of | D32×#509, #72222759, #72222768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152548);