Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×D4×#624 |
| Sylow | C32 ⋊ C22×C4×D4 |
5737 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D32×D4 |
| maximal normal subgroup of | C2×C4×D32×D4 |
| maximal quotient of | #72222723, #72227360 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133905);