Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#63825 |
| Sylow | C32 ⋊ C4×AGL(1,ℤ/8) |
1309 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #72222697, #72227387, C4×#10595100, … |
| maximal normal subgroup of | #72222697, #72227387, C4×#10595100, … |
| maximal quotient of | AGL(1,𝔽5)×#63825 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 94322);