Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×C4×#932 |
| Fitting | C2×C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ C4×AGL(1,ℤ/8) |
1309 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11659463, #72227387, C4×#10595100, … |
| maximal normal subgroup of | C3×#11659463, #72227387, C4×#10595100, … |
| maximal quotient of | C3×AGL(1,𝔽5)×#932 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 94276);