Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | C4×#64149 |
| Fitting | C2×C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ C4×#127 |
2772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C3⋊D3×#127, AGL(1,𝔽5)×#64149, C4×#10591510, … |
| maximal normal subgroup of | C4×C3⋊D3×#127, C4×#10591510, C4×#10591522 |
| maximal quotient of | AGL(1,𝔽5)×#64149 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 36530);