Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C4×#64146 |
| Fitting | C2×C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ C4×#120 |
3672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#64146, C4×C3⋊D3×#120, C4×#10591531 |
| maximal normal subgroup of | C4×C3⋊D3×#120, C4×#10591531 |
| maximal quotient of | AGL(1,𝔽5)×#64146 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 35983);