Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#64330 |
| Fitting | C23×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ C4×H(5,𝔽2) |
3533 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10596675, AGL(1,𝔽5)×#64330, C4×#10590410, … |
| maximal normal subgroup of | C4×#10596675, C4×#10590410, C4×#10591725 |
| maximal quotient of | AGL(1,𝔽5)×#64330 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134202);