Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#64314 |
| Fitting | C32×C4×D4 ⋊ C22 |
| Sylow | C32 ⋊ C4×H(5,𝔽2) |
3533 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72222679, C4×#10596675, #72227390, … |
| maximal normal subgroup of | #72222679, C4×#10596675, #72227390 |
| maximal quotient of | AGL(1,𝔽5)×#64314 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134200);