Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#87239 |
| Fitting | C23×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ #3484 |
4481 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #72215172, C3×#11703805, C3×D3×#3484, … |
| maximal normal subgroup of | #72215172, C3×#11703805, C3×D3×#3484, … |
| maximal quotient of | #72268918 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 138301);