Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#5241 |
| Fitting | C32×H(5,𝔽2) ⋊ C22 |
| Sylow | C32 ⋊ C2×#453 |
1772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10591510, #72220390, D32×#453, … |
| maximal normal subgroup of | D32×#453, C2×D3×#5241 |
| maximal quotient of | D3×#10591510, #72220390, C2×D3×#5241 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98789);