Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#5175 |
| Fitting | C2×C32×SD16 ⋊ C22 |
| Sylow | C32 ⋊ C2×#492 |
1383 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#492, D3×#83937, D3×#81845 |
| maximal normal subgroup of | D32×#492, D3×#83937, D3×#81845 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108162);