Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C26×C42 |
| direct product | C3×D3×H(3,𝔽4) |
| Fitting | C32×H(3,𝔽4) ⋊ C2 |
| Sylow | C32 ⋊ C2×H(3,𝔽4) |
2946 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 144214);