Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×C3×D3×#99 |
| Fitting | C2×C32×#99 ⋊ C2 |
| Sylow | C32 ⋊ C22×#99 |
2329 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×D3×B(4,𝔽2), D3×#99×AGL(1,𝔽7), C2×#99×AGL(1,ℤ/9) |
| maximal normal subgroup of | C2×C3×D3×B(4,𝔽2) |
| maximal quotient of | D3×#99×AGL(1,𝔽7), C2×#99×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91495);