Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C8 |
| direct product | C3×#68062 |
| Fitting | C32×C82 ⋊ C2 |
| Sylow | C32 ⋊ #1712 |
597 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#1712, C3×#10784425, C3×#10784428, … |
| maximal normal subgroup of | C3×D3×#1712, C3×#10784425, C3×#10784428 |
| maximal quotient of | #72245284 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 16600);