Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D9×#99 |
| Fitting | C2×C9×#99 ⋊ C2 |
| Sylow | C9 ⋊ C22×#99 |
1668 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×B(4,𝔽2), D9×#1898, D9×#1781, … |
| maximal normal subgroup of | C2×D9×B(4,𝔽2), D9×#1898, D9×#1781, … |
| maximal quotient of | D9×#1898, D9×#1781 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91493);