Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#66365 |
| Fitting | C23×3−1+2 ⋊ C3 |
| Sylow | C23 ⋊ #731 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #66365⋊C4, C4×#66365, C2×#66365⋊C2, … |
| maximal normal subgroup of | #66365⋊C4, C4×#66365, C2×#66365⋊C2, … |
| maximal quotient of | C4×#66365, C2×#10619582, #13047275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 317);