Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#66364 |
| Sylow | C23 ⋊ #733 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #66364⋊C4, C4×#66364, C2×#66364⋊C2, … |
| maximal normal subgroup of | #66364⋊C4, C4×#66364, C2×#66364⋊C2, … |
| maximal quotient of | C4×#66364, C2×#10619581, #13047274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 316);