Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#66353 |
| Sylow | C23 ⋊ C27⋊C3 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #66353⋊C4, C4×#66353, C2×((C22⋊C27)⋊C2)⋊C3, … |
| maximal normal subgroup of | #66353⋊C4, C4×#66353, C2×((C22⋊C27)⋊C2)⋊C3, … |
| maximal quotient of | C4×#66353, C2×#10619570, #13047263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 305);