Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | D12×3−1+2 |
| unambiguous semidirect product | C4⋊(D3×3−1+2) |
| unambiguous semidirect product | (C9×D12)⋊C3 |
| Fitting | C3×C4×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ D4 |
161 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | #88421⋊C3, #88422⋊C3, #88423⋊C3, … |
| maximal normal subgroup of | #88421⋊C3, #88422⋊C3, #88423⋊C3, … |
| maximal quotient of | 3−1+2×#204, 3−1+2×D24, 3−1+2×Dic12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 456);