Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C1 |
| direct product | Dic6×3−1+2 |
| unambiguous semidirect product | C3⋊(Q8×3−1+2) |
| unambiguous semidirect product | (C9×Dic6)⋊C3 |
| Sylow | C3×3−1+2 ⋊ Q8 |
129 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | #88425⋊C3, #88426⋊C3, #88427⋊C3, … |
| maximal normal subgroup of | #88425⋊C3, #88426⋊C3, #88427⋊C3, … |
| maximal quotient of | 3−1+2×Dic3⋊C4, 3−1+2×C4⋊Dic3, C2×Dic6×3−1+2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 452);