Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#66357 |
| Fitting | C23×C3×C9 ⋊ C3 |
| Sylow | C23 ⋊ #731 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #13046971, #13047010, #13047055, … |
| maximal normal subgroup of | #13046971, #13047010, #13047055, … |
| maximal quotient of | C4×#66357, C2×#10619574, #13047267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 309);