Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#66362 |
| Fitting | C23×H(3,𝔽3) ⋊ C3 |
| Sylow | C23 ⋊ #732 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #13046974, #13047015, #13047058, … |
| maximal normal subgroup of | #13046974, #13047015, #13047058, … |
| maximal quotient of | C4×#66362, C2×#10619579, #13047272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 314);