Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#66410 |
| Sylow | #737 ⋊ C2×C4 |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13047774, #13047775, #13047776, … |
| maximal normal subgroup of | #13047774, #13047775, #13047776, … |
| maximal quotient of | C2×#10619725, #13047953, C4×#66410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 501);