Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #4177 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#66324 |
| derived | C3×C9 ⋊ C2×C3×C4 |
| Sylow | #731 ⋊ C2×C4 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #13046487, #13046488, #13046489, … |
| maximal normal subgroup of | #13046487, #13046488, #13046489, … |
| maximal quotient of | C2×#10619503, #13046642, C4×#66324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 163);