Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #4207 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#66409 |
| derived | C3×C9 ⋊ C2×C3×C4 |
| Sylow | #737 ⋊ C2×C4 |
165 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13047774, #13047775, #13047776, … |
| maximal normal subgroup of | #13047774, #13047775, #13047776, … |
| maximal quotient of | C2×#10619724, #13047951, C4×#66409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 500);