Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #4207 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C32 |
| direct product | C3×#66409 |
| derived | C3×C9 ⋊ C32×C4 |
| Sylow | C3×#737 ⋊ C4 |
328 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #14518707, #14518709, D3×#66409, … |
| maximal normal subgroup of | #14518707, #14518709, D3×#66409, … |
| maximal quotient of | C3×#10619724, C2×C3×#66409 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 735);