Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D3×#4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×#4169 |
| Fitting, Sylow | C3×C32⋊C9 ⋊ C22 |
| derived | C32×C9 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C22×C3 |
| Frattini | C32 | C3×D32 |
| Fitting | C3×C32⋊C9 | C22 |
| socle | C33 | C2×C3×D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
231 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D3×((C3⋊D3)⋊C9)⋊C2, C2×D3×#4169, D3×#92299, … |
| maximal normal subgroup of | D3×((C3⋊D3)⋊C9)⋊C2, C2×D3×#4169, D3×#4169⋊C3 |
| maximal quotient of | #14516762, Dic3×#4169, #14516764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 422);