Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C32 |
| direct product | C3×#66316 |
| derived | C3×C9 ⋊ C32×C4 |
| Sylow | C3×C32⋊C9 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4169 |
| commutator, hypocenter | C3×C9 | C32×C4 |
| Frattini | C2×C32 | C32×D3 |
| Fitting | C2×C3×C32⋊C9 | C2 |
| socle | C2×C33 | C3×D3 |
| prime radical | C2×C34 | D3 |
| cosocle | C2×C3×C9 | C2×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C3 | |
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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 | C3×#4181⋊C4, C3×((C3⋊D3)⋊C9)⋊C4, C3×#10619535, … |
| maximal normal subgroup of | C3×#4181⋊C4, C3×((C3⋊D3)⋊C9)⋊C4, C3×#10619535, … |
| maximal quotient of | C3×#10619495, C2×C3×#66316 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 278);