Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D3×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×D27 |
| Fitting, Sylow | C32×C27 ⋊ C22 |
| derived | C3×C27 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D27 |
| commutator, cosocle, hypocenter | C3×C27 | C22×C3 |
| Frattini | C9 | C3×D32 |
| Fitting | C32×C27 | C22 |
| socle | C33 | C2×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C3 | |
118 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D27, C2×C3×D3×D27, C3×D3×D27⋊C3 |
| maximal normal subgroup of | D32×D27, C2×C3×D3×D27, C3×D3×D27⋊C3 |
| maximal quotient of | C3×#10619539, C3×Dic3×D27, C3×(C3⋊D27)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 433);