Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×D27⋊C3 |
| unambiguous semidirect product | D27⋊(C2×C32) |
| unambiguous semidirect product | (C2×D27)⋊C32 |
| unambiguous semidirect product | (C2×C3×D27)⋊C3 |
| Fitting | C2×C3×C27⋊C3 ⋊ C2 |
| derived | C27 ⋊ C22×C32 |
| Sylow | C3×C27⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D27⋊C3 |
| commutator, cosocle, hypocenter | C27 | C22×C32 |
| Frattini | C9 | C2×C32×D3 |
| Fitting | C2×C3×C27⋊C3 | C2 |
| socle | C2×C32 | C3×D9 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C2×C3 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×D27⋊C3, #10619542⋊C3, #10619544⋊C3, … |
| maximal normal subgroup of | Dic3×D27⋊C3, #10619542⋊C3, #10619544⋊C3, … |
| maximal quotient of | C3×(C27⋊C3)⋊Q8, C3×C4×D27⋊C3, C3×C4⋊(D27⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 614);