Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D81⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D81⋊C3 |
| unambiguous semidirect product | D81⋊(C2×C3) |
| unambiguous semidirect product | (C81⋊C3)⋊C22 |
| unambiguous semidirect product | (C2×D81)⋊C3 |
| unambiguous semidirect product | (C2×C81⋊C3)⋊C2 |
| Fitting | C2×C81⋊C3 ⋊ C2 |
| derived | C81 ⋊ C22×C3 |
| Sylow | C81⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D81⋊C3 |
| commutator, cosocle, hypocenter | C81 | C22×C3 |
| Frattini | C27 | C2×C3×D3 |
| Fitting | C2×C81⋊C3 | C2 |
| socle | C2×C3 | C3×D27 |
| LCS | G ▷ C81 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D81⋊C3, C4⋊(D81⋊C3), #10619489⋊C3, … |
| maximal normal subgroup of | C4×D81⋊C3, C4⋊(D81⋊C3), #10619489⋊C3, … |
| maximal quotient of | (C81⋊C3)⋊Q8, C4×D81⋊C3, C4⋊(D81⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 218);