Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#10624500⋊C2 |
| Fitting | C2×#10624500 ⋊ C2 |
| derived | C81 ⋊ C22×C9 |
| Sylow | #10624500 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10624500⋊C2 |
| commutator, hypocenter | C81 | C22×C9 |
| Frattini | C3×C27 | C2×C3×D3 |
| Fitting | C2×#10624500 | C2 |
| socle | C2×C3 | #6864⋊C2 |
| prime radical | C2×D81⋊C3 | C3 |
| cosocle | C81⋊C3 | C22×C3 |
| LCS | G ▷ C81 | |
| UCS | C1 ◁ C2 | |
93 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221799 |
| maximal normal subgroup of | C2×#72221799 |
Past the SmallGroups library coverage — no SmallGroups id.