Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×#10624462⋊C2 |
| Fitting | C2×#10624462 ⋊ C2 |
| derived | C27 ⋊ C22×C27 |
| Sylow | #10624462 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AGL(1,ℤ/27) |
| commutator, hypocenter | C27 | C22×C27 |
| Frattini | C92 | C2×C3×D3 |
| Fitting | C2×#10624462 | C2 |
| socle | C2×C32 | D9⋊C9 |
| prime radical | C2×C3×D27 | C9 |
| cosocle | #6864 | C22×C3 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C2×C3 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221799 |
| maximal quotient of | C2×#72221799 |
Past the SmallGroups library coverage — no SmallGroups id.