Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3×C3⋊#4175 |
| Fitting | C2×C32×AΣL(1,𝔽27) ⋊ C2 |
| derived | C34 ⋊ C22×C32 |
| Sylow | C32×AΣL(1,𝔽27) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊#4175 |
| commutator, cosocle, hypocenter | C34 | C22×C32 |
| Frattini | C32 | C2×C32×C3⋊D3 |
| Fitting | C2×C32×AΣL(1,𝔽27) | C2 |
| socle | C2×C33 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2×C3 | |
2200 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 2200 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221906, C2×#72221887, C2×C3×#13091108 |
| maximal normal subgroup of | C2×C3×#13091108 |
Past the SmallGroups library coverage — no SmallGroups id.