Finite Group DatabasebetaFinite Group Databasebeta| order | 3402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C3×#10588046⋊C2 |
| Fitting | C3×C7×3−1+2 ⋊ C2×C3 |
| Hall | C3×#10588046 ⋊ C2 |
| Hall | D7 ⋊ C3×AΣL(1,𝔽27) |
| Sylow | C7 ⋊ C2×C3×AΣL(1,𝔽27) |
504 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 189 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽7)×AΣL(1,𝔽27), #72249139, #72249140, … |
| maximal normal subgroup of | C3×AGL(1,𝔽7)×AΣL(1,𝔽27), #72249139, #72249140, … |
Past the SmallGroups library coverage — no SmallGroups id.