Finite Group DatabasebetaFinite Group Databasebeta| order | 3402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C32 |
| direct product | C7×#4207⋊C3 |
| Fitting, Hall | C7×3−1+4 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C32×C7 |
| Sylow | 3−1+4 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #4207⋊C3 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C32×C7 |
| Frattini | C3 | C32×C7×C3⋊D3 |
| Fitting | C7×3−1+4 | C2 |
| socle | C3×C7 | C32×C3⋊D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C7 | |
362 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 362 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 |
385 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#13091120, ΓL(1,𝔽8)×#4207⋊C3, D7×#4207⋊C3 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#4207⋊C3, D7×#4207⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.