Finite Group DatabasebetaFinite Group Databasebeta| order | 10206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×#13091120 |
| Fitting, Hall | C7×#10624749 ⋊ C2 |
| derived, Sylow | #10624749 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13091120 |
| commutator, cosocle, hypocenter | #10624749 | C2×C7 |
| Frattini | C33 | C7×C3⋊(C3⋊D3) |
| Fitting | C7×#10624749 | C2 |
| socle | C3×C7 | #92338 |
| LCS | G ▷ #10624749 | |
| UCS | C1 ◁ C7 | |
700 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 189 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)×#13091120, D7×#13091120 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#13091120, D7×#13091120 |
Past the SmallGroups library coverage — no SmallGroups id.