Finite Group DatabasebetaFinite Group Databasebeta| order | 10206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C39 |
| direct product | AGL(1,𝔽7)×C32⋊H(3,𝔽3) |
| Fitting | C7×C32⋊H(3,𝔽3) ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×C32⋊H(3,𝔽3) ⋊ C2 |
| Hall | D7 ⋊ C3×C32⋊H(3,𝔽3) |
| Sylow | C7 ⋊ C2×C3×C32⋊H(3,𝔽3) |
7648 conjugacy classes of subgroups; only the 665 normal subgroups are shown.
This group has 7648 conjugacy classes of subgroups — too many to draw. Only its 665 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 189 |
357 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽7)×#10624749, AGL(1,𝔽7)×#92300, AGL(1,𝔽7)×#92338 |
| maximal normal subgroup of | AGL(1,𝔽7)×#10624749, AGL(1,𝔽7)×#92300, AGL(1,𝔽7)×#92338 |
| maximal quotient of | AGL(1,𝔽7)×#10624749 |
Past the SmallGroups library coverage — no SmallGroups id.