Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C3×#10620710 |
| Fitting | C3×C42×C7 ⋊ C2×C3 |
| Hall | #6437 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #127 |
| Sylow | C7 ⋊ C32×#127 |
648 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#127×AGL(1,𝔽7), D3×#10620710, #72244271, … |
| maximal normal subgroup of | C3×#127×AGL(1,𝔽7), D3×#10620710, #72244271, … |
| maximal quotient of | #72245701, C32×#10620710 |
Past the SmallGroups library coverage — no SmallGroups id.