Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×ΓL(1,𝔽8)×AGL(1,𝔽7) |
| Fitting | C4×C72 ⋊ C2×C32 |
| derived, Sylow | C72 ⋊ C2×C32×C4 |
| Hall | ΓL(1,𝔽8)2 ⋊ C2×C4 |
| Hall | C4×C7×D7 ⋊ C32 |
198 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#1157⋊C3, C4×AGL(1,𝔽7)2, #72245303, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#1157⋊C3, C4×AGL(1,𝔽7)2, #72245303, … |
| maximal quotient of | AGL(1,𝔽5)×ΓL(1,𝔽8)×AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.