Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C3 |
| direct product | M16×ΓL(1,𝔽8)2 |
| Fitting, Hall | C72×M16 ⋊ C32 |
| Sylow | C72 ⋊ C32×M16 |
280 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | M16×ΓL(1,𝔽8)⋊AGL(1,𝔽7), ΓL(1,𝔽8)2×AGL(1,ℤ/8), #72245379, … |
| maximal normal subgroup of | M16×ΓL(1,𝔽8)⋊AGL(1,𝔽7), ΓL(1,𝔽8)2×AGL(1,ℤ/8), #72245379, … |
Past the SmallGroups library coverage — no SmallGroups id.