Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C7 |
| direct product | M16×#64425 |
| Fitting | C72×M16 ⋊ C2×C3 |
| Hall | M16×C7⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×M16 |
| Sylow | C72 ⋊ C2×C3×M16 |
340 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 87 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 | AGL(1,ℤ/8)×#64425, M16×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #100×#64425, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×#64425, M16×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #100×#64425, … |
Past the SmallGroups library coverage — no SmallGroups id.