Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C7 |
| direct product | C2×#13096577 |
| Fitting | C22×C72×D4 ⋊ C2 |
| Sylow | C72 ⋊ C2×AGL(1,ℤ/8) |
1490 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1490 conjugacy classes of subgroups — too many to draw. Only its 351 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
502 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×AGL(1,ℤ/8)×C7⋊D7, C2×#72245161 |
| maximal normal subgroup of | C2×AGL(1,ℤ/8)×C7⋊D7, C2×#72245161 |
Past the SmallGroups library coverage — no SmallGroups id.