Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#89804 |
| Fitting | C72×#120 ⋊ C2 |
| Sylow | C72 ⋊ B(4,𝔽2) |
591 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#1020⋊D7, #72215131, #72215173, … |
| maximal normal subgroup of | #72215131, #72215173, C7×#89804⋊C3, … |
Past the SmallGroups library coverage — no SmallGroups id.