Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C7 |
| direct product | #100×C7⋊D7 |
| Fitting | C72×#100 ⋊ C2 |
| Sylow | C72 ⋊ C2×#100 |
930 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 392 |
286 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×C7⋊D7, #100×#64424, #100×ΓL(1,𝔽8)⋊D7, … |
| maximal normal subgroup of | #453×C7⋊D7, #100×#64424, #100×ΓL(1,𝔽8)⋊D7, … |
Past the SmallGroups library coverage — no SmallGroups id.