Finite Group DatabasebetaFinite Group Databasebeta| order | 15876 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#72224657 |
| Hall | #72224635 ⋊ C22 |
| Hall | C2×C7⋊D7 ⋊ C3×3−1+2 |
| Sylow | C72 ⋊ C22×C3×3−1+2 |
1040 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
212 conjugacy classes — view the full character table.
| holomorph of | C2×C7⋊C9 |
Past the SmallGroups library coverage — no SmallGroups id.