Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C7×#13109897⋊C2 |
| unambiguous semidirect product | #13109897⋊(C2×C7) |
| unambiguous semidirect product | #13109901⋊(C2×C7) |
| unambiguous semidirect product | #13109903⋊(C2×C7) |
| derived | C7×C13 ⋊ C22×C7×C9 |
| Hall | C7×#11717942 ⋊ C22 |
| Hall | C7×D7×D13 ⋊ C9 |
| Hall | C72×C13 ⋊ C22×C9 |
| Sylow | C72 ⋊ C2×D13⋊C9 |
| Sylow | C13 ⋊ C2×C7×D7⋊C9 |
128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1638 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 349);