Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#26039446 |
| derived, Hall | C72×C13 ⋊ C22×C9 |
| Hall | #19153200 ⋊ C22 |
| Hall | C2×C13×C7⋊D7 ⋊ C9 |
| Hall | C2×C7⋊D7 ⋊ C13⋊C9 |
| Sylow | C72 ⋊ C22×C13⋊C9 |
| Sylow | C13 ⋊ C2×#11725077 |
300 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11466 |
708 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 464);