Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C4×C7×#63271 |
| Fitting | C3×C4×C72×C13 ⋊ C3 |
| derived | C7×C13 ⋊ C32×C4×C7 |
| Hall | C4×C72×C13 ⋊ C32 |
| Hall | C72×C13 ⋊ C32×C4 |
| Hall | C4×C72 ⋊ C3×C13⋊C3 |
| Hall | C4×C13 ⋊ C3×C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C3×C4×C13⋊C3 |
| Sylow | C13 ⋊ C3×C4×C7×ΓL(1,𝔽8) |
168 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3276 |
2772 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 762);