Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)⋊Dic91 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×Dic91) |
| derived, Hall | C72×C13 ⋊ C32×C4 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7⋊Dic91 ⋊ C32 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ Dic13 |
| Sylow | C72 ⋊ C32×Dic13 |
| Sylow | C13 ⋊ C3×ΓL(1,𝔽8)⋊Dic7 |
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3276 |
1392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 679);