Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| derived, Hall | C13×C49 ⋊ C32×C4 |
| Hall | C13⋊C3×C49⋊C3 ⋊ C4 |
| Hall | Dic637 ⋊ C32 |
| Sylow | C49 ⋊ C3×Dic13⋊C3 |
| Sylow | C13 ⋊ C3×(C49⋊C3)⋊C4 |
108 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2548 |
Polycyclic presentation:
2,3^2,7,13,2,7|a^2=f,d^7=g^6,d^a=d^6g,e^a=e^12,g^a=g^6,e^b=e^3,d^c=d^4g^5,g^c=g^4160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 80);