Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C13×#3862 ⋊ C3×C4 |
| Hall | C13⋊C3×#3862 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ C3⋊(Dic13⋊C3) |
| Sylow | C13 ⋊ C3×#10596868 |
104 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 364 |
Polycyclic presentation:
2,3^2,13,7^2,2|a^2=g,c^a=c^2,d^a=d^12,e^a=e^2f^3,f^a=e^6f^5,d^b=d^3,e^c=e^4f^4,f^c=f^2196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 629);