Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C49 ⋊ C4×C9 |
| Hall | C49×C13⋊C9 ⋊ C4 |
| Hall | C49⋊#261 ⋊ C9 |
| Hall | C13⋊C9 ⋊ Dic49 |
| Sylow | C49 ⋊ #261⋊C9 |
| Sylow | C13 ⋊ C9×Dic49 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5733 |
Polycyclic presentation:
2,3,2,7,13,3,7|a^2=c,b^3=f,d^7=g^6,d^a=d^6g,e^a=e^8,g^a=g^6,e^b=e^3,e^c=e^12615 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 27);