Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C49⋊C3)⋊Dic13) |
| unambiguous semidirect product | (C49⋊C3)⋊Dic39 |
| derived | C3×C13×C49 ⋊ C3×C4 |
| Hall | C3×C13×C49⋊C3 ⋊ C4 |
| Hall | C13×C49 ⋊ C3×Dic3 |
| Hall | C3×C49⋊C3 ⋊ Dic13 |
| Sylow | C49 ⋊ C3×Dic39 |
| Sylow | C13 ⋊ C3⋊((C49⋊C3)⋊C4) |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7644 |
Polycyclic presentation:
2,3^2,7,13,2,7|a^2=f,d^7=g^6,c^a=c^2,d^a=d^6g,e^a=e^12,g^a=g^6,d^b=d^4g^5,g^b=g^4750 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 105);