Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#10621721⋊C3) |
| unambiguous semidirect product | (C11⋊#10621721)⋊C3 |
| Fitting, derived, Hall | C11×C169 ⋊ C3×C4 |
| Hall | C11⋊#10621721 ⋊ C3 |
| Hall | C11×C169⋊C3 ⋊ C4 |
| Hall | C169⋊C3 ⋊ Dic11 |
| Sylow | C169 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ #10621721⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C11×C169 | C3×C4 |
| Frattini | C13 | C11⋊AGL(1,𝔽13) |
| socle | C11×C13 | AGL(1,𝔽13) |
| prime radical | C11×D169⋊C3 | C2 |
| cosocle | C11×D169 | C2×C3 |
| LCS | G ▷ C11×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1859 |
Polycyclic presentation:
2,3,2,11,13^2|a^2=c,e^13=f^2,d^a=d^10,e^a=e^8f,f^a=f^8,e^b=e^9f^2,f^b=f^9,e^c=e^12f^11,f^c=f^12196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 15);