Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439458 |
| Fitting, derived | C3×C13×C49 ⋊ C3×C4 |
| Hall | C3×C13⋊C3×C49 ⋊ C4 |
| Hall | C13×C49 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ Dic49 |
| Sylow | C49 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×Dic147 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C13×C49 | C3×C4 |
| Frattini | C7 | C3⋊#11763979 |
| socle | C3×C7×C13 | C3×Dic7 |
| prime radical | C3×C7×D13⋊C3 | D7 |
| cosocle | C3×D13×C49 | C2×C3 |
| LCS | G ▷ C3×C13×C49 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1911 |
Polycyclic presentation:
2,3,2,3,7,13,7|a^2=c,e^7=g^6,d^a=d^2,e^a=e^6g,f^a=f^5,g^a=g^6,f^b=f^3,f^c=f^12597 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 170);