Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439460 |
| Fitting, derived | C3×C13×C49 ⋊ C3×C4 |
| Hall | C3×#14274255 ⋊ C4 |
| Hall | C13×C49 ⋊ C3×Dic3 |
| Sylow | C49 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ Dic3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C13×C49 | C3×C4 |
| Frattini | C7 | C3⋊#11763981 |
| socle | C3×C7×C13 | C4×ΓL(1,𝔽8) |
| prime radical | C3×#16838414 | C2 |
| 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^2,d^a=d^2,f^a=f^5,e^b=e^2g,f^b=f^9,g^b=g^2,f^c=f^12261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 165);