Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#21439563 |
| derived, Hall | C3×C13×#3862 ⋊ C4 |
| Hall | C72×C13 ⋊ C3⋊Dic3 |
| Hall | C3×#3862 ⋊ Dic13 |
| Sylow | C72 ⋊ C3⋊Dic39 |
| Sylow | C13 ⋊ C3⋊#10596868 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C13⋊#64418) |
| commutator, hypocenter | C3×C13×#3862 | C4 |
| Fitting, socle | C2×C3×C72×C13 | D3 |
| prime radical, cosocle | C2×C3×C13×#3862 | C2 |
| LCS | G ▷ C3×C13×#3862 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1092 |
Polycyclic presentation:
2,3^2,13,7^2,2|a^2=g,b^a=b^2,c^a=c^2,d^a=d^12,e^a=e^4f,f^a=e^6f^3,e^b=e^2f^6,f^b=f^4762 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 758);