Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#11758266⋊C3) |
| unambiguous semidirect product | (C11⋊#11758266)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C11 | C3×C4 |
| prime radical | C11×C5⋊#64424 | C2 |
| cosocle | C11×C5⋊(C7⋊D7) | C2×C3 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 770 |
Polycyclic presentation:
2,3,2,5,7^2,11|a^2=c,d^a=d^2,e^a=e^4f^3,f^a=e^6f^3,g^a=g^10,e^b=e^4,f^b=f^4,d^c=d^4,e^c=e^6,f^c=f^6295 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 350);