Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C11⋊#15668774 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×C11×#3862 | C4 |
| Fitting, socle | C5×C72×C11 | Dic3 |
| prime radical, cosocle | C11×C5⋊#64425 | C2 |
| LCS | G ▷ C5×C11×#3862 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 770 |
Polycyclic presentation:
2^2,3,5,11,7^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,f^a=f^5g^2,g^a=fg^2,d^b=d^4,f^b=f^6,g^b=g^6,f^c=f^4g^4,g^c=g^2289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 348);