Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | (C11⋊C5)⋊#10596885 |
| unambiguous semidirect product | (C11⋊#10596885)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C11×#3862 | C4×C5 |
| Fitting, socle | C72×C11 | C5×Dic3 |
| prime radical | C11⋊C5×#64425 | C2 |
| cosocle | C11×#64425 | C2×C5 |
| LCS | G ▷ C11×#3862 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
Polycyclic presentation:
2,5,2,3,11,7^2|a^2=c,d^a=d^2,e^a=e^10,f^a=f^3g^4,g^a=fg^4,e^b=e^4,f^c=f^6,g^c=g^6,f^d=f^2g^6,g^d=g^464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 243);