Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊(C11⋊#11758267) |
| unambiguous semidirect product | C11⋊(C3⋊#11758267) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C72×C11 | C4 |
| prime radical, cosocle | C3×C5×C11×C7⋊D7 | C2 |
| LCS | G ▷ C3×C5×C72×C11 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2310 |
Polycyclic presentation:
2^2,3,5,7^2,11|a^2=b,c^a=c^2,d^a=d^4,e^a=e^4f^3,f^a=e^6f^3,g^a=g^10,e^b=e^6,f^b=f^62148 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 568);