Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#15668724 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C11⋊#64418) |
| commutator, hypocenter | C5×C11×#3862 | C4 |
| Fitting, socle | C2×C5×C72×C11 | D3 |
| prime radical, cosocle | C2×C5×C11×#3862 | C2 |
| LCS | G ▷ C5×C11×#3862 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1540 |
Polycyclic presentation:
2,3,5,11,7^2,2|a^2=g,b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^4f,f^a=e^6f^3,e^b=e^2f^6,f^b=f^41066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 213);