Finite Group DatabasebetaFinite Group Databasebeta| order | 34860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊D415 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C83 | C22 |
| LCS | G ▷ C3×C5×C7×C83 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8715 |
Polycyclic presentation:
2^2,3,5,7,83|d^a=d^4,e^a=e^6,f^a=f^82,c^b=c^2,e^b=e^62499 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34860, 85);