Finite Group DatabasebetaFinite Group Databasebeta| order | 34860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C83 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D7×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C83 | D5×D7 |
| commutator, cosocle, hypocenter | C5×C7 | C22×C3×C83 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C83 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C3×C83 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8715 |
4980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34860, 51);