Finite Group DatabasebetaFinite Group Databasebeta| order | 32370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C83 · Schur multiplier (H2) = C1 |
| direct product | C3×C83×D65 |
| unambiguous semidirect product | C5⋊(C3×D13×C83) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C83 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C83 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C83 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C3×C83 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16185 |
8466 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32370, 8);