Finite Group DatabasebetaFinite Group Databasebeta| order | 32370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D415 |
| unambiguous semidirect product | C5⋊(C13⋊C3×D83) |
| unambiguous semidirect product | C83⋊(D5×C13⋊C3) |
| unambiguous semidirect product | (C13×D415)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C83 | C2×C3 |
| LCS | G ▷ C5×C13×C83 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5395 |
1463 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32370, 22);