Finite Group DatabasebetaFinite Group Databasebeta| order | 32430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | D15×C47⋊C23 |
| unambiguous semidirect product | C3⋊(D5×C47⋊C23) |
| unambiguous semidirect product | C5⋊(D3×C47⋊C23) |
| unambiguous semidirect product | (D15×C47)⋊C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C47 | C2×C23 |
| LCS | G ▷ C3×C5×C47 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 705 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32430, 23);