Finite Group DatabasebetaFinite Group Databasebeta| order | 32550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D525 |
| unambiguous semidirect product | C3⋊(C31×D175) |
| unambiguous semidirect product | C7⋊(C31×D75) |
| unambiguous semidirect product | C25⋊(C31×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D525 |
| commutator, cosocle, hypocenter | C3×C7×C25 | C2×C31 |
| Frattini | C5 | C31×D105 |
| Fitting | C3×C7×C25×C31 | C2 |
| socle | C3×C5×C7×C31 | D5 |
| LCS | G ▷ C3×C7×C25 | |
| UCS | C1 ◁ C31 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16275 |
8184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32550, 24);