Finite Group DatabasebetaFinite Group Databasebeta| order | 20475 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#11717941 |
| derived, Hall | C7×C13 ⋊ C9×C25 |
| Hall | C7×C13×C25 ⋊ C9 |
| Hall | C13×C25 ⋊ C7⋊C9 |
| Hall | C7×C25 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C25×C7⋊C9 |
| Sylow | C7 ⋊ C25×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | #63270 |
| commutator, hypocenter | C7×C13 | C9×C25 |
| Frattini | C3×C5 | C5×#63270 |
| Fitting | C3×C7×C13×C25 | C3 |
| socle, prime radical, cosocle | C3×C5×C7×C13 | C3×C5 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20475 |
2475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20475, 5);