Finite Group DatabasebetaFinite Group Databasebeta| order | 20475 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9×C13 · Schur multiplier (H2) = C5 |
| direct product | C7×C13×C52⋊C9 |
| unambiguous semidirect product | C52⋊(C7×C9×C13) |
| derived, Sylow | C52 ⋊ C7×C9×C13 |
| Hall | C52×C7×C13 ⋊ C9 |
| Hall | C52×C13 ⋊ C7×C9 |
| Hall | C52×C7 ⋊ C9×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C13 | C52⋊C3 |
| commutator, hypocenter | C52 | C7×C9×C13 |
| Frattini | C3 | C7×C13×C52⋊C3 |
| Fitting, socle, prime radical | C3×C52×C7×C13 | C3 |
| cosocle | C3×C52 | C3×C7×C13 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C7×C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4095 |
3003 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20475, 17);