Finite Group DatabasebetaFinite Group Databasebeta| order | 20475 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C5 |
| direct product | C13×C7⋊(C52⋊C9) |
| unambiguous semidirect product | C7⋊(C13×C52⋊C9) |
| unambiguous semidirect product | C52⋊(C13×C7⋊C9) |
| derived, Hall | C52×C7 ⋊ C9×C13 |
| Hall | C52×C7×C13 ⋊ C9 |
| Hall | C52×C13 ⋊ C7⋊C9 |
| Hall | C7×C13 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ C13×C7⋊C9 |
| Sylow | C7 ⋊ C13×C52⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C7⋊(C52⋊C3) |
| commutator, hypocenter | C52×C7 | C9×C13 |
| Frattini | C3 | C13×C7⋊(C52⋊C3) |
| Fitting, socle, prime radical | C3×C52×C7×C13 | C3 |
| cosocle | C3×C52×C7 | C3×C13 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C3×C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4095 |
2379 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20475, 15);