Finite Group DatabasebetaFinite Group Databasebeta| order | 20475 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×#11717941 |
| derived, Hall | C7×C13 ⋊ C52×C9 |
| Hall | C52×C7×C13 ⋊ C9 |
| Hall | C52×C13 ⋊ C7⋊C9 |
| Hall | C52×C7 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C52×C7⋊C9 |
| Sylow | C7 ⋊ C52×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | #63270 |
| commutator, hypocenter | C7×C13 | C52×C9 |
| Frattini | C3 | C52×#63270 |
| Fitting, socle, prime radical | C3×C52×C7×C13 | C3 |
| cosocle | C3×C7×C13 | C3×C52 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C52 | |
96 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, 18);