Finite Group DatabasebetaFinite Group Databasebeta| order | 20475 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3×C5 |
| direct product | C7×C13⋊C3×C52⋊C3 |
| unambiguous semidirect product | (C52×C13⋊C3)⋊(C3×C7) |
| unambiguous semidirect product | (C13×C52⋊C3)⋊(C3×C7) |
| unambiguous semidirect product | (C13⋊(C52⋊C3))⋊(C3×C7) |
| Fitting, socle, Hall | C52×C7×C13 ⋊ C32 |
| derived, Hall | C52×C13 ⋊ C32×C7 |
| Hall | C52×C7 ⋊ C3×C13⋊C3 |
| Hall | C7×C13 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×C7×C13⋊C3 |
| Sylow | C13 ⋊ C3×C7×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C13⋊C3×C52⋊C3 |
| commutator, cosocle, hypocenter | C52×C13 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C13 | C32 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C7 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1365 |
539 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20475, 23);