Finite Group DatabasebetaFinite Group Databasebeta| order | 20540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C79⋊C13 |
| unambiguous semidirect product | (Dic5×C79)⋊C13 |
| derived, Hall | C5×C79 ⋊ C4×C13 |
| Hall | C5×C79⋊C13 ⋊ C4 |
| Hall | Dic5×C79 ⋊ C13 |
| Sylow | C79 ⋊ C13×Dic5 |
| Sylow | C5 ⋊ C4×C79⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C79⋊C13 |
| commutator, hypocenter | C5×C79 | C4×C13 |
| Fitting, socle, cosocle | C2×C5×C79 | C2×C13 |
| prime radical | C2×C5×C79⋊C13 | C2 |
| LCS | G ▷ C5×C79 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1580 |
152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20540, 11);