Finite Group DatabasebetaFinite Group Databasebeta| order | 20540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic79⋊C13 |
| unambiguous semidirect product | Dic79⋊(C5×C13) |
| unambiguous semidirect product | (C79⋊C13)⋊(C4×C5) |
| unambiguous semidirect product | (C5×Dic79)⋊C13 |
| derived, Sylow | C79 ⋊ C4×C5×C13 |
| Hall | C5×C79⋊C13 ⋊ C4 |
| Hall | C5×Dic79 ⋊ C13 |
| Hall | C79⋊C13 ⋊ C4×C5 |
| Hall | C5×C79 ⋊ C4×C13 |
| Hall | Dic79 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D79⋊C13 |
| commutator, hypocenter | C79 | C4×C5×C13 |
| Frattini | C2 | C5×D79⋊C13 |
| Fitting, socle | C2×C5×C79 | C2×C13 |
| prime radical | C2×C5×C79⋊C13 | C2 |
| cosocle | C2×C79 | C2×C5×C13 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1580 |
290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20540, 10);