Finite Group DatabasebetaFinite Group Databasebeta| order | 20540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×Dic65 |
| derived, Hall | C5×C13 ⋊ C4×C79 |
| Hall | C5×C13×C79 ⋊ C4 |
| Hall | C13×C79 ⋊ Dic5 |
| Hall | C5×C79 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic5×C79 |
| Sylow | C5 ⋊ Dic13×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C79 | D65 |
| commutator, hypocenter | C5×C13 | C4×C79 |
| Frattini | C2 | C79×D65 |
| Fitting, socle, prime radical | C2×C5×C13×C79 | C2 |
| cosocle | C2×C5×C13 | C2×C79 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2×C79 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20540 |
5372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20540, 8);