Finite Group DatabasebetaFinite Group Databasebeta| order | 20410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D157⋊C13) |
| unambiguous semidirect product | D785⋊C13 |
| unambiguous semidirect product | (C157⋊C13)⋊D5 |
| Fitting, socle, derived, Hall | C5×C157 ⋊ C2×C13 |
| Hall | C5×C157⋊C13 ⋊ C2 |
| Hall | C157⋊C13 ⋊ D5 |
| Hall | D785 ⋊ C13 |
| Sylow | C157 ⋊ D5×C13 |
| Sylow | C5 ⋊ D157⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C157 | C2×C13 |
| LCS | G ▷ C5×C157 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 785 |
Polycyclic presentation:
2,5,13,157|b^a=b^4,d^a=d^156,d^c=d^13082 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20410, 12);