Finite Group DatabasebetaFinite Group Databasebeta| order | 20410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C5×D157⋊C13 |
| unambiguous semidirect product | D157⋊(C5×C13) |
| unambiguous semidirect product | (C5×D157)⋊C13 |
| unambiguous semidirect product | (C157⋊C13)⋊(C2×C5) |
| Fitting, socle, Hall | C5×C157 ⋊ C2×C13 |
| derived, Sylow | C157 ⋊ C2×C5×C13 |
| Hall | C5×C157⋊C13 ⋊ C2 |
| Hall | C157⋊C13 ⋊ C2×C5 |
| Hall | C5×D157 ⋊ C13 |
| Hall | D157 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D157⋊C13 |
| commutator, cosocle, hypocenter | C157 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C157 | C2×C13 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 785 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20410, 10);