Finite Group DatabasebetaFinite Group Databasebeta| order | 20410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C157⋊C13 |
| unambiguous semidirect product | (C2×C157)⋊(C5×C13) |
| unambiguous semidirect product | (C2×C5×C157)⋊C13 |
| Fitting, socle, Hall | C2×C5×C157 ⋊ C13 |
| derived, Sylow | C157 ⋊ C2×C5×C13 |
| Hall | C5×C157 ⋊ C2×C13 |
| Hall | C2×C157 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C157⋊C13 |
| commutator, cosocle, hypocenter | C157 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C157 | C13 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1570 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20410, 2);