Finite Group DatabasebetaFinite Group Databasebeta| order | 17410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1741⋊C5 |
| unambiguous semidirect product | (C1741⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C1741 ⋊ C2×C5 |
| Hall | C1741⋊C5 ⋊ C2 |
| Hall | D1741 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1741 | C2×C5 |
| LCS | G ▷ C1741 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1741 |
Polycyclic presentation:
2,5,1741|c^a=c^1740,c^b=c^1697184 conjugacy classes — view the full character table.
| maximal subgroup of | #20294399⋊C5, C2×D1741⋊C5 |
| maximal normal subgroup of | #20294399⋊C5, C2×D1741⋊C5 |
| maximal quotient of | Dic1741⋊C5, C2×D1741⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17410, 1);