Finite Group DatabasebetaFinite Group Databasebeta| order | 17410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C1741⋊C5 |
| unambiguous semidirect product | (C2×C1741)⋊C5 |
| Fitting, socle, Hall | C2×C1741 ⋊ C5 |
| derived, Sylow | C1741 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C1741⋊C5 |
| commutator, cosocle, hypocenter | C1741 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1741 | C5 |
| LCS | G ▷ C1741 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3482 |
706 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic1741⋊C5, C4×C1741⋊C5, C2×D1741⋊C5, … |
| maximal normal subgroup of | Dic1741⋊C5, C4×C1741⋊C5, C2×D1741⋊C5, … |
| maximal quotient of | C4×C1741⋊C5, C22×C1741⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17410, 2);