Finite Group DatabasebetaFinite Group Databasebeta| order | 8410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D841 |
| unambiguous semidirect product | C841⋊(C2×C5) |
| Fitting, Hall | C5×C841 ⋊ C2 |
| derived, Sylow | C841 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D841 |
| commutator, hypocenter | C841 | C2×C5 |
| Frattini | C29 | C5×D29 |
| Fitting | C5×C841 | C2 |
| socle | C5×C29 | D29 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
2110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#16809850, #30681255, D5×D841, … |
| maximal normal subgroup of | C5×#16809850, #30681255, D5×D841, … |
| maximal quotient of | C5×Dic841, C2×C5×D841, C3×C5×D841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8410, 3);