Finite Group DatabasebetaFinite Group Databasebeta| order | 8210 |
| automorphism | Aut(G) order 13464400 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4105 |
| unambiguous semidirect product | C5⋊D821 |
| unambiguous semidirect product | C821⋊D5 |
| Fitting, socle, derived, Hall | C5×C821 ⋊ C2 |
| Sylow | C821 ⋊ D5 |
| Sylow | C5 ⋊ D821 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C821 | C2 |
| LCS | G ▷ C5×C821 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,821|b^a=b^4,c^a=c^8202054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30655967, #30655968, D5×D821, … |
| maximal normal subgroup of | #30655967, #30655968, D5×D821, … |
| maximal quotient of | Dic4105, C2×D4105, C3×D4105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8210, 5);