Finite Group DatabasebetaFinite Group Databasebeta| order | 8420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic421⋊C5 |
| derived, Sylow | C421 ⋊ C4×C5 |
| Hall | C421⋊C5 ⋊ C4 |
| Hall | Dic421 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D421⋊C5 |
| commutator, hypocenter | C421 | C4×C5 |
| Fitting, socle | C2×C421 | C2×C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,421,2|a^2=d,c^a=c^420,c^b=c^279104 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic421⋊C5, C3⋊(Dic421⋊C5), (Dic421⋊C3)⋊C5 |
| maximal normal subgroup of | C3×Dic421⋊C5, (Dic421⋊C3)⋊C5 |
| maximal quotient of | C3×Dic421⋊C5, C3⋊(Dic421⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8420, 2);