Finite Group DatabasebetaFinite Group Databasebeta| order | 8420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D421⋊C5 |
| unambiguous semidirect product | D421⋊(C2×C5) |
| unambiguous semidirect product | (C2×D421)⋊C5 |
| unambiguous semidirect product | (C421⋊C5)⋊C22 |
| unambiguous semidirect product | (C2×C421⋊C5)⋊C2 |
| Fitting, socle | C2×C421 ⋊ C2×C5 |
| derived, Sylow | C421 ⋊ C22×C5 |
| Hall | C421⋊C5 ⋊ C22 |
| Hall | C2×D421 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D421⋊C5 |
| commutator, hypocenter | C421 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C421 | C2×C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D421⋊C3)⋊C5, D3×D421⋊C5, C2×C3×D421⋊C5, … |
| maximal normal subgroup of | C2×(D421⋊C3)⋊C5, C2×C3×D421⋊C5 |
| maximal quotient of | D3×D421⋊C5, C2×C3×D421⋊C5, C2×C3⋊(D421⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8420, 9);