Finite Group DatabasebetaFinite Group Databasebeta| order | 8420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C4×C421⋊C5 |
| unambiguous semidirect product | (C4×C421)⋊C5 |
| Fitting, Hall | C4×C421 ⋊ C5 |
| derived, Sylow | C421 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C421⋊C5 |
| commutator, hypocenter | C421 | C4×C5 |
| Frattini | C2 | C2×C421⋊C5 |
| Fitting | C4×C421 | C5 |
| socle | C2×C421 | C2×C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
356 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C421⋊C5, C4×(C421⋊C3)⋊C5, Dic3×C421⋊C5 |
| maximal normal subgroup of | C3×C4×C421⋊C5, C4×(C421⋊C3)⋊C5 |
| maximal quotient of | C3×C4×C421⋊C5, Dic3×C421⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8420, 3);