Finite Group DatabasebetaFinite Group Databasebeta| order | 8420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×C421⋊C5 |
| unambiguous semidirect product | (C22×C421)⋊C5 |
| Fitting, socle, Hall | C22×C421 ⋊ C5 |
| derived, Sylow | C421 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C421⋊C5 |
| commutator, hypocenter | C421 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C421 | C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
356 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊((C421⋊C3)⋊C5), A4×C421⋊C5, C22×(C421⋊C3)⋊C5, … |
| maximal normal subgroup of | C22⋊((C421⋊C3)⋊C5), A4×C421⋊C5, C22×(C421⋊C3)⋊C5, … |
| maximal quotient of | C2×D3×C421⋊C5, C22×C3×C421⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8420, 10);