Finite Group DatabasebetaFinite Group Databasebeta| order | 8420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13132997⋊C5 |
| Fitting, socle, derived, Sylow | C421 ⋊ C4×C5 |
| Hall | C421⋊C5 ⋊ C4 |
| Hall | #13132997 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C421 | C4×C5 |
| LCS | G ▷ C421 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,421|a^2=c,d^a=d^29,d^b=d^354,d^c=d^42041 conjugacy classes — view the full character table.
| maximal subgroup of | (#13132997⋊C3)⋊C5, C3×#13132997⋊C5, C3⋊(#13132997⋊C5) |
| maximal normal subgroup of | (#13132997⋊C3)⋊C5, C3×#13132997⋊C5 |
| maximal quotient of | C3×#13132997⋊C5, C3⋊(#13132997⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8420, 8);