Finite Group DatabasebetaFinite Group Databasebeta| order | 35364 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (#13132997⋊C3)⋊C7 |
| unambiguous semidirect product | (#13132997⋊C7)⋊C3 |
| Fitting, socle, derived, Sylow | C421 ⋊ C3×C4×C7 |
| Hall | #13132997⋊C7 ⋊ C3 |
| Hall | (C421⋊C3)⋊C7 ⋊ C4 |
| Hall | #13132997⋊C3 ⋊ C7 |
| Hall | C421⋊C7 ⋊ C3×C4 |
| Hall | #13132997 ⋊ C3×C7 |
| Hall | C421⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C421 | C3×C4×C7 |
| prime radical | (D421⋊C3)⋊C7 | C2 |
| cosocle | D421 | C2×C3×C7 |
| LCS | G ▷ C421 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 421 |
Polycyclic presentation:
2,3,7,2,421|a^2=d,e^a=e^29,e^b=e^20,e^c=e^370,e^d=e^42089 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35364, 32);