Finite Group DatabasebetaFinite Group Databasebeta| order | 35364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#13132997⋊C7) |
| unambiguous semidirect product | (C3⋊#13132997)⋊C7 |
| Fitting, socle, derived, Hall | C3×C421 ⋊ C4×C7 |
| Hall | C3×C421⋊C7 ⋊ C4 |
| Hall | C3⋊#13132997 ⋊ C7 |
| Hall | C421⋊C7 ⋊ Dic3 |
| Sylow | C421 ⋊ C7×Dic3 |
| Sylow | C3 ⋊ #13132997⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C421 | C4×C7 |
| prime radical | C3×D421⋊C7 | C2 |
| cosocle | C3×D421 | C2×C7 |
| LCS | G ▷ C3×C421 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1263 |
Polycyclic presentation:
2,7,2,3,421|a^2=c,d^a=d^2,e^a=e^29,e^b=e^370,e^c=e^42087 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35364, 35);