Finite Group DatabasebetaFinite Group Databasebeta| order | 35364 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×#13132997⋊C7 |
| unambiguous semidirect product | (C3×#13132997)⋊C7 |
| Fitting, socle, Hall | C3×C421 ⋊ C4×C7 |
| derived, Sylow | C421 ⋊ C3×C4×C7 |
| Hall | C3×C421⋊C7 ⋊ C4 |
| Hall | C3×#13132997 ⋊ C7 |
| Hall | C421⋊C7 ⋊ C3×C4 |
| Hall | #13132997 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13132997⋊C7 |
| commutator, hypocenter | C421 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C421 | C4×C7 |
| prime radical | C3×D421⋊C7 | C2 |
| cosocle | D421 | C2×C3×C7 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1263 |
129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35364, 34);