Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C49×C61 ⋊ C3×C4 |
| Hall | C49×#6923 ⋊ C3 |
| Hall | #22582218 ⋊ C4 |
| Hall | #6923 ⋊ C49⋊C3 |
| Sylow | C61 ⋊ C4×C49⋊C3 |
| Sylow | C49 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C49×C61 | C3×C4 |
| Frattini | C7 | #19103986 |
| socle | C7×C61 | C4×ΓL(1,𝔽8) |
| prime radical | #31822415 | C2 |
| cosocle | C49×D61 | C2×C3 |
| LCS | G ▷ C49×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2989 |
Polycyclic presentation:
2,3,2,7,61,7|a^2=c,d^7=f^2,e^a=e^50,d^b=d^2f,e^b=e^47,f^b=f^2,e^c=e^60321 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 34);