Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C61 ⋊ C3×C4 |
| Hall | C7×C7⋊#6923 ⋊ C3 |
| Hall | C7×#13046196 ⋊ C4 |
| Sylow | C61 ⋊ ΓL(1,𝔽8)×Dic7 |
| Sylow | C72 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C61 | C3×C4 |
| prime radical | C7×#14579421 | C2 |
| cosocle | C72×D61 | C2×C3 |
| LCS | G ▷ C72×C61 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2562 |
Polycyclic presentation:
2,3,2,7^2,61|a^2=c,d^a=d^6,f^a=f^50,e^b=e^2,f^b=f^13,f^c=f^60295 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 202);