Finite Group DatabasebetaFinite Group Databasebeta| order | 35855 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C71×C101 ⋊ C5 |
| Sylow | C101 ⋊ C71⋊C5 |
| Sylow | C71 ⋊ C101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C71×C101 | C5 |
| LCS | G ▷ C71×C101 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7171 |
Polycyclic presentation:
5,71,101|b^a=b^57,c^a=c^361439 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35855, 6);