Finite Group DatabasebetaFinite Group Databasebeta| order | 35019 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1297 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1297 | C27 |
| prime radical | C1297⋊C3 | C9 |
| cosocle | #26042991 | C3 |
| LCS | G ▷ C1297 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1297 |
Polycyclic presentation:
3^3,1297|a^3=b,b^3=c,d^a=d^729,d^b=d^104,d^c=d^36575 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35019, 16);