Finite Group DatabasebetaFinite Group Databasebeta| order | 30861 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | H(3,𝔽3)⋊#11765917 |
| Sylow | C127 ⋊ H(3,𝔽3)⋊C9 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10287 |
Polycyclic presentation:
3^5,127|a^3=d,b^a=bc,c^a=ce,f^a=f^107,c^b=ce1437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30861, 104);