Finite Group DatabasebetaFinite Group Databasebeta| order | 30861 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C127⋊C3)⋊C81 |
| derived, Sylow | C127 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | #11765919 |
| commutator, hypocenter | C127 | C3×C81 |
| Frattini | C9 | C3×#11765919 |
| Fitting | C27×C127 | C9 |
| socle | C3×C127 | C3×C27 |
| prime radical | C3×C127⋊C3 | C27 |
| cosocle | #16812178 | C32 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C27 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10287 |
Polycyclic presentation:
3^5,127|a^3=c,c^3=d,d^3=e,f^a=f^22,f^b=f^19,f^c=f^107621 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30861, 342);