Finite Group DatabasebetaFinite Group Databasebeta| order | 27060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22583174 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C41 | C4×C5 |
| prime radical | C3×#17985235 | C2 |
| cosocle | C3×C11×D41 | C2×C5 |
| LCS | G ▷ C3×C11×C41 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1353 |
Polycyclic presentation:
2,5,2,3,11,41|a^2=c,d^a=d^2,f^a=f^32,e^b=e^4,f^b=f^10,f^c=f^40108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27060, 116);