Finite Group DatabasebetaFinite Group Databasebeta| order | 27090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#19129337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊#14268591 |
| commutator, hypocenter | C5×C7×C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C7×C43 | C2×C3 |
| prime radical | C3×C43×D35 | C3 |
| LCS | G ▷ C5×C7×C43 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13545 |
Polycyclic presentation:
2,3,5,7,43,3|b^3=f,c^a=c^4,d^a=d^6,d^b=d^2,e^b=e^6849 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27090, 53);