Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of C5⋊#4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#4183 |
| Fitting, derived, Hall | C5×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | AΣL(1,𝔽27) ⋊ D5 |
| Sylow | C5 ⋊ #4183 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×AΣL(1,𝔽27) | C2 |
| Frattini | C32 | C3⋊D15 |
| socle | C3×C5 | #272 |
| LCS | G ▷ C5×AΣL(1,𝔽27) | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2,3^2,5,3^2|b^a=b^2,c^a=c^2,d^a=d^4,e^a=ef^2,f^a=f^2,c^b=ce,e^b=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4183, #4174⋊D5, #4175⋊D5, … |
| maximal normal subgroup of | D5×#4183, #4174⋊D5, #4175⋊D5, … |
| maximal quotient of | #13108152, C2×C5⋊#4183, C3×C5⋊#4183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 50);