Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of C5⋊#4179 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C5⋊#4179 |
| Fitting, Hall | C5×#732 ⋊ C2 |
| derived | C3×C5×C9 ⋊ C2×C3 |
| Sylow | #732 ⋊ D5 |
| Sylow | C5 ⋊ #4179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×C9 | C2×C3 |
| Frattini | C32 | C3×D15 |
| Fitting | C5×#732 | C2 |
| socle | C3×C5 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×C5×C9 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
Polycyclic presentation:
2,3^3,5,3|c^3=f,c^a=c^2f^2,d^a=d^2,e^a=e^4,f^a=f^2,c^b=cd,d^b=df^247 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4179, #4178⋊D5, #4185⋊D5, … |
| maximal normal subgroup of | D5×#4179, #4178⋊D5, #4185⋊D5, … |
| maximal quotient of | #13108141, C2×C5⋊#4179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 39);