Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16809980⋊C3 |
| Fitting, derived, Hall | C5×C169 ⋊ C3×C4 |
| Hall | #16809980 ⋊ C3 |
| Hall | C5×C169⋊C3 ⋊ C4 |
| Hall | C169⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C169 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #10621721⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C169 | C3×C4 |
| Frattini | C13 | #63121⋊C3 |
| socle | C5×C13 | AGL(1,𝔽13) |
| prime radical | C5⋊(D169⋊C3) | C2 |
| cosocle | D845 | C2×C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,13^2|a^2=c,e^13=f^8,d^a=d^3,e^a=e^5f,f^a=f^5,e^b=e^3f^10,f^b=f^3,d^c=d^4,e^c=e^12f^5,f^c=f^1285 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16809980⋊C3, C3⋊(#16809980⋊C3) |
| maximal normal subgroup of | C3×#16809980⋊C3 |
| maximal quotient of | #16809980⋊C9, C3×#16809980⋊C3, C3⋊(#16809980⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 17);