Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16810006 |
| Fitting, socle, derived, Hall | C3×C5×C132 ⋊ C4 |
| Hall | C5×C132 ⋊ Dic3 |
| Hall | C3×C132 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ #10621730 |
| Sylow | C5 ⋊ C3⋊#10621730 |
| Sylow | C3 ⋊ #16810006 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C132 | C4 |
| prime radical, cosocle | C3×C13×D65 | C2 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,13^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^8,f^a=f^12,d^b=d^4,e^b=e^12666 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16810006, C3⋊#23778472, C3⋊#23778476, … |
| maximal normal subgroup of | C3⋊#23778472, C3⋊#23778476, C3⋊#23778460, … |
| maximal quotient of | C9⋊#16810006, C3×C3⋊#16810006, C3⋊(C3⋊#16810006) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 235);