Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16809980 |
| Fitting, derived, Hall | C3×C5×C169 ⋊ C4 |
| Hall | C5×C169 ⋊ Dic3 |
| Hall | C3×C169 ⋊ AGL(1,𝔽5) |
| Sylow | C169 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ #10621721 |
| Sylow | C5 ⋊ C3⋊#10621721 |
| Sylow | C3 ⋊ #16809980 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C5×C169 | C4 |
| Frattini | C13 | C3⋊#63121 |
| socle | C3×C5×C13 | #261 |
| prime radical, cosocle | C3×D845 | C2 |
| LCS | G ▷ C3×C5×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,13^2|a^2=b,e^13=f^8,c^a=c^2,d^a=d^3,e^a=e^5f,f^a=f^5,d^b=d^4,e^b=e^12f^5,f^b=f^12639 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16809980, C3⋊(#16809980⋊C3), C3×C3⋊#16809980, … |
| maximal normal subgroup of | C3⋊(#16809980⋊C3), C3×C3⋊#16809980 |
| maximal quotient of | C9⋊#16809980, C3×C3⋊#16809980, C3⋊(C3⋊#16809980) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 32);