Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C5×C132 ⋊ Dic3 |
| derived, Hall | C5×#92789 ⋊ C4 |
| Hall | #92789 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ ΓL(1,𝔽16) |
| Sylow | C5 ⋊ #14523126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×#92789 | C4 |
| Fitting, socle | C5×C132 | Dic3 |
| prime radical, cosocle | D5×#92789 | C2 |
| LCS | G ▷ C5×#92789 | |
| UCS | C1 | |
48 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^3f^8,f^a=e^12f^10,d^b=d^4,e^c=e^9f^5,f^c=f^3157 conjugacy classes — view the full character table.
| maximal subgroup of | #23778485⋊C3, C3×#23778485, C3⋊#23778485 |
| maximal normal subgroup of | #23778485⋊C3, C3×#23778485 |
| maximal quotient of | #44477667, C3×#23778485, C3⋊#23778485 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 143);