Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| derived, Hall | C5×C132 ⋊ C3×C4 |
| Hall | #16809991 ⋊ C3 |
| Hall | C5×#92789 ⋊ C4 |
| Hall | #92789 ⋊ Dic5 |
| Sylow | C132 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ #14523129 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊#11759816 |
| commutator, hypocenter | C5×C132 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C132 | C2×C3 |
| prime radical | C2×C5×#92789 | C2 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,13^2,2|a^2=f,c^a=c^4,d^a=d^12,e^a=e^12,d^b=d^3,e^b=e^9304 conjugacy classes — view the full character table.
| maximal subgroup of | #23778406⋊C3, C3×#23778407, C3⋊#23778407 |
| maximal normal subgroup of | #23778406⋊C3, C3×#23778407 |
| maximal quotient of | #44477589, C3×#23778407, C3⋊#23778407 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 65);