Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C132 ⋊ C3×C4 |
| Hall | C13×#63120 ⋊ C3 |
| Hall | C5×#92788 ⋊ C4 |
| Hall | #92788 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #14523130 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C3×C4 |
| prime radical | D5×#92788 | C2 |
| cosocle | D5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,13^2|a^2=c,d^a=d^2,e^a=e^12,e^b=e^3,f^b=f^3,d^c=d^4139 conjugacy classes — view the full character table.
| maximal subgroup of | #23778485⋊C3, C13⋊C3×#63120⋊C3, C3×#23778477, … |
| maximal normal subgroup of | C13⋊C3×#63120⋊C3, C3×#23778477 |
| maximal quotient of | #44477659, C3×#23778477, C3⋊#23778477 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 135);