Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#14523154 |
| Fitting, socle, Hall | C5×C132 ⋊ C3×C4 |
| derived, Sylow | C132 ⋊ C3×C4×C5 |
| Hall | C5×#10621730 ⋊ C3 |
| Hall | C5×C13×C13⋊C3 ⋊ C4 |
| Hall | #10621730 ⋊ C3×C5 |
| Hall | C13×C13⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14523154 |
| commutator, hypocenter | C132 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | C3×C4 |
| prime radical | C5×C13×D13⋊C3 | C2 |
| cosocle | C13×D13 | C2×C3×C5 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C5 | |
50 conjugacy classes of subgroups.
305 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14523148⋊C3, C3×C5×#14523154, C5×C3⋊#14523154 |
| maximal normal subgroup of | C5×#14523148⋊C3, C3×C5×#14523154 |
| maximal quotient of | C5×#20258778, C3×C5×#14523154, C5×C3⋊#14523154 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 99);