Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#14523126 |
| derived, Hall | #92789 ⋊ C4×C5 |
| Hall | C5×#92789 ⋊ C4 |
| Hall | C5×C132 ⋊ Dic3 |
| Sylow | C132 ⋊ C5×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #11759813 |
| commutator, hypocenter | #92789 | C4×C5 |
| Frattini | C2 | C5×#11759813 |
| Fitting, socle | C2×C5×C132 | D3 |
| prime radical | C2×C5×#92789 | C2 |
| cosocle | C2×#92789 | C2×C5 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
490 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14523126⋊C3, C3×C5×#14523126, C5×C3⋊#14523126 |
| maximal normal subgroup of | C5×#14523126⋊C3, C3×C5×#14523126 |
| maximal quotient of | C5×#20258750, C3×C5×#14523126, C5×C3⋊#14523126 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 61);