Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| isoclinism | isoclinic class of #63121 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×#63121 |
| Fitting, socle, Hall | C3×C5×C132 ⋊ C4 |
| derived | C5×C13 ⋊ C3×C4×C13 |
| Hall | C5×C132 ⋊ C3×C4 |
| Hall | C3×C132 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ C13×#261 |
| Sylow | C5 ⋊ C3×C13×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | #63121 |
| commutator, hypocenter | C5×C13 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C4 |
| prime radical | C3×C13×D65 | C2 |
| cosocle | D65 | C2×C3×C13 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C3×C13 | |
60 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#63121⋊C9, #44477650, #44477652, … |
| maximal normal subgroup of | C13×#63121⋊C9, #44477650, #44477652, … |
| maximal quotient of | C9×C13×#63121, C32×C13×#63121, C3×C13×C3⋊#63121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 203);