Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C13 |
| direct product | C3×#16810007 |
| Fitting, socle, Hall | C3×C5×C132 ⋊ C4 |
| derived, Hall | C5×C132 ⋊ C3×C4 |
| Hall | C3×C132 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ #10621725 |
| Sylow | C5 ⋊ C3×#10621725 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16810007 |
| commutator, hypocenter | C5×C132 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C4 |
| prime radical | C3×D5×C132 | C2 |
| cosocle | D5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
192 conjugacy classes of subgroups.
1023 conjugacy classes — view the full character table.
| maximal subgroup of | #44477655, #44477656, #44477661, … |
| maximal normal subgroup of | #44477655, #44477656, #44477661, … |
| maximal quotient of | C9×#16810007, C32×#16810007, C3×C3⋊#16810007 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 210);