Finite Group DatabasebetaFinite Group Databasebeta| order | 10170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D339 |
| unambiguous semidirect product | C3⋊(C5×D339) |
| unambiguous semidirect product | C113⋊(C5×C3⋊D3) |
| Fitting, socle, Hall | C32×C5×C113 ⋊ C2 |
| derived, Hall | C32×C113 ⋊ C2×C5 |
| Hall | C5×C113 ⋊ C3⋊D3 |
| Sylow | C113 ⋊ C5×C3⋊D3 |
| Hall | C32×C5 ⋊ D113 |
| Sylow | C32 ⋊ C5×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D339 |
| commutator, cosocle, hypocenter | C32×C113 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C113 | C2 |
| LCS | G ▷ C32×C113 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
2550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#16861297, #35204816, C5×D3×D339, … |
| maximal normal subgroup of | C5×#16861297, #35204816, C5×D3×D339, … |
| maximal quotient of | C5×C3⋊Dic339, C2×C5×C3⋊D339 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10170, 12);