Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| isoclinism | isoclinic class of D169 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D169 |
| Fitting, Hall | C3×C5×C169 ⋊ C2 |
| derived, Sylow | C169 ⋊ C2×C3×C5 |
| Hall | C5×C169 ⋊ C2×C3 |
| Hall | C3×C169 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D169 |
| commutator, hypocenter | C169 | C2×C3×C5 |
| Frattini | C13 | C3×C5×D13 |
| Fitting | C3×C5×C169 | C2 |
| socle | C3×C5×C13 | D13 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
1290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D169⋊C9, C5×C9×D169, C3×C5×D169⋊C3, … |
| maximal normal subgroup of | C5×D169⋊C9, C5×C9×D169, C3×C5×D169⋊C3, … |
| maximal quotient of | C5×C9×D169, C32×C5×D169, C3×C5×D507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 6);