Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C13×D13 |
| Fitting, socle, Hall | C3×C5×C132 ⋊ C2 |
| derived | C13 ⋊ C2×C3×C5×C13 |
| Hall | C5×C132 ⋊ C2×C3 |
| Hall | C3×C132 ⋊ C2×C5 |
| Sylow | C132 ⋊ C2×C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C13 | D13 |
| commutator, hypocenter | C13 | C2×C3×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C5×C13 | |
56 conjugacy classes of subgroups.
1560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C13×D13⋊C9, C5×#15690150, C5×#15690151, … |
| maximal normal subgroup of | C5×C13×D13⋊C9, C5×#15690150, C5×#15690151, … |
| maximal quotient of | C5×C9×C13×D13, C3×C5×C13×D39, C32×C5×C13×D13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 36);