Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | Aut(G) order 3163680 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2535 |
| unambiguous semidirect product | C3⋊D845 |
| unambiguous semidirect product | C5⋊D507 |
| unambiguous semidirect product | C169⋊D15 |
| Fitting, derived, Hall | C3×C5×C169 ⋊ C2 |
| Hall | C5×C169 ⋊ D3 |
| Hall | C3×C169 ⋊ D5 |
| Sylow | C169 ⋊ D15 |
| Hall | C3×C5 ⋊ D169 |
| Sylow | C5 ⋊ D507 |
| Sylow | C3 ⋊ D845 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C5×C169 | C2 |
| Frattini | C13 | D195 |
| socle | C3×C5×C13 | D13 |
| LCS | G ▷ C3×C5×C169 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,13^2|d^13=e^12,b^a=b^2,c^a=c^4,d^a=d^12e,e^a=e^121269 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7605, C3⋊(C5⋊(D169⋊C3)), C3×D2535, … |
| maximal normal subgroup of | C3⋊(C5⋊(D169⋊C3)), C3×D2535, C5×D2535, … |
| maximal quotient of | D7605, C3×D2535, C3⋊D2535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 12);