Finite Group DatabasebetaFinite Group Databasebeta| order | 8070 |
| automorphism | Aut(G) order 8651040 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4035 |
| unambiguous semidirect product | C3⋊D1345 |
| unambiguous semidirect product | C5⋊D807 |
| unambiguous semidirect product | C269⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C269 ⋊ C2 |
| Hall | C5×C269 ⋊ D3 |
| Hall | C3×C269 ⋊ D5 |
| Sylow | C269 ⋊ D15 |
| Hall | C3×C5 ⋊ D269 |
| Sylow | C5 ⋊ D807 |
| Sylow | C3 ⋊ D1345 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C269 | C2 |
| LCS | G ▷ C3×C5×C269 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,269|b^a=b^2,c^a=c^4,d^a=d^2682019 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D269, D5×D807, D3×D1345, … |
| maximal normal subgroup of | D15×D269, D5×D807, D3×D1345, … |
| maximal quotient of | Dic4035, C2×D4035, D12105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8070, 8);