Finite Group DatabasebetaFinite Group Databasebeta| order | 7002 |
| automorphism | Aut(G) order 8150328 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3501 |
| unambiguous semidirect product | C9⋊D389 |
| unambiguous semidirect product | C389⋊D9 |
| Fitting, derived, Hall | C9×C389 ⋊ C2 |
| Sylow | C389 ⋊ D9 |
| Sylow | C9 ⋊ D389 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C389 | C2 |
| Frattini | C3 | D1167 |
| socle | C3×C389 | D3 |
| LCS | G ▷ C9×C389 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,389,3|b^3=d^2,b^a=b^2d,c^a=c^388,d^a=d^21752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D389, C2×D3501, C5×D3501, … |
| maximal normal subgroup of | D9×D389, C2×D3501, C5×D3501 |
| maximal quotient of | Dic3501, C2×D3501, C5×D3501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7002, 4);