Finite Group DatabasebetaFinite Group Databasebeta| order | 6998 |
| automorphism | Aut(G) order 12239502 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3499 |
| unambiguous semidirect product | C3499⋊C2 |
| Fitting, socle, derived, Sylow | C3499 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3499 | C2 |
| LCS | G ▷ C3499 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3499|b^a=b^34981751 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3499, D3499⋊C3, C3×D3499, … |
| maximal normal subgroup of | C2×D3499, D3499⋊C3, C3×D3499, … |
| maximal quotient of | Dic3499, C2×D3499, C3×D3499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6998, 1);