Finite Group DatabasebetaFinite Group Databasebeta| order | 6958 |
| automorphism | Aut(G) order 10228260 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3479 |
| unambiguous semidirect product | C49⋊D71 |
| unambiguous semidirect product | C71⋊D49 |
| Fitting, derived, Hall | C49×C71 ⋊ C2 |
| Sylow | C71 ⋊ D49 |
| Sylow | C49 ⋊ D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C49×C71 | C2 |
| Frattini | C7 | D497 |
| socle | C7×C71 | D7 |
| LCS | G ▷ C49×C71 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,71,7|b^7=d^6,b^a=b^6d,c^a=c^70,d^a=d^61741 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D49×D71, C2×D3479, C3×D3479, … |
| maximal normal subgroup of | D49×D71, C2×D3479, C3×D3479, … |
| maximal quotient of | Dic3479, C2×D3479, C3×D3479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6958, 6);