Finite Group DatabasebetaFinite Group Databasebeta| order | 6980 |
| automorphism | Aut(G) order 4858080 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3490 |
| direct product | C2×D1745 |
| unambiguous semidirect product | (C2×C5)⋊D349 |
| unambiguous semidirect product | (C2×C349)⋊D5 |
| Fitting, socle | C2×C5×C349 ⋊ C2 |
| derived, Hall | C5×C349 ⋊ C22 |
| Sylow | C349 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D349 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1745 |
| commutator, hypocenter | C5×C349 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C349 | C2 |
| LCS | G ▷ C5×C349 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1748 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊(D349⋊C3), D3×D1745, C2×C3×D1745, … |
| maximal normal subgroup of | C2×C5⋊(D349⋊C3), C2×C3×D1745, C2×C5×D1745, … |
| maximal quotient of | D3×D1745, C2×C3×D1745, C2×D5235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6980, 13);