Finite Group DatabasebetaFinite Group Databasebeta| order | 6980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D349 |
| unambiguous semidirect product | (D5×C349)⋊C2 |
| unambiguous semidirect product | (C5×D349)⋊C2 |
| unambiguous semidirect product | D1745⋊C2 |
| Fitting, socle, derived, Hall | C5×C349 ⋊ C22 |
| Sylow | C349 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C349 | C22 |
| LCS | G ▷ C5×C349 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D349⋊C3, C3×D5×D349, D15×D349, … |
| maximal normal subgroup of | D5×D349⋊C3, C3×D5×D349, C5×D5×D349 |
| maximal quotient of | C3×D5×D349, D15×D349, D5×D1047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6980, 12);