Finite Group DatabasebetaFinite Group Databasebeta| order | 6980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D349 |
| unambiguous semidirect product | C349⋊(C22×C5) |
| unambiguous semidirect product | (C2×C349)⋊(C2×C5) |
| Fitting, socle | C2×C5×C349 ⋊ C2 |
| derived, Sylow | C349 ⋊ C22×C5 |
| Hall | C5×C349 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D349 |
| commutator, hypocenter | C349 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C349 | C2 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C2×C5 | |
20 conjugacy classes of subgroups.
1760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×D349⋊C3, C5×D3×D349, C2×C3×C5×D349, … |
| maximal normal subgroup of | C2×C5×D349⋊C3, C2×C3×C5×D349, C2×C25×D349, … |
| maximal quotient of | C5×D3×D349, C2×C3×C5×D349, C2×C5×D1047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6980, 15);