Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C4×C7×D5 |
| Fitting | C2×C3×C4×C5×C7 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C3×C4×C7 |
| Hall | C3×C5×C7 ⋊ C22×C4 |
| Hall | C5×C7 ⋊ C22×C3×C4 |
| Hall | C3×C5 ⋊ C22×C4×C7 |
216 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 840 |
672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C4×C7×AGL(1,𝔽5), C2×C4×D3×C7×D5, C2×C4×C7×ΓL(1,𝔽16) |
| maximal normal subgroup of | C2×C3×C4×C7×AGL(1,𝔽5), C2×C4×D3×C7×D5, C2×C4×C7×ΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 861);