Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D7×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D7×D5⋊C8 |
| unambiguous semidirect product | D5⋊(C8×D7) |
| unambiguous semidirect product | (D5×D7)⋊C8 |
| derived, Hall | C5×C7 ⋊ C22×C8 |
| Sylow | C7 ⋊ C2×D5⋊C8 |
| Sylow | C5 ⋊ C2×C8×D7 |
152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D5⋊AGL(1,𝔽9), AGL(1,𝔽7)×D5⋊C8, C8×D7×AGL(1,𝔽5), … |
| maximal normal subgroup of | AGL(1,𝔽7)×D5⋊C8, C8×D7×AGL(1,𝔽5), D7×#3992, … |
| maximal quotient of | D7×D5⋊AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 919);