Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D7×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D7×AGL(1,𝔽5) |
| Fitting | C4×C5×C7 ⋊ C2×C4 |
| derived, Hall | C5×C7 ⋊ C2×C42 |
| Sylow | C7 ⋊ C2×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C42×D7 |
216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 927);