Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×C7×C4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C7×C4⋊C4) |
| Fitting | C2×C4×C5×C7 ⋊ C4 |
| Hall | C5×C7 ⋊ C2×C4⋊C4 |
| Sylow | C5 ⋊ C2×C7×C4⋊C4 |
184 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 952);