Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C7⋊AGL(1,𝔽5))⋊Q8 |
| Hall | C5×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ Q8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #6450 |
140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|a^2=e,b^2=d,c^2=e,c^a=ce,g^a=g^6,c^b=ce,f^b=f^2,f^d=f^467 conjugacy classes — view the full character table.
| maximal subgroup of | #72217834, #72218120, #72218183, … |
| maximal normal subgroup of | #72217834, #72218120, #72218183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 916);