Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C7 ⋊ C22⋊Q8 |
| Sylow | C7 ⋊ #4024 |
| Sylow | C5 ⋊ #6441 |
148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|a^2=e,c^2=e,c^a=ce,f^a=f^4,g^a=g^6,c^b=cd184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 814);