Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C5×C7 ⋊ C4×D4 |
| Sylow | C7 ⋊ #4039 |
| Sylow | C5 ⋊ C4×D28 |
188 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 64 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,b^2=e,c^2=d,c^a=cd,g^a=g^6,f^b=f^4136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 458);