Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C5×C7 ⋊ C2×C22⋊C4 |
| Sylow | C7 ⋊ D5×C22⋊C4 |
| Sylow | C5 ⋊ D7×C22⋊C4 |
264 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 68 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=e,c^a=cd,g^a=g^6,c^b=cd,f^b=f^4118 conjugacy classes — view the full character table.
| maximal subgroup of | #72218149, D5×D7×C22⋊C4, #72218524, … |
| maximal normal subgroup of | #72218149, D5×D7×C22⋊C4, #72218524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 610);