Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×C7×C4⋊C4 ⋊ C2 |
| Hall | C5×C7 ⋊ #117 |
| Sylow | C7 ⋊ #4038 |
| Sylow | C5 ⋊ #6455 |
152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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|b^2=e,c^2=d,c^a=ce,f^a=f^4,g^a=g^6,c^b=ce190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 829);