Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C7×D4 ⋊ C4 |
| Hall | C5×C7 ⋊ #102 |
| Sylow | C7 ⋊ #4007 |
| Sylow | C5 ⋊ #6406 |
100 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|a^2=c,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^6,d^b=de,f^c=f^479 conjugacy classes — view the full character table.
| maximal subgroup of | #72217800, D8×C7⋊AGL(1,𝔽5), #72218028, … |
| maximal normal subgroup of | #72217800, D8×C7⋊AGL(1,𝔽5), #72218028, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 291);