Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C7 ⋊ SD32 |
| Sylow | C7 ⋊ #3932 |
| Sylow | C5 ⋊ #6402 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|a^2=c,b^2=e,c^2=de,d^2=e,b^a=bce,g^a=g^6,c^b=cd,d^b=de,f^b=f^4112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 21);