Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4×C7 |
No aliases for this group.
| Sylow | C72 ⋊ #117 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
Polycyclic presentation:
2^5,7^2|a^2=e,b^2=d,c^a=cd,f^a=f^6,g^a=g^6404 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 732);