Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^5,53|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^52,c^b=ce274 conjugacy classes — view the full character table.
| maximal subgroup of | #103×D53, C2×#13133141, #16810618, … |
| maximal normal subgroup of | #103×D53, C2×#13133141, #16810618, … |
| maximal quotient of | Q8⋊#88322, #16810360, #16810369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 70);