Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^5,53|a^2=d,d^2=e,b^a=bc,f^a=f^30,f^b=f^52,f^d=f^52124 conjugacy classes — view the full character table.
| maximal subgroup of | #16811474, #16811475, #16811476, … |
| maximal normal subgroup of | #16811474, #16811475, #16811476, … |
| maximal quotient of | #16811467, #16811469, #16811471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 203);