Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#88324 |
| Sylow | C53 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^5,53|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^30,f^d=f^52124 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#88324, #16811471, Q8⋊#88324, … |
| maximal normal subgroup of | D4⋊#88324, #16811471, Q8⋊#88324, … |
| maximal quotient of | #16811484, #16811486, #16811489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 212);