Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^5,53|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^30,c^b=ce,f^b=f^52,f^d=f^5279 conjugacy classes — view the full character table.
| maximal subgroup of | D53⋊#104, C2×#13133282, #16811620, … |
| maximal normal subgroup of | D53⋊#104, C2×#13133282, #16811620, … |
| maximal quotient of | #16811471, Q8⋊#88324, #16811475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 211);