Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C53 ⋊ C2 |
| Sylow | C53 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^5,53|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^52,d^b=de271 conjugacy classes — view the full character table.
| maximal subgroup of | #16810789, #16810790, #16810794, … |
| maximal normal subgroup of | #16810789, #16810790, #16810794, … |
| maximal quotient of | #16810622, #16810628, #16810663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 172);