Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^5,53|a^2=d,b^a=bc,c^a=ce,f^a=f^30,d^b=de,f^b=f^52,f^d=f^52115 conjugacy classes — view the full character table.
| maximal subgroup of | #16811527, #16811528, #16811529, … |
| maximal normal subgroup of | #16811527, #16811528, #16811529, … |
| maximal quotient of | #16811467, #16811468, #16811475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 205);