Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ SD32 |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^5,53|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^52,c^b=cd,d^b=de,f^b=f^52427 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D53, C2×#13133162, #16811054, … |
| maximal normal subgroup of | SD32×D53, C2×#13133162, #16811054, … |
| maximal quotient of | #16810425, #16810428, #16810451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 91);