Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #108 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^5,53|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^b=f^52274 conjugacy classes — view the full character table.
| maximal subgroup of | #108×D53, C2×#13133152, #16810670, … |
| maximal normal subgroup of | #108×D53, C2×#13133152, #16810670, … |
| maximal quotient of | #16810373, #16810375, #16810387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 81);