Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #100 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^5,53|a^2=d,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^52271 conjugacy classes — view the full character table.
| maximal subgroup of | #100×D53, C2×#13133133, #16810605, … |
| maximal normal subgroup of | #100×D53, C2×#13133133, #16810605, … |
| maximal quotient of | #16810346, #16810362, #16810366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 62);