Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D17⋊AΣL(1,𝔽16) |
| Fitting | C17×#120 ⋊ C4 |
| Sylow | C17 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^7,17|a^2=e,b^a=bd,d^a=df,f^a=fg,h^a=h^13,e^b=ef,h^c=h^16,e^d=eg,h^e=h^1682 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×#595, #17960827, #17961294, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×#595, #17960827, #17961294, … |
| maximal quotient of | #17958122, #17958212, #17958284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20756);