Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1401 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^9,c^b=cg,d^b=dg,h^d=h^13,h^e=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545880, #17982757, #17982759, … |
| maximal normal subgroup of | C2×#14545880, #17982757, #17982759, … |
| maximal quotient of | #17981353, #17981397, D4⋊#10587528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21606);