Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1376 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=cg,e^a=eg,h^a=h^13,h^b=h^16,h^d=h^16184 conjugacy classes — view the full character table.
| maximal subgroup of | #17948441, #17948442, #17948451, … |
| maximal normal subgroup of | #17948441, #17948442, #17948451, … |
| maximal quotient of | #17948492, #17948506, #17948516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19555);