Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #1839 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^13,h^f=h^16184 conjugacy classes — view the full character table.
| maximal subgroup of | #17948240, #17948251, #17949712, … |
| maximal normal subgroup of | #17948240, #17948251, #17949712, … |
| maximal quotient of | #17953791, #17953797, #17956919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20437);