Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C17×Q32 ⋊ C4 |
| Sylow | C17 ⋊ #1416 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=g,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^13,c^b=ce,e^b=ef,f^b=fg,h^d=h^1682 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543934, #17962789, #17962790, … |
| maximal normal subgroup of | C2×#14543934, #17962789, #17962790, … |
| maximal quotient of | #17949213, #17949214, #17949297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19660);