Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4×C8×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1414 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=f,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,c^b=cfg,d^b=defg,e^b=eg,h^b=h^16,d^c=dfg,e^d=eg,h^d=h^16145 conjugacy classes — view the full character table.
| maximal subgroup of | D17⋊#1414, C2×#14543932, #17962729, … |
| maximal normal subgroup of | D17⋊#1414, C2×#14543932, #17962729, … |
| maximal quotient of | #17949162, #17949175, #17949282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19658);