Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C16×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1380 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=fg,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^13,h^d=h^16172 conjugacy classes — view the full character table.
| maximal subgroup of | #17949295, #17949296, #17949297, … |
| maximal normal subgroup of | #17949295, #17949296, #17949297, … |
| maximal quotient of | #17948542, #17948598, #17948758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19568);