Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#542 ⋊ C2 |
| Sylow | C17 ⋊ #3179 |
374 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=dg,h^c=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3179, C2×#14539461, #17904216, … |
| maximal normal subgroup of | D17×#3179, C2×#14539461, #17904216, … |
| maximal quotient of | #17034899, #17038616, #17038624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15187);