Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#488 ⋊ C2 |
| Sylow | C17 ⋊ #3137 |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^b=h^16,h^d=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3137, C2×#14539148, #17903578, … |
| maximal normal subgroup of | D17×#3137, C2×#14539148, #17903578, … |
| maximal quotient of | #17034531, #17036971, #17036978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14874);