Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C17×#520 ⋊ C2 |
| Sylow | C17 ⋊ C4×2−1+4 |
1492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=f,c^2=f,e^2=g,b^a=bf,d^a=df,c^b=cf,h^c=h^16,h^e=h^16340 conjugacy classes — view the full character table.
| maximal subgroup of | #17040217, #17040223, #17040228, … |
| maximal normal subgroup of | #17040217, #17040223, #17040228, … |
| maximal quotient of | #17192562, #17192565, #520×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17721);