Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#482 ⋊ C2 |
| Sylow | C17 ⋊ #3325 |
460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=eg,b^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^16,f^c=fg,h^c=h^16181 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3325, C2×#14541024, #17911284, … |
| maximal normal subgroup of | D17×#3325, C2×#14541024, #17911284, … |
| maximal quotient of | #17049937, #17050777, #17051636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16750);