Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#449 ⋊ C2 |
| Sylow | C17 ⋊ #3319 |
414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=eg,b^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,c^b=cg,d^b=de,h^b=h^16,f^c=fg181 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3319, C2×#14540944, #17911084, … |
| maximal normal subgroup of | D17×#3319, C2×#14540944, #17911084, … |
| maximal quotient of | #17049883, #17050625, #17051401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16670);