Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#460 ⋊ C2 |
| Sylow | C17 ⋊ #3333 |
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=eg,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^16,c^b=cg,d^b=de,h^b=h^16,f^c=fg,h^c=h^16,h^d=h^16181 conjugacy classes — view the full character table.
| maximal subgroup of | #17024054, #17024056, #17024114, … |
| maximal normal subgroup of | #17024054, #17024056, #17024114, … |
| maximal quotient of | #17049990, #17050770, #17051563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16851);