Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #1932 |
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=df,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^16,h^b=h^16,e^c=eg,h^c=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1932, C2×#14529456, #17036909, … |
| maximal normal subgroup of | D17×#1932, C2×#14529456, #17036909, … |
| maximal quotient of | #16932556, #16932563, #16932570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5182);