Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1917 |
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^16364 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1917, C2×#14529345, #17036386, … |
| maximal normal subgroup of | D17×#1917, C2×#14529345, #17036386, … |
| maximal quotient of | #16932466, #16932473, #16932480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5071);