Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #2026 |
258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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=d,b^2=dg,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^16,c^b=cf,e^c=eg256 conjugacy classes — view the full character table.
| maximal subgroup of | #16921911, #16921913, D17×#2026, … |
| maximal normal subgroup of | #16921911, #16921913, D17×#2026, … |
| maximal quotient of | #16937319, #16937329, #16937356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5661);