Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #2063 |
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=de,b^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^16,c^b=cf,d^c=dg,f^c=fg250 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2063, C2×#14530142, #17062868, … |
| maximal normal subgroup of | D17×#2063, C2×#14530142, #17062868, … |
| maximal quotient of | #16938839, #16938853, #16938867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5868);