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 ⋊ #1833 |
172 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,b^2=e,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^16,f^b=fg,f^c=fg352 conjugacy classes — view the full character table.
| maximal subgroup of | #16950440, #16950441, #16950447, … |
| maximal normal subgroup of | #16950440, #16950441, #16950447, … |
| maximal quotient of | #16927970, #16927974, #16927978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4634);