Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #2079 |
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=eg,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,e^c=eg,f^c=fg,h^c=h^16250 conjugacy classes — view the full character table.
| maximal subgroup of | #16921854, #16921856, #16921857, … |
| maximal normal subgroup of | #16921854, #16921856, #16921857, … |
| maximal quotient of | #16939044, #16939051, #16939058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5955);