Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #2028 |
246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 246 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=d,b^2=d,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^16,c^b=cf,e^b=eg,e^c=eg250 conjugacy classes — view the full character table.
| maximal subgroup of | #16921917, #16921919, #16947086, … |
| maximal normal subgroup of | #16921917, #16921919, #16947086, … |
| maximal quotient of | #16937299, #16937304, #16937319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5671);