Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1614 |
236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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=fg,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^16,d^b=df,e^b=eg,h^b=h^16,d^c=dg199 conjugacy classes — view the full character table.
| maximal subgroup of | #16947111, #16947112, #16947122, … |
| maximal normal subgroup of | #16947111, #16947112, #16947122, … |
| maximal quotient of | #16923370, #16923424, #16923457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 3537);