Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×H(3,ℤ/4) ⋊ C2 |
| Sylow | C17 ⋊ #2010 |
394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,h^a=h^16,c^b=cf,d^b=dg,e^b=eg,h^b=h^16,h^c=h^16202 conjugacy classes — view the full character table.
| maximal subgroup of | #16946490, #16946495, #16946501, … |
| maximal normal subgroup of | #16946490, #16946495, #16946501, … |
| maximal quotient of | #16934691, #16934698, #16934705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5578);