Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C17×H(3,ℤ/4) ⋊ C2 |
| Sylow | C17 ⋊ #1827 |
262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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|a^2=f,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^16,f^c=fg208 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1827, C2×#14528886, #17034170, … |
| maximal normal subgroup of | D17×#1827, C2×#14528886, #17034170, … |
| maximal quotient of | #16927766, #16927770, #16927774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4612);