Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C17 ⋊ #2244 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=eg,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,c^b=cg,h^b=h^16,h^c=h^16202 conjugacy classes — view the full character table.
| maximal subgroup of | #16947970, #16947971, #16947977, … |
| maximal normal subgroup of | #16947970, #16947971, #16947977, … |
| maximal quotient of | #16950711, #16952257, #16952557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6751);