Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #2255 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^16,c^b=cg,h^c=h^16202 conjugacy classes — view the full character table.
| maximal subgroup of | #16948328, #16948329, #16948335, … |
| maximal normal subgroup of | #16948328, #16948329, #16948335, … |
| maximal quotient of | #16950770, #16952361, #16952366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6797);