Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C17 ⋊ #1425 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=ce,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^16550 conjugacy classes — view the full character table.
| maximal subgroup of | #16922208, #16922209, #16922214, … |
| maximal normal subgroup of | #16922208, #16922209, #16922214, … |
| maximal quotient of | #16922001, #16922003, #16922027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2714);