Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #1742 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,c^2=g,e^2=g,b^a=bd,d^a=dg,e^b=eg,h^b=h^16364 conjugacy classes — view the full character table.
| maximal subgroup of | #16939536, #16939537, #16939675, … |
| maximal normal subgroup of | #16939536, #16939537, #16939675, … |
| maximal quotient of | #16923914, #16923917, #16923926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4248);