Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #1837 |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^13,h^b=h^16,h^f=h^16172 conjugacy classes — view the full character table.
| maximal subgroup of | #17948765, #17948767, #17948776, … |
| maximal normal subgroup of | #17948765, #17948767, #17948776, … |
| maximal quotient of | #17953761, #17953763, #17953765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20435);