Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1400 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^9,d^b=dg,h^b=h^16,h^d=h^13,h^e=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | #17982751, C2×#14545879, #17982754, … |
| maximal normal subgroup of | #17982751, C2×#14545879, #17982754, … |
| maximal quotient of | #17981352, #17981396, #17981422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21605);