Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1401 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^13,c^b=cg,d^b=dg,h^b=h^16,h^d=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17962582, C2×#14543902, #17962585, … |
| maximal normal subgroup of | #17962582, C2×#14543902, #17962585, … |
| maximal quotient of | #17949110, #17949170, #17949204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19628);