Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1313 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^4,c^b=cg,h^b=h^13,h^c=h^16,h^d=h^16172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543703, #17958015, #17958021, … |
| maximal normal subgroup of | C2×#14543703, #17958015, #17958021, … |
| maximal quotient of | #17948322, #17948489, #17949105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19429);