Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q16×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1334 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=g,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^9,c^b=ceg,d^b=dg,e^b=eg,h^d=h^13,h^f=h^1646 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545833, #17982068, #17982069, … |
| maximal normal subgroup of | C2×#14545833, #17982068, #17982069, … |
| maximal quotient of | #17981127, #17981128, #17981135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21559);