Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1333 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^13,c^b=ceg,d^b=dg,e^b=eg,h^d=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543742, #17958724, #17958729, … |
| maximal normal subgroup of | C2×#14543742, #17958724, #17958729, … |
| maximal quotient of | #17948356, #17948364, #17948437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19468);