Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #3243 |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^16,f^c=fg178 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3243, C2×#14540063, #17906569, … |
| maximal normal subgroup of | D17×#3243, C2×#14540063, #17906569, … |
| maximal quotient of | #17043871, #17044088, #17044917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15789);