Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #3352 |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^16229 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3352, C2×#14541353, #17913078, … |
| maximal normal subgroup of | D17×#3352, C2×#14541353, #17913078, … |
| maximal quotient of | #17050726, #17050732, #17052102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17079);