Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#475 ⋊ C2 |
| Sylow | C17 ⋊ #3258 |
334 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^16,c^b=ce,d^b=dg,h^b=h^16,f^c=fg,h^c=h^16,h^d=h^16178 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3258, C2×#14540217, #17907311, … |
| maximal normal subgroup of | D17×#3258, C2×#14540217, #17907311, … |
| maximal quotient of | #17044305, #17044323, #17044730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15943);