Finite Group Databasebeta

← Group #338317

Character table — Group #338317

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888224444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111111111111111-1-11-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ51111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11
χ61111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-111111111-11-1-111-1-111-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11-11-11111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-111-111
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111111-11
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-11111111-1-1-11-1
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111-11-111-1-1-1-111-11-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1111-1-111-1-1-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-1-1-11111-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-111111-1-1
χ17222222222-22-22-22-2-2-2222200002200-2-2000000000000-2-20200000000000
χ18222222222-22-22-22-2-2-222220000-2-200-2-2000000000000220-200000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000220022000000000000-220-200000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000-2-200220000000000002-20200000000000
χ2122222222-22-22-22-22-2-20000222200-2-200220000-2-2000000-2000000000000
χ2222222222-22-22-22-22-2-2000022-2-200-2-200-2-20000220000002000000000000
χ2322222222-22-22-22-22-2-20000-2-222002200-2-2000022000000-2000000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-2002200220000-2-20000002000000000000
χ2522-2-2-22-2222-2-222-2-22-2000000000000000022-2-200000000002i−2i00002i−2i000
χ2622-2-2-22-2222-2-222-2-22-2000000000000000022-2-20000000000−2i2i0000−2i2i000
χ2722-2-2-22-2222-2-222-2-22-20000000000000000-2-22200000000002i−2i0000−2i2i000
χ2822-2-2-22-2222-2-222-2-22-20000000000000000-2-2220000000000−2i2i00002i−2i000
χ292-222-22-2-20-20-202020022−2−2002i−2i002i−2i2−200i2−i2i2−i22-222−2−200000000i2−i200000
χ302-222-22-2-20-20-202020022−2−2002i−2i00−2i2i2−200−i2i2−i2i2-22−2−22200000000i2−i200000
χ312-222-22-2-20-20-202020022−2−200−2i2i002i−2i2−200i2−i2i2−i2-22−2−22200000000−i2i200000
χ322-222-22-2-20-20-202020022−2−200−2i2i00−2i2i2−200−i2i2−i2i22-222−2−200000000−i2i200000
χ332-222-22-2-20-20-2020200−2−222002i−2i002i−2i−2200−i2i2−i2i22-2−2−22200000000−i2i200000
χ342-222-22-2-20-20-2020200−2−222002i−2i00−2i2i−2200i2−i2i2−i2-2222−2−200000000−i2i200000
χ352-222-22-2-20-20-2020200−2−22200−2i2i002i−2i−2200−i2i2−i2i2-2222−2−200000000i2−i200000
χ362-222-22-2-20-20-2020200−2−22200−2i2i00−2i2i−2200i2−i2i2−i22-2−2−22200000000i2−i200000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-44-4-4-440-40-4040004-44-40000000000000000000000000000000000000
χ39444-44-4-4-440-40-404000-44-440000000000000000000000000000000000000
χ40444-44-4-4-4-404040-4000000000000000000000000022−2222−22000000000000000
χ41444-44-4-4-4-404040-40000000000000000000000000−2222−2222000000000000000
χ4244-44-4-44-44040-40-40000000000000000000000000000000000022−220000000
χ4344-44-4-44-44040-40-400000000000000000000000000000000000−22220000000
χ4444-44-4-44-4-40-40404000000000004i−4i0000000000000000000000000000000
χ4544-44-4-44-4-40-4040400000000000−4i4i0000000000000000000000000000000
χ4644-4-4-44-444-4-444-4-44-4400000000000000000000000000000000000000000
χ4744-4-4-44-44-444-4-444-4-4400000000000000000000000000000000000000000
χ4844-4-4-44-44-4-444-4-4444-400000000000000000000000000000000000000000
χ494-444-44-4-404040-40-4002222−22−2200000000−2222000000000000000000000000000
χ504-444-44-4-404040-40-400−22−2222220000000022−22000000000000000000000000000
χ514-44-4-4-444000000000022−22−2222000000000022−220000002-2-22000000000000000
χ524-44-4-4-444000000000022−22−22220000000000−2222000000-222-2000000000000000
χ534-44-4-4-4440000000000−222222−22000000000022−22000000-222-2000000000000000
χ544-44-4-4-4440000000000−222222−220000000000−22220000002-2-22000000000000000
χ554-4-4-4444-4040-40-4040000004i−4i00000000000000000000000000000000000
χ564-4-4-4444-4040-40-404000000−4i4i00000000000000000000000000000000000
χ574-4-4-4444-40-404040-40000000000000000002i2−2i2−2i22i2000000000000000000000
χ584-4-4-4444-40-404040-4000000000000000000−2i22i22i2−2i2000000000000000000000
χ598-8-888-8-88000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).