Finite Group Databasebeta

← Group #337813

Character table — Group #337813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888824448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1111111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-11111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-11-1-1
χ17222222222-22-22-22-2-2-20000222222000000-2-2-2-200-2-200000000000020000000000
χ18222222222-22-22-22-2-2-200002222-2-2000000222200-2-2000000000000-20000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-222000000-2-2220022000000000000-20000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2-2-200000022-2-2002200000000000020000000000
χ2122222222-22-22-22-22-2-2222200000022-2-2220000-2-2000000000000000-2000000000
χ2222222222-22-22-22-22-2-22222000000-2-222-2-20000-2-20000000000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200000022-2-2-2-20000220000000000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000-2-22222000022000000000000000-2000000000
χ2522-22-2-22-20-20-202020022-2-222−2−2002i−2i002i−2i0000002−2i2i2−i2−i2000022−2−2000000i2−i2000
χ2622-22-2-22-20-20-202020022-2-222−2−200−2i2i00−2i2i0000002−2−i2−i2i2i2000022−2−2000000−i2i2000
χ2722-22-2-22-20-20-202020022-2-2−2−222002i−2i002i−2i000000−22−i2−i2i2i20000−2−222000000−i2i2000
χ2822-22-2-22-20-20-202020022-2-2−2−22200−2i2i00−2i2i000000−22i2i2−i2−i20000−2−222000000i2−i2000
χ2922-22-2-22-20-20-2020200-2-22222−2−2002i−2i00−2i2i0000002−2i2i2−i2−i20000−2−222000000−i2i2000
χ3022-22-2-22-20-20-2020200-2-22222−2−200−2i2i002i−2i0000002−2−i2−i2i2i20000−2−222000000i2−i2000
χ3122-22-2-22-20-20-2020200-2-222−2−222002i−2i00−2i2i000000−22−i2−i2i2i2000022−2−2000000i2−i2000
χ3222-22-2-22-20-20-2020200-2-222−2−22200−2i2i002i−2i000000−22i2i2−i2−i2000022−2−2000000−i2i2000
χ332-2222-2-2-2-20-202020002−22−22-22-2000000002i−2i2i−2i2−2000000i2i2−i2−i22−22−20000i2−i200000
χ342-2222-2-2-2-20-202020002−22−22-22-200000000−2i2i−2i2i2−2000000−i2−i2i2i22−22−20000−i2i200000
χ352-2222-2-2-2-20-202020002−22−2-22-22000000002i−2i−2i2i2−2000000i2i2−i2−i2−22−220000−i2i200000
χ362-2222-2-2-2-20-202020002−22−2-22-2200000000−2i2i2i−2i2−2000000−i2−i2i2i2−22−220000i2−i200000
χ372-2222-2-2-2-20-20202000−22−222-22-2000000002i−2i2i−2i−22000000−i2−i2i2i2−22−220000−i2i200000
χ382-2222-2-2-2-20-20202000−22−222-22-200000000−2i2i−2i2i−22000000i2i2−i2−i2−22−220000i2−i200000
χ392-2222-2-2-2-20-20202000−22−22-22-22000000002i−2i−2i2i−22000000−i2−i2i2i22−22−20000i2−i200000
χ402-2222-2-2-2-20-20202000−22−22-22-2200000000−2i2i2i−2i−22000000i2i2−i2−i22−22−20000−i2i200000
χ412-22-2-2-22222-2-222-2-22-20000000000000000000000002-22-22i−2i2i−2i0000002i−2i0000000
χ422-22-2-2-22222-2-222-2-22-20000000000000000000000002-22-2−2i2i−2i2i000000−2i2i0000000
χ432-22-2-2-22222-2-222-2-22-2000000000000000000000000-22-222i−2i2i−2i000000−2i2i0000000
χ442-22-2-2-22222-2-222-2-22-2000000000000000000000000-22-22−2i2i−2i2i0000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-44-4-440-40-404000000000004-40000000000000000000000000000000000000
χ47444-4-44-4-440-40-40400000000000-440000000000000000000000000000000000000
χ48444-4-44-4-4-404040-4000000000000000000000000000000022−22−2222000000000000000
χ49444-4-44-4-4-404040-40000000000000000000000000000000−222222−22000000000000000
χ5044-44-4-44-404040-40-40000002222−22−2200000000000000−222200000000000000000000000
χ5144-44-4-44-404040-40-4000000−22−2222220000000000000022−2200000000000000000000000
χ524-4444-4-4-44040-40-400022−2222−220000000000000000−22220000000000000000000000000
χ534-4444-4-4-44040-40-4000−2222−2222000000000000000022−220000000000000000000000000
χ544-44-4-4-4444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ554-44-4-4-444-444-4-444-4-4400000000000000000000000000000000000000000000000
χ564-44-4-4-444-4-444-4-4444-400000000000000000000000000000000000000000000000
χ574-4-44-44-44000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ584-4-44-44-44000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ594-4-44-44-440000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ604-4-44-44-440000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ614-4-4-4444-4040-40-404000000000000004i−4i000000000000000000000000000000000
χ624-4-4-4444-4040-40-40400000000000000−4i4i000000000000000000000000000000000
χ634-4-4-4444-40-404040-4000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ644-4-4-4444-40-404040-400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ6588-8-88-8-88000000000000000000000000000000000000000000000000000000000

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