Finite Group Databasebeta

← Group #337758

Character table — Group #337758

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-111-1-1-1111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-111
χ9111111111111111111-1-1-1-111111111-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-111-111-1-1-1-11
χ11111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-11-1
χ17222222222-22-22-22-2-2-22222000022-2-2220000000000-2-20000000000-20000000000
χ18222222222-22-22-22-2-2-222220000-2-222-2-20000000000-2-2000000000020000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000022-2-2-2-2000000000022000000000020000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000-2-222220000000000220000000000-20000000000
χ2122222222-22-22-22-22-2-20000222200000022-2-222000000-2-200000000000-20000000
χ2222222222-22-22-22-22-2-200002222000000-2-222-2-2000000-2-20000000000020000000
χ2322222222-22-22-22-22-2-20000-2-2-2-200000022-2-2-2-2000000220000000000020000000
χ2422222222-22-22-22-22-2-20000-2-2-2-2000000-2-222220000002200000000000-20000000
χ252222-2-2-2-22020-20-200022-2-222−2−22-2002-200000022−2−2002−2000022−2−20000002−2000
χ262222-2-2-2-22020-20-200022-2-222−2−2-2200-22000000−2−222002−2000022−2−2000000−22000
χ272222-2-2-2-22020-20-200022-2-2−2−2222-2002-2000000−2−22200−220000−2−222000000−22000
χ282222-2-2-2-22020-20-200022-2-2−2−222-2200-2200000022−2−200−220000−2−2220000002−2000
χ292222-2-2-2-22020-20-2000-2-22222−2−22-200-2200000022−2−2002−20000−2−222000000−22000
χ302222-2-2-2-22020-20-2000-2-22222−2−2-22002-2000000−2−222002−20000−2−2220000002−2000
χ312222-2-2-2-22020-20-2000-2-222−2−2222-200-22000000−2−22200−22000022−2−20000002−2000
χ322222-2-2-2-22020-20-2000-2-222−2−222-22002-200000022−2−200−22000022−2−2000000−22000
χ3322-2-22-22-20-20-20202002−22−22i−2i2i−2i0000002-2002i−2i00002−20022−2−2i2−i2i2−i20000i2−i200000
χ3422-2-22-22-20-20-20202002−22−22i−2i2i−2i000000-2200−2i2i00002−200−2−222i2−i2i2−i20000−i2i200000
χ3522-2-22-22-20-20-20202002−22−2−2i2i−2i2i0000002-200−2i2i00002−20022−2−2−i2i2−i2i20000−i2i200000
χ3622-2-22-22-20-20-20202002−22−2−2i2i−2i2i000000-22002i−2i00002−200−2−222−i2i2−i2i20000i2−i200000
χ3722-2-22-22-20-20-2020200−22−222i−2i2i−2i0000002-2002i−2i0000−2200−2−222−i2i2−i2i20000−i2i200000
χ3822-2-22-22-20-20-2020200−22−222i−2i2i−2i000000-2200−2i2i0000−220022−2−2−i2i2−i2i20000i2−i200000
χ3922-2-22-22-20-20-2020200−22−22−2i2i−2i2i0000002-200−2i2i0000−2200−2−222i2−i2i2−i20000i2−i200000
χ4022-2-22-22-20-20-2020200−22−22−2i2i−2i2i000000-22002i−2i0000−220022−2−2i2−i2i2−i20000−i2i200000
χ412-22-2-2-22222-2-222-2-22-2000000000000000000002-22-200002i−2i2i−2i000002i−2i00000000
χ422-22-2-2-22222-2-222-2-22-2000000000000000000002-22-20000−2i2i−2i2i00000−2i2i00000000
χ432-22-2-2-22222-2-222-2-22-200000000000000000000-22-2200002i−2i2i−2i00000−2i2i00000000
χ442-22-2-2-22222-2-222-2-22-200000000000000000000-22-220000−2i2i−2i2i000002i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ464444-4-4-4-4-40-4040400000002222−22−22000000000000000000−22220000000000000000000
χ474444-4-4-4-4-40-404040000000−22−22222200000000000000000022−220000000000000000000
χ4844-4-44-44-404040-40-40022−2222−2200000000000000000000−2222000000000000000000000
χ4944-4-44-44-404040-40-400−2222−22220000000000000000000022−22000000000000000000000
χ5044-4-4-44-44000000000022−22−22222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ5144-4-4-44-44000000000022−22−2222−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ5244-4-4-44-440000000000−222222−222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ5344-4-4-44-440000000000−222222−22−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ544-44-444-4-440-40-4040000000000000000000000022−22−222200000000000000000000000
χ554-44-444-4-440-40-40400000000000000000000000−222222−2200000000000000000000000
χ564-44-444-4-4-404040-400000000000004-400000000000000000000000000000000000
χ574-44-444-4-4-404040-40000000000000-4400000000000000000000000000000000000
χ584-44-4-4-4444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ594-44-4-4-444-444-4-444-4-4400000000000000000000000000000000000000000000000
χ604-44-4-4-444-4-444-4-4444-400000000000000000000000000000000000000000000000
χ614-4-44-444-4040-40-4040000000000000000004i−4i00000000000000000000000000000
χ624-4-44-444-4040-40-404000000000000000000−4i4i00000000000000000000000000000
χ634-4-44-444-40-404040-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ644-4-44-444-40-404040-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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