Finite Group Databasebeta

← Group #305705

Character table — Group #305705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-111-1111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111111111-1-1-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-1111111-1-11-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-11111-1-1-111111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-111-1-111-1-111-1
χ172222222222-2-22-22-20000-2-222222200-2-22200-2-200000000000000-2000000000000
χ182222222222-2-22-22-20000-2-22222-2-20022-2-200-2-2000000000000002000000000000
χ192222222222-2-22-22-20000-2-2-2-2-2-22200-2-2-2-20022000000000000002000000000000
χ202222222222-2-22-22-20000-2-2-2-2-2-2-2-2002222002200000000000000-2000000000000
χ2122222222-2-222-22-222222-2-2000000-2-200002200-2-20000220000000-200000000000
χ2222222222-2-222-22-222222-2-2000000-2-20000-2-200220000-2-20000000200000000000
χ2322222222-2-222-22-22-2-2-2-2-2-20000002200002200220000-2-20000000-200000000000
χ2422222222-2-222-22-22-2-2-2-2-2-2000000220000-2-200-2-20000220000000200000000000
χ252222-2-2-2-22222-2-2-2-222-2-22-200002-22-22-20000000000000000002-20000000000000
χ262222-2-2-2-22222-2-2-2-222-2-22-20000-222-2-22000000000000000000-220000000000000
χ272222-2-2-2-22222-2-2-2-2-2-2222-200002-2-222-2000000000000000000-220000000000000
χ282222-2-2-2-22222-2-2-2-2-2-2222-20000-22-22-220000000000000000002-20000000000000
χ292222-2-2-2-222-2-2-22-220000-2200002-200-22000000002i2i−2i−2i0000000000002i−2i0000000
χ302222-2-2-2-222-2-2-22-220000-2200002-200-2200000000−2i−2i2i2i000000000000−2i2i0000000
χ312222-2-2-2-222-2-2-22-220000-220000-22002-2000000002i2i−2i−2i000000000000−2i2i0000000
χ322222-2-2-2-222-2-2-22-220000-220000-22002-200000000−2i−2i2i2i0000000000002i−2i0000000
χ332222-2-2-2-2-2-2222-22-222-2-2-22000000-220000000000000000000000002i−2i00002i−2i000
χ342222-2-2-2-2-2-2222-22-222-2-2-22000000-22000000000000000000000000−2i2i0000−2i2i000
χ352222-2-2-2-2-2-2222-22-2-2-222-220000002-20000000000000000000000002i−2i0000−2i2i000
χ362222-2-2-2-2-2-2222-22-2-2-222-220000002-2000000000000000000000000−2i2i00002i−2i000
χ372-22-22-22-2002-2020-22-22-20022−2−2000000002i−2i2−2002−22−22i−2ii2i2−i2−i200000000i2−i200000
χ382-22-22-22-2002-2020-22-22-20022−2−200000000−2i2i2−2002−22−2−2i2i−i2−i2i2i200000000−i2i200000
χ392-22-22-22-2002-2020-22-22-200−2−222000000002i−2i−2200−22−222i−2i−i2−i2i2i200000000−i2i200000
χ402-22-22-22-2002-2020-22-22-200−2−22200000000−2i2i−2200−22−22−2i2ii2i2−i2−i200000000i2−i200000
χ412-22-22-22-2002-2020-2-22-220022−2−2000000002i−2i2−200−22−22−2i2i−i2−i2i2i200000000i2−i200000
χ422-22-22-22-2002-2020-2-22-220022−2−200000000−2i2i2−200−22−222i−2ii2i2−i2−i200000000−i2i200000
χ432-22-22-22-2002-2020-2-22-2200−2−222000000002i−2i−22002−22−2−2i2ii2i2−i2−i200000000−i2i200000
χ442-22-22-22-2002-2020-2-22-2200−2−22200000000−2i2i−22002−22−22i−2i−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ4744-4-444-4-4000000000000002i2−2i22i2−2i200000000000022−220000002i−2i2i−2i000000000000000
χ4844-4-444-4-4000000000000002i2−2i22i2−2i2000000000000−2222000000−2i2i−2i2i000000000000000
χ4944-4-444-4-400000000000000−2i22i2−2i22i200000000000022−22000000−2i2i−2i2i000000000000000
χ5044-4-444-4-400000000000000−2i22i2−2i22i2000000000000−22220000002i−2i2i−2i000000000000000
χ514-44-44-44-400-440-4040000002222−22−220000000000−2222000000000000000000000000000
χ524-44-44-44-400-440-404000000−22−222222000000000022−22000000000000000000000000000
χ534-44-4-44-44004-40-4044-4-44000000000000000000000000000000000000000000000
χ544-44-4-44-44004-40-404-444-4000000000000000000000000000000000000000000000
χ554-44-4-44-4400-44040-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ564-44-4-44-4400-44040-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ574-4-444-4-444-40040-400000004i−4i−4i4i000000000000000000000000000000000000000
χ584-4-444-4-444-40040-40000000−4i4i4i−4i000000000000000000000000000000000000000
χ594-4-444-4-44-4400-404000000000000000000000000000000022−22−2222000000000000000
χ604-4-444-4-44-4400-4040000000000000000000000000000000−222222−22000000000000000
χ614-4-44-444-44-400-404000000000000000004-40000000000000000000000000000000
χ624-4-44-444-44-400-40400000000000000000-440000000000000000000000000000000
χ634-4-44-444-4-440040-4000000000000000000000000000000000000000000000002i2−2i20
χ644-4-44-444-4-440040-400000000000000000000000000000000000000000000000−2i22i20
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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