Finite Group Databasebeta

← Group #309775

Character table — Group #309775

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-11111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1
χ71111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ111111111111111111-1-1-1-1111111-1-11111-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1111-1-111-1-111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1111
χ1722222222222-2-2-2-222222-2-20000220000-2-2000022-2-2000000000-20000000000000
χ1822222222222-2-2-2-222222-2-20000-2-20000-2-20000-2-22200000000020000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-20000220000220000-2-222000000000-20000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-20000-2-2000022000022-2-200000000020000000000000
χ2122222222-2-2-22222-20000-2-2222200222200-2-2-2-2000000000000-200000000000000
χ2222222222-2-2-22222-20000-2-2222200-2-2-2-20022-2-2000000000000200000000000000
χ2322222222-2-2-22222-20000-2-2-2-2-2-20022-2-2002222000000000000-200000000000000
χ2422222222-2-2-22222-20000-2-2-2-2-2-200-2-22200-2-222000000000000200000000000000
χ252-222-22-2-22-2-222-2-222i2i−2i−2i-2200000000002i−2i00000000000000000000002i−2i00002-20
χ262-222-22-2-22-2-222-2-222i2i−2i−2i-2200000000002i−2i0000000000000000000000−2i2i0000-220
χ272-222-22-2-22-2-222-2-22−2i−2i2i2i-220000000000−2i2i00000000000000000000002i−2i0000-220
χ282-222-22-2-22-2-222-2-22−2i−2i2i2i-220000000000−2i2i0000000000000000000000−2i2i00002-20
χ292-222-22-2-22-2-2-2-22222i2i−2i−2i2-2000000002i−2i−2i2i2i−2i0000000000000000002-2000000000
χ302-222-22-2-22-2-2-2-22222i2i−2i−2i2-200000000−2i2i−2i2i−2i2i000000000000000000-22000000000
χ312-222-22-2-22-2-2-2-2222−2i−2i2i2i2-2000000002i−2i2i−2i2i−2i000000000000000000-22000000000
χ322-222-22-2-22-2-2-2-2222−2i−2i2i2i2-200000000−2i2i2i−2i−2i2i0000000000000000002-2000000000
χ332-222-22-2-2-222-2-222-20000-22000000002i−2i00−2i2i00000022-2-20000002i−2i00000000000
χ342-222-22-2-2-222-2-222-20000-22000000002i−2i00−2i2i000000-2-222000000−2i2i00000000000
χ352-222-22-2-2-222-2-222-20000-2200000000−2i2i002i−2i00000022-2-2000000−2i2i00000000000
χ362-222-22-2-2-222-2-222-20000-2200000000−2i2i002i−2i000000-2-2220000002i−2i00000000000
χ372-22-2-2-22222-20000-22i−2i2i−2i0022−2−22-2000000002−22i−2i00i2−i2i2−i2i2i2−i2−i2000000002−200000
χ382-22-2-2-22222-20000-22i−2i2i−2i0022−2−2-22000000002−2−2i2i00i2−i2i2−i2−i2−i2i2i200000000−2200000
χ392-22-2-2-22222-20000-22i−2i2i−2i00−2−2222-200000000−222i−2i00−i2i2−i2i2−i2−i2i2i200000000−2200000
χ402-22-2-2-22222-20000-22i−2i2i−2i00−2−222-2200000000−22−2i2i00−i2i2−i2i2i2i2−i2−i2000000002−200000
χ412-22-2-2-22222-20000-2−2i2i−2i2i0022−2−22-2000000002−2−2i2i00−i2i2−i2i2−i2−i2i2i2000000002−200000
χ422-22-2-2-22222-20000-2−2i2i−2i2i0022−2−2-22000000002−22i−2i00−i2i2−i2i2i2i2−i2−i200000000−2200000
χ432-22-2-2-22222-20000-2−2i2i−2i2i00−2−2222-200000000−22−2i2i00i2−i2i2−i2i2i2−i2−i200000000−2200000
χ442-22-2-2-22222-20000-2−2i2i−2i2i00−2−222-2200000000−222i−2i00i2−i2i2−i2−i2−i2i2i2000000002−200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-44-440000-44-4-44000000000000000000000000000000000000000000000
χ47444-44-4-4-44-440000-4-444-4000000000000000000000000000000000000000000000
χ48444-44-4-4-4-44-400004000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ49444-44-4-4-4-44-40000400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5044-44-4-4-440004-44-400000000000004i−4i00000000000000000000000000000000000
χ5144-44-4-4-440004-44-40000000000000−4i4i00000000000000000000000000000000000
χ5244-44-4-4-44000-44-440000000000000000000000000000000000000000000002i2−2i2000
χ5344-44-4-4-44000-44-44000000000000000000000000000000000000000000000−2i22i2000
χ5444-4-4-444-4000000000000002i2−2i22i2−2i2000000000000002i2−2i200002-22-2000000000000000
χ5544-4-4-444-4000000000000002i2−2i22i2−2i200000000000000−2i22i20000-22-22000000000000000
χ5644-4-4-444-400000000000000−2i22i2−2i22i2000000000000002i2−2i20000-22-22000000000000000
χ5744-4-4-444-400000000000000−2i22i2−2i22i200000000000000−2i22i200002-22-2000000000000000
χ584-444-44-4-4-44444-4-4-400004-40000000000000000000000000000000000000000000
χ594-44-4-4-444-4-44000040000002222−22−220000000000−2222000000000000000000000000000
χ604-44-4-4-444-4-4400004000000−22−222222000000000022−22000000000000000000000000000
χ614-4-444-44-40004-4-4400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ624-4-444-44-40004-4-440000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ634-4-444-44-4000-444-400000004i−4i−4i4i000000000000000000000000000000000000000
χ644-4-444-44-4000-444-40000000−4i4i4i−4i000000000000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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