Finite Group Databasebeta

← Group #289708

Character table — Group #289708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888822224444444488888888888888888824882244
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ711111111111111111111111111-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11
χ10111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-1-111-1
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-11-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111111111-1-1-11-11
χ17222222222-2-22-222-2-2-22222-2-2-2-2000000220000-2-2000000000000000000002-2000000
χ18222222222-2-22-222-2-2-22222-2-2-2-2000000-2-200002200000000000000000000-22000000
χ19222222222-2-22-222-2-2-2-2-2-2-22222000000220000-2-200000000000000000000-22000000
χ20222222222-2-22-222-2-2-2-2-2-2-22222000000-2-2000022000000000000000000002-2000000
χ2122222222-222-22-2-22-2-20000000022222200-2-2-2-20022-2-2000000000000000000000000
χ2222222222-222-22-2-22-2-2000000002222-2-200222200-2-2-2-2000000000000000000000000
χ2322222222-222-22-2-22-2-200000000-2-2-2-2220022-2-200-2-222000000000000000000000000
χ2422222222-222-22-2-22-2-200000000-2-2-2-2-2-200-2-222002222000000000000000000000000
χ2522-22-2-22-202-20200-20022−2−222−2−22i2i−2i−2i00002-22i−2i00000022−2−2i2i2−i2−i20000i2i2−i2−i200000000
χ2622-22-2-22-202-20200-20022−2−222−2−22i2i−2i−2i0000-22−2i2i000000−2−222−i2−i2i2i20000i2i2−i2−i200000000
χ2722-22-2-22-202-20200-20022−2−222−2−2−2i−2i2i2i00002-2−2i2i00000022−2−2−i2−i2i2i20000−i2−i2i2i200000000
χ2822-22-2-22-202-20200-20022−2−222−2−2−2i−2i2i2i0000-222i−2i000000−2−222i2i2−i2−i20000−i2−i2i2i200000000
χ2922-22-2-22-202-20200-200−2−222−2−2222i2i−2i−2i00002-22i−2i000000−2−222−i2−i2i2i20000−i2−i2i2i200000000
χ3022-22-2-22-202-20200-200−2−222−2−2222i2i−2i−2i0000-22−2i2i00000022−2−2i2i2−i2−i20000−i2−i2i2i200000000
χ3122-22-2-22-202-20200-200−2−222−2−222−2i−2i2i2i00002-2−2i2i000000−2−222i2i2−i2−i20000i2i2−i2−i200000000
χ3222-22-2-22-202-20200-200−2−222−2−222−2i−2i2i2i0000-222i−2i00000022−2−2−i2−i2i2i20000i2i2−i2−i200000000
χ332-22-22-22-2222-2-22-2-2-22000000002i−2i2i−2i0000000000002i−2i2-22-22i−2i2i−2i0000000000000000
χ342-22-22-22-2222-2-22-2-2-22000000002i−2i2i−2i0000000000002i−2i-22-22−2i2i−2i2i0000000000000000
χ352-22-22-22-2222-2-22-2-2-2200000000−2i2i−2i2i000000000000−2i2i2-22-2−2i2i−2i2i0000000000000000
χ362-22-22-22-2222-2-22-2-2-2200000000−2i2i−2i2i000000000000−2i2i-22-222i−2i2i−2i0000000000000000
χ372-22-22-22-2-2222-2-22-22-22-22-22-22-22i−2i2i−2i000000000000−2i2i0000000000002i−2i2i−2i00000000
χ382-22-22-22-2-2222-2-22-22-22-22-22-22-2−2i2i−2i2i0000000000002i−2i000000000000−2i2i−2i2i00000000
χ392-22-22-22-2-2222-2-22-22-2-22-22-22-222i−2i2i−2i000000000000−2i2i000000000000−2i2i−2i2i00000000
χ402-22-22-22-2-2222-2-22-22-2-22-22-22-22−2i2i−2i2i0000000000002i−2i0000000000002i−2i2i−2i00000000
χ412-22-22-22-2-2-2-222-222-222-22-2-22-220000000000000000000000000022-2-20000002-20000
χ422-22-22-22-2-2-2-222-222-222-22-2-22-2200000000000000000000000000-2-222000000-220000
χ432-22-22-22-2-2-2-222-222-22-22-222-22-20000000000000000000000000022-2-2000000-220000
χ442-22-22-22-2-2-2-222-222-22-22-222-22-200000000000000000000000000-2-2220000002-20000
χ452-2-2-2-222202-20-2002002−2−222−2−222-2-222-2000000002-2002−2−222−2−2200002−2−2200000000
χ462-2-2-2-222202-20-2002002−2−222−2−222-2-22-2200000000-2200−222−2−222−200002−2−2200000000
χ472-2-2-2-222202-20-2002002−2−222−2−22-222-22-200000000-2200−222−22−2−220000−222−200000000
χ482-2-2-2-222202-20-2002002−2−222−2−22-222-2-22000000002-2002−2−22−222−20000−222−200000000
χ492-2-2-2-222202-20-200200−222−2−222−22-2-222-2000000002-200−222−2−222−20000−222−200000000
χ502-2-2-2-222202-20-200200−222−2−222−22-2-22-2200000000-22002−2−222−2−220000−222−200000000
χ512-2-2-2-222202-20-200200−222−2−222−2-222-22-200000000-22002−2−22−222−200002−2−2200000000
χ522-2-2-2-222202-20-200200−222−2−222−2-222-2-22000000002-200−222−22−2−2200002−2−2200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5444-44-4-44-40-440-4004002222−22−22−22−222222000000000000000000000000000000000000000000
χ5544-44-4-44-40-440-400400−22−2222222222−22−22000000000000000000000000000000000000000000
χ5644-4-444-4-440040-4-4000000000000000000000004i−4i0000000000000000000000000000
χ5744-4-444-4-440040-4-400000000000000000000000−4i4i0000000000000000000000000000
χ5844-4-444-4-4-400-4044000000000000000000000000000000000000022−2222−22000000000000
χ5944-4-444-4-4-400-40440000000000000000000000000000000000000−2222−2222000000000000
χ604-44-44-44-44-4-4-444-444-400000000000000000000000000000000000000000000000000
χ614-4-444-4-44400-40-44000000000000000000000000000000000000022−22−2222000000000000
χ624-4-444-4-44400-40-440000000000000000000000000000000000000−222222−22000000000000
χ634-4-444-4-44-400404-4000000000000000004-40000000000000000000000000000000000
χ644-4-444-4-44-400404-400000000000000000-440000000000000000000000000000000000
χ654-4-4-4-44440-440400-40022−22−2222−222222−22000000000000000000000000000000000000000000
χ664-4-4-4-44440-440400-400−222222−2222−22−2222000000000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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