Finite Group Databasebeta

← Group #271021

Character table — Group #271021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444422224444448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ91111111111111111-1-11-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11111-1-11-1
χ101111111111111111-1-11-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1-111-11
χ111111111111111111-1-11-1-1-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-1-1-111-11
χ121111111111111111-1-11-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-111-1-11-1
χ131111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1111-1
χ141111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-11
χ151111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-111111-1-1-11
χ161111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1111-1-1111-1
χ172222222222-2-2-222-222-2-2-222-2-22222-2-2-2000022-2-20000000000000000000000000000
χ182222222222-2-2-222-222-2-2-222-2-2-2-2-2-2-2220000-2-2220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-222-2-2222222-2-2-20000-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-222-2-222-2-2-2-2-222000022-2-20000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-2-2220000-20022-2-20000000000000000000000-2200000000
χ2222222222-2-2222-2-2222-2-2-2-2-2220000-200-2-22200000000000000000000002-200000000
χ2322222222-2-2222-2-22-2-2-22222-2-20000-20022220000000000000000000000-2-200000000
χ2422222222-2-2222-2-22-2-2-22222-2-20000-200-2-2-2-200000000000000000000002200000000
χ2522222222-2-2-2-2-2-2-2-222222-2-2-2-200002000000000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-222222-2-2-2-20000200000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22-2-2222200002000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22-2-222220000200000000000000000000000000-22002-2000000
χ2922-22-22-2-22-20002-200002i−2i002i−2i2i2i−2i−2i0000000002-222−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000
χ3022-22-22-2-22-20002-200002i−2i002i−2i2i2i−2i−2i0000000002-2−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000
χ3122-22-22-2-22-20002-200002i−2i002i−2i−2i−2i2i2i000000000-2222−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000
χ3222-22-22-2-22-20002-200002i−2i002i−2i−2i−2i2i2i000000000-22−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000
χ3322-22-22-2-22-20002-20000−2i2i00−2i2i2i2i−2i−2i000000000-2222−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000
χ3422-22-22-2-22-20002-20000−2i2i00−2i2i2i2i−2i−2i000000000-22−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000
χ3522-22-22-2-22-20002-20000−2i2i00−2i2i−2i−2i2i2i0000000002-222−2−2−i2−i2i2i2−i2−i2i2i222−2−2000000000000
χ3622-22-22-2-22-20002-20000−2i2i00−2i2i−2i−2i2i2i0000000002-2−2−222i2i2−i2−i2i2i2−i2−i2−2−222000000000000
χ372-22-2-222-222000-2-202-20002-2002i−2i2i−2i00000002i−2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-22-2-222-222000-2-202-20002-2002i−2i2i−2i00000002i−2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ392-22-2-222-222000-2-202-20002-200−2i2i−2i2i0000000−2i2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-22-2-222-222000-2-202-20002-200−2i2i−2i2i0000000−2i2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ412-22-2-222-222000-2-20-22000-22002i−2i2i−2i0000000−2i2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ422-22-2-222-222000-2-20-22000-22002i−2i2i−2i0000000−2i2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ432-22-2-222-222000-2-20-22000-2200−2i2i−2i2i00000002i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ442-22-2-222-222000-2-20-22000-2200−2i2i−2i2i00000002i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-2-222-222-222-2-22-20020000002-2-22-22-20000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ462-2-2-222-222-222-2-22-20020000002-2-22-22-2000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ472-2-2-222-222-222-2-22-2002000000-222-2-2-220000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ482-2-2-222-222-222-2-22-2002000000-222-2-2-22000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ492-2-2-222-222-2-2-22-22200-20000002-2-222-22000000002-2-2200002-2-220000000000000000
χ502-2-2-222-222-2-2-22-22200-20000002-2-222-2200000000-222-20000-222-20000000000000000
χ512-2-2-222-222-2-2-22-22200-2000000-222-222-2000000002-2-220000-222-20000000000000000
χ522-2-2-222-222-2-2-22-22200-2000000-222-222-200000000-222-200002-2-220000000000000000
χ5344-44-44-4-4-44000-4400004i−4i00−4i4i0000000000000000000000000000000000000000000
χ5444-44-44-4-4-44000-440000−4i4i004i−4i0000000000000000000000000000000000000000000
χ5544-4-4-4-444004-4400-40000000000000000004i−4i00000000000000000000000000000000
χ5644-4-4-4-444004-4400-4000000000000000000−4i4i00000000000000000000000000000000
χ5744-4-4-4-44400-44-400400000000000000004-40000000000000000000000000000000000
χ5844-4-4-4-44400-44-40040000000000000000-440000000000000000000000000000000000
χ594-444-4-4-44004-4-4004000000000000000000000000000000000000000000000022−220000
χ604-444-4-4-44004-4-40040000000000000000000000000000000000000000000000−22220000
χ614-444-4-4-4400-44400-40000000000000000000000000000000000000000000000002i2−2i200
χ624-444-4-4-4400-44400-4000000000000000000000000000000000000000000000000−2i22i200
χ634-44-4-444-4-4-40004404-4000-44000000000000000000000000000000000000000000000
χ644-44-4-444-4-4-4000440-440004-4000000000000000000000000000000000000000000000
χ654-4-4-444-44-4444-44-4-400-40000000000400000000000000000000000000000000000000
χ664-4-4-444-44-44-4-444-440040000000000-400000000000000000000000000000000000000
χ67888-88-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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