Finite Group Databasebeta

← Group #285821

Character table — Group #285821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444488888888888888882244444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1111111-1-1-1-1-1-111111-1
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-1111111-1-1-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-111-1-111-1-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-111-1-111-1-1111-1
χ172222222222-2-22-2-2222-2-2-2-222000000000000000022-2-2-2-2-2220000000000000000000000
χ182222222222-2-22-2-2222-2-2-2-2220000000000000000-2-222-222-2-20000000000000000000000
χ192222222222-2-22-2-22-2-2-2-222-2-2000000000000000022222-2-2-2-20000000000000000000000
χ202222222222-2-22-2-22-2-2-2-222-2-20000000000000000-2-2-2-2222220000000000000000000000
χ2122222222-2-222-222-222-2-2-2-2-2-22222-2-2-2-200000000000020000-2-222000000000000000000
χ2222222222-2-222-222-222-2-2-2-2-2-2-2-2-2-222220000000000002000022-2-2000000000000000000
χ2322222222-2-222-222-2-2-2-2-2222222222222000000000000-20000-2-2-2-2000000000000000000
χ2422222222-2-222-222-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000-200002222000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2000000002i2i2i2i−2i−2i−2i−2i0000-2000000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-200000000−2i−2i−2i−2i2i2i2i2i0000-200000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i0000200000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i00002000000002i2i−2i−2i00000000000000
χ292-22-222-2-22-222-2-2-22002-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000000002i−2i00002-20000
χ302-22-222-2-22-222-2-2-22002-20000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000−2i2i0000-220000
χ312-22-222-2-22-222-2-2-22002-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000002i−2i0000-220000
χ322-22-222-2-22-222-2-2-22002-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000−2i2i00002-20000
χ332-22-222-2-2-22-2-2222-2002-200000000000022-2-2-2-222000000000000000002i−2i00002i−2i000000
χ342-22-222-2-2-22-2-2222-2002-200000000000022-2-2-2-22200000000000000000−2i2i0000−2i2i000000
χ352-22-222-2-2-22-2-2222-2002-2000000000000-2-22222-2-2000000000000000002i−2i0000−2i2i000000
χ362-22-222-2-2-22-2-2222-2002-2000000000000-2-22222-2-200000000000000000−2i2i00002i−2i000000
χ372-2-2-2-22222200-200-22-200002-222−2−222−2−2i2−i2i2−i2i2−i2i2−i2002i−2i02i−2i002−22−2i2−i2i2−i200000000000000
χ382-2-2-2-22222200-200-22-200002-222−2−222−2−2−i2i2−i2i2−i2i2−i2i200−2i2i0−2i2i002−22−2−i2i2−i2i200000000000000
χ392-2-2-2-22222200-200-22-200002-2−2−222−2−222i2−i2i2−i2i2−i2i2−i200−2i2i0−2i2i00−22−22i2−i2i2−i200000000000000
χ402-2-2-2-22222200-200-22-200002-2−2−222−2−222−i2i2−i2i2−i2i2−i2i2002i−2i02i−2i00−22−22−i2i2−i2i200000000000000
χ412-2-2-2-22222200-200-2-220000-2222−2−2−2−222i2−i2i2−i2i2−i2i2−i2002i−2i0−2i2i002−2−22−i2i2−i2i200000000000000
χ422-2-2-2-22222200-200-2-220000-2222−2−2−2−222−i2i2−i2i2−i2i2−i2i200−2i2i02i−2i002−2−22i2−i2i2−i200000000000000
χ432-2-2-2-22222200-200-2-220000-22−2−22222−2−2i2−i2i2−i2i2−i2i2−i200−2i2i02i−2i00−222−2−i2i2−i2i200000000000000
χ442-2-2-2-22222200-200-2-220000-22−2−22222−2−2−i2i2−i2i2−i2i2−i2i2002i−2i0−2i2i00−222−2i2−i2i2−i200000000000000
χ452-2-2-2-2222-2-20020022-20000-2222−2−2−2−2222−22−2−22−222-2000002-2−222−22−2−2200000000000000
χ462-2-2-2-2222-2-20020022-20000-2222−2−2−2−222−22−222−22−2-2200000-22−222−2−222−200000000000000
χ472-2-2-2-2222-2-20020022-20000-22−2−22222−2−22−22−2−22−22-2200000-222−2−222−2−2200000000000000
χ482-2-2-2-2222-2-20020022-20000-22−2−22222−2−2−22−222−22−22-2000002-22−2−22−222−200000000000000
χ492-2-2-2-2222-2-2002002-2200002-222−2−222−2−22−22−2−22−22-22000002-2−22−22−222−200000000000000
χ502-2-2-2-2222-2-2002002-2200002-222−2−222−2−2−22−222−22−22-200000-22−22−222−2−2200000000000000
χ512-2-2-2-2222-2-2002002-2200002-2−2−222−2−2222−22−2−22−222-200000-222−22−2−222−200000000000000
χ522-2-2-2-2222-2-2002002-2200002-2−2−222−2−222−22−222−22−2-22000002-22−22−22−2−2200000000000000
χ5344-44-44-4-44-400400-4000000000000000022−22−222222−22−22220000000000000000000000000000000
χ5444-44-44-4-44-400400-40000000000000000−222222−22−222222−220000000000000000000000000000000
χ5544-44-44-4-4-4400-400400000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ5644-44-44-4-4-4400-40040000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ5744-4-44-4-44004-404-400000000000004i−4i4i−4i000000000000000000000000000000000000000
χ5844-4-44-4-44004-404-40000000000000−4i4i−4i4i000000000000000000000000000000000000000
χ5944-4-44-4-4400-440-440000000004i−4i4i−4i0000000000000000000000000000000000000000000
χ6044-4-44-4-4400-440-44000000000−4i4i−4i4i0000000000000000000000000000000000000000000
χ614-444-4-4-440000000000004-4002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ624-444-4-4-440000000000004-400−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ634-444-4-4-44000000000000-44002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ644-444-4-4-44000000000000-4400−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ654-44-444-4-44-4-4-4-444400-44000000000000000000000000000000000000000000000000000
χ664-44-444-4-4-44444-4-4-400-44000000000000000000000000000000000000000000000000000
χ674-4-444-44-4004-40-4400000000000000000000000000000000000000000000002i2−2i200000000
χ684-4-444-44-4004-40-440000000000000000000000000000000000000000000000−2i22i200000000
χ694-4-444-44-400-4404-400000000000000000000000000000000000000000000000000002i2−2i200
χ704-4-444-44-400-4404-40000000000000000000000000000000000000000000000000000−2i22i200
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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