Finite Group Databasebeta

← Group #271016

Character table — Group #271016

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444422444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-11
χ111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-111-1-111-11
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1111-1
χ172222222222-2-2-222-222222222-2-2-2-2-2-22200-2-2-2-2000000000000000000000000000000
χ182222222222-2-2-222-22222-2-2-2-2-2-2-2-2-2-2-2-2002222000000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-22222-22222-2-2-200-2-222000000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-2-22222-2220022-2-2000000000000000000000000000000
χ2122222222-2-2222-2-2222-2-20000-222-2-2-200220000-2-20000000000000000-220000000000
χ2222222222-2-2222-2-2222-2-20000-222-2-2-200-2-200002200000000000000002-20000000000
χ2322222222-2-2222-2-22-2-2220000-2-2-222-200220000220000000000000000-2-20000000000
χ2422222222-2-2222-2-22-2-2220000-2-2-222-200-2-20000-2-20000000000000000220000000000
χ2522222222-2-2-2-2-2-2-2-222-2-200002-2-222200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-200002-2-22220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2220000222-2-2200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2220000222-2-220000000000000000000000000000-222-2000000
χ29222-22-2-2-222000-2-202-22-222-2-20000002-20000000022−2−222−2−222−2−222−2−2000000000000
χ30222-22-2-2-222000-2-202-22-222-2-20000002-200000000−2−222−2−222−2−222−2−222000000000000
χ31222-22-2-2-222000-2-202-22-2-2-222000000-220000000022−2−222−2−2−2−222−2−222000000000000
χ32222-22-2-2-222000-2-202-22-2-2-222000000-2200000000−2−222−2−22222−2−222−2−2000000000000
χ33222-22-2-2-222000-2-20-22-2222-2-2000000-220000000022−2−2−2−22222−2−2−2−222000000000000
χ34222-22-2-2-222000-2-20-22-2222-2-2000000-2200000000−2−22222−2−2−2−22222−2−2000000000000
χ35222-22-2-2-222000-2-20-22-22-2-2220000002-20000000022−2−2−2−222−2−22222−2−2000000000000
χ36222-22-2-2-222000-2-20-22-22-2-2220000002-200000000−2−22222−2−222−2−2−2−222000000000000
χ372-2-2222-2-22-20002-2000002-22-202i−2i2i−2i00000002i−2i00i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-2-2222-2-22-20002-2000002-22-202i−2i2i−2i00000002i−2i00−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-2-2222-2-22-20002-2000002-22-20−2i2i−2i2i0000000−2i2i00i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ402-2-2222-2-22-20002-2000002-22-20−2i2i−2i2i0000000−2i2i00−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ412-2-2222-2-22-20002-200000-22-2202i−2i2i−2i0000000−2i2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ422-2-2222-2-22-20002-200000-22-2202i−2i2i−2i0000000−2i2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ432-2-2222-2-22-20002-200000-22-220−2i2i−2i2i00000002i−2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-2-2222-2-22-20002-200000-22-220−2i2i−2i2i00000002i−2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-2-2-22-2222-222-2-22-200002-2-2220000-200002-200002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ462-2-2-22-2222-222-2-22-200002-2-2220000-200002-20000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ472-2-2-22-2222-222-2-22-20000-222-220000-20000-2200002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ482-2-2-22-2222-222-2-22-20000-222-220000-20000-220000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ492-2-2-22-2222-2-2-22-22200002-2-22-2000020000-22000000002-2-2200002-2-22000000000000
χ502-2-2-22-2222-2-2-22-22200002-2-22-2000020000-2200000000-222-20000-222-2000000000000
χ512-2-2-22-2222-2-2-22-2220000-222-2-20000200002-2000000002-2-220000-222-2000000000000
χ522-2-2-22-2222-2-2-22-2220000-222-2-20000200002-200000000-222-200002-2-22000000000000
χ53444-44-4-4-4-4-40004404-4-44000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-4000440-444-4000000000000000000000000000000000000000000000000
χ5544-44-4-44-4004-4400-400000000000000004-40000000000000000000000000000000000
χ5644-44-4-44-4004-4400-40000000000000000-440000000000000000000000000000000000
χ5744-44-4-44-400-44-400400000000000000000000004i−4i0000000000000000000000000000
χ5844-44-4-44-400-44-40040000000000000000000000−4i4i0000000000000000000000000000
χ594-44-4-444-4004-4-4004000000000000000000000000000000000000000000000022−220000
χ604-44-4-444-4004-4-40040000000000000000000000000000000000000000000000−22220000
χ614-44-4-444-400-44400-40000000000000000000000000000000000000000000000002i2−2i200
χ624-44-4-444-400-44400-4000000000000000000000000000000000000000000000000−2i22i200
χ634-4-4444-4-4-44000-4400000000004i−4i−4i4i000000000000000000000000000000000000000
χ644-4-4444-4-4-44000-440000000000−4i4i4i−4i000000000000000000000000000000000000000
χ654-4-4-44-444-4444-44-4-400000000-40000400000000000000000000000000000000000000
χ664-4-4-44-444-44-4-444-440000000040000-400000000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-888-8-8-88000000000000000000000000000000000000000000000000000000000000

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