Finite Group Databasebeta

← Group #252588

Character table — Group #252588

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-1
χ3111111111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11-1-1111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-11111-1-1-1-1
χ91111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-1-11111-1-1
χ101111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-111
χ111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-111-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-11111-1-1-1-1111111-1111-1-1-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1111111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111111111-1-1-1-1-1-1111-1-1-111-1-111
χ1722222222222222-2-222-2-222-2-20000-2-2220000-20022000000000000000000-200-200000000
χ1822222222222222-2-222-2-222-2-20000-2-2-2-20000-200-2-2000000000000000000200200000000
χ192222222222-2-2-2-2-2-222-2-2-2-2220000-2-2220000200-2-2000000000000000000200-200000000
χ202222222222-2-2-2-2-2-222-2-2-2-2220000-2-2-2-2000020022000000000000000000-200200000000
χ2122222222-2-2222222-2-222-2-2222222-2-200-2-222-2-2-200000000000000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-2-20022-2-2-22200000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-20000220000002000000000000000000002-20000002-20000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2000022000000200000000000000000000-22000000-220000
χ2522222222-2-2-2-2-2-222-2-22222-2-22222-2-200-2-2-2-222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2-20022222-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022000000-2000000000000000000002-2000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022000000-200000000000000000000-220000002-20000
χ2922-2-22-22-2002i2i−2i−2i2-2002-2002i−2i2i2i−2i−2i0000002-2000000000000022−2−2i2i2−i2−i20000000000i2−i22−2
χ3022-2-22-22-2002i2i−2i−2i2-2002-2002i−2i2i2i−2i−2i0000002-20000000000000−2−222−i2−i2i2i20000000000−i2i2−22
χ3122-2-22-22-2002i2i−2i−2i2-2002-2002i−2i−2i−2i2i2i000000-22000000000000022−2−2i2i2−i2−i20000000000−i2i2−22
χ3222-2-22-22-2002i2i−2i−2i2-2002-2002i−2i−2i−2i2i2i000000-220000000000000−2−222−i2−i2i2i20000000000i2−i22−2
χ3322-2-22-22-200−2i−2i2i2i2-2002-200−2i2i2i2i−2i−2i000000-22000000000000022−2−2−i2−i2i2i20000000000i2−i2−22
χ3422-2-22-22-200−2i−2i2i2i2-2002-200−2i2i2i2i−2i−2i000000-220000000000000−2−222i2i2−i2−i20000000000−i2i22−2
χ3522-2-22-22-200−2i−2i2i2i2-2002-200−2i2i−2i−2i2i2i0000002-2000000000000022−2−2−i2−i2i2i20000000000−i2i22−2
χ3622-2-22-22-200−2i−2i2i2i2-2002-200−2i2i−2i−2i2i2i0000002-20000000000000−2−222i2i2−i2−i20000000000i2−i2−22
χ372-22-22-2-22222-22-200-2-2002-2000000002-200000002-2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ382-22-22-2-22222-22-200-2-2002-2000000002-200000002-2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ392-22-22-2-22222-22-200-2-2002-200000000-220000000-22i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ402-22-22-2-22222-22-200-2-2002-200000000-220000000-22−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ412-22-22-2-2222-22-2200-2-200-22000000002-20000000-22i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ422-22-22-2-2222-22-2200-2-200-22000000002-20000000-22−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ432-22-22-2-2222-22-2200-2-200-2200000000-2200000002-2i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ442-22-22-2-2222-22-2200-2-200-2200000000-2200000002-2−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ452-22-2-222-22-20000222-2-2-200002i−2i2i−2i2-2002i−2i000000000002i−2i2i−2i000000000000002-2000000
χ462-22-2-222-22-20000222-2-2-200002i−2i2i−2i2-2002i−2i00000000000−2i2i−2i2i00000000000000-22000000
χ472-22-2-222-22-20000222-2-2-20000−2i2i−2i2i2-200−2i2i000000000002i−2i2i−2i00000000000000-22000000
χ482-22-2-222-22-20000222-2-2-20000−2i2i−2i2i2-200−2i2i00000000000−2i2i−2i2i000000000000002-2000000
χ492-22-2-222-2-22000022-22-2-200002i−2i2i−2i-2200−2i2i00000002i−2i2i−2i0000000000000002-2000000000
χ502-22-2-222-2-22000022-22-2-200002i−2i2i−2i-2200−2i2i0000000−2i2i−2i2i000000000000000-22000000000
χ512-22-2-222-2-22000022-22-2-20000−2i2i−2i2i-22002i−2i00000002i−2i2i−2i000000000000000-22000000000
χ522-22-2-222-2-22000022-22-2-20000−2i2i−2i2i-22002i−2i0000000−2i2i−2i2i0000000000000002-2000000000
χ534444-4-4-4-44-4000000-4400000000000000000000000000022−22−22220000000000000000000000
χ544444-4-4-4-44-4000000-44000000000000000000000000000−222222−220000000000000000000000
χ554444-4-4-4-4-440000004-40000000000000000000000022−22−222200000000000000000000000000
χ564444-4-4-4-4-440000004-400000000000000000000000−222222−2200000000000000000000000000
χ5744-4-44-44-4004i4i−4i−4i-4400-4400−4i4i00000000000000000000000000000000000000000000000
χ5844-4-44-44-400−4i−4i4i4i-4400-44004i−4i00000000000000000000000000000000000000000000000
χ594-44-44-4-44-4-44-44-4004400-440000000000000000000000000000000000000000000000000
χ604-44-44-4-44-4-4-44-440044004-40000000000000000000000000000000000000000000000000
χ614-44-4-444-44-40000-4-44-44400000000-4400000000000000000000000000000000000000000
χ624-44-4-444-4-440000-4-4-4444000000004-400000000000000000000000000000000000000000
χ634-4-4444-4-4004i−4i−4i4i000000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ644-4-4444-4-4004i−4i−4i4i00000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ654-4-4444-4-400−4i4i4i−4i000000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ664-4-4444-4-400−4i4i4i−4i00000000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ674-4-44-4-4440000004-400-4400004-4-440000000000000000000000000000000000000000000
χ684-4-44-4-4440000004-400-440000-444-40000000000000000000000000000000000000000000
χ694-4-44-4-444000000-44004-4000000000000000004-400000000000000000000000000000000
χ704-4-44-4-444000000-44004-400000000000000000-4400000000000000000000000000000000
χ7188-8-8-88-88000000000000000000000000000000000000000000000000000000000000000

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