Finite Group Databasebeta

← Group #305754

Character table — Group #305754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-11-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1111111-1111-1-1-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1111-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-11111-1-111-1
χ172222222222-2-222-2-20000-2-2222222220000-2-2-2-200000000000000-2000000000000
χ182222222222-2-222-2-20000-2-22222-2-2-2-2000022-2-2000000000000002000000000000
χ192222222222-2-222-2-20000-2-2-2-2-2-222-2-20000-2-222000000000000002000000000000
χ202222222222-2-222-2-20000-2-2-2-2-2-2-2-2220000222200000000000000-2000000000000
χ2122222222-2-222-2-2222222-2-20000000022-2-20000000022-2-2000000000-2000000000
χ2222222222-2-222-2-2222222-2-200000000-2-2-2-200000000-2-2220000000002000000000
χ2322222222-2-222-2-222-2-2-2-2-2-200000000222200000000-2-222000000000-2000000000
χ2422222222-2-222-2-222-2-2-2-2-2-200000000-2-2220000000022-2-20000000002000000000
χ252-222-2-2-222222-2-2-2-222-2-22-200002-200002-22-2000000000000000000002-20000000
χ262-222-2-2-222222-2-2-2-222-2-22-20000-2200002-2-2200000000000000000000-220000000
χ272-222-2-2-222222-2-2-2-2-2-2222-200002-20000-222-200000000000000000000-220000000
χ282-222-2-2-222222-2-2-2-2-2-2222-20000-220000-22-22000000000000000000002-20000000
χ292-222-2-2-2222-2-2-2-2220000-2200002-2000000-22002i2i−2i−2i000000000002i−2i0000000000
χ302-222-2-2-2222-2-2-2-2220000-2200002-2000000-2200−2i−2i2i2i00000000000−2i2i0000000000
χ312-222-2-2-2222-2-2-2-2220000-220000-220000002-2002i2i−2i−2i00000000000−2i2i0000000000
χ322-222-2-2-2222-2-2-2-2220000-220000-220000002-200−2i−2i2i2i000000000002i−2i0000000000
χ332-222-2-2-22-2-22222-2-222-2-2-220000000000-2200000000000000002i−2i000000002i−2i000
χ342-222-2-2-22-2-22222-2-222-2-2-220000000000-220000000000000000−2i2i00000000−2i2i000
χ352-222-2-2-22-2-22222-2-2-2-222-2200000000002-200000000000000002i−2i00000000−2i2i000
χ362-222-2-2-22-2-22222-2-2-2-222-2200000000002-20000000000000000−2i2i000000002i−2i000
χ372-22-22-22-2002-2002-22-22-200i2i2−i2−i200002i−2i0000i2−i2i2−i2i2−i22i−2i0022−2−2000000002−200000
χ382-22-22-22-2002-2002-22-22-200i2i2−i2−i20000−2i2i0000i2−i2i2−i2i2−i2−2i2i00−2−22200000000−2200000
χ392-22-22-22-2002-2002-22-22-200−i2−i2i2i200002i−2i0000−i2i2−i2i2−i2i22i−2i00−2−22200000000−2200000
χ402-22-22-22-2002-2002-22-22-200−i2−i2i2i20000−2i2i0000−i2i2−i2i2−i2i2−2i2i0022−2−2000000002−200000
χ412-22-22-22-2002-2002-2-22-2200i2i2−i2−i200002i−2i0000i2−i2−i2i2−i2i2−2i2i00−2−222000000002−200000
χ422-22-22-22-2002-2002-2-22-2200i2i2−i2−i20000−2i2i0000i2−i2−i2i2−i2i22i−2i0022−2−200000000−2200000
χ432-22-22-22-2002-2002-2-22-2200−i2−i2i2i200002i−2i0000−i2i2i2−i2i2−i2−2i2i0022−2−200000000−2200000
χ442-22-22-22-2002-2002-2-22-2200−i2−i2i2i20000−2i2i0000−i2i2i2−i2i2−i22i−2i00−2−222000000002−200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-4004-400-444-4-44000000000000000000000000000000000000000000000
χ47444-4-44-4-4004-400-44-444-4000000000000000000000000000000000000000000000
χ48444-4-44-4-400-44004-4000000000000000000000022−22−222200000000000000000000000
χ49444-4-44-4-400-44004-40000000000000000000000−222222−2200000000000000000000000
χ5044-444-4-4-44-4004-4000000000000004-400000000000000000000000000000000000
χ5144-444-4-4-44-4004-400000000000000-4400000000000000000000000000000000000
χ5244-444-4-4-4-4400-4400000000000000000000000000000000000000000000000022−220
χ5344-444-4-4-4-4400-44000000000000000000000000000000000000000000000000−22220
χ5444-4-4-4-4440000000000000022−2222−220000000000000000002i2−2i22i−2i2i−2i000000000000000
χ5544-4-4-4-4440000000000000022−2222−22000000000000000000−2i22i2−2i2i−2i2i000000000000000
χ5644-4-4-4-44400000000000000−2222−22220000000000000000002i2−2i2−2i2i−2i2i000000000000000
χ5744-4-4-4-44400000000000000−2222−2222000000000000000000−2i22i22i−2i2i−2i000000000000000
χ584-444-4-4-44-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ594-44-44-44-400-4400-440000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ604-44-44-44-400-4400-44000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ614-4-44-444-44-400-44000000004i−4i−4i4i000000000000000000000000000000000000000
χ624-4-44-444-44-400-4400000000−4i4i4i−4i000000000000000000000000000000000000000
χ634-4-44-444-4-44004-4000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ644-4-44-444-4-44004-400000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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