Finite Group Databasebeta

← Group #309835

Character table — Group #309835

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11111-1-11
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-111-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1111111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-111-1-1111-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-111-1-1-1-1-111-1-1111
χ17222222222-222-2-22-20000-2-222222200-2-20022-2-2000000000000-200000000000000
χ18222222222-222-2-22-20000-2-22222-2-2002200-2-2-2-2000000000000200000000000000
χ19222222222-222-2-22-20000-2-2-2-2-2-222002200-2-222000000000000-200000000000000
χ20222222222-222-2-22-20000-2-2-2-2-2-2-2-200-2-2002222000000000000200000000000000
χ2122222222-22-2-222-222222-2-2000000-2-20022000022-2-20000000000000-2000000000
χ2222222222-22-2-222-222222-2-2000000-2-200-2-20000-2-22200000000000002000000000
χ2322222222-22-2-222-22-2-2-2-2-2-20000002200220000-2-2220000000000000-2000000000
χ2422222222-22-2-222-22-2-2-2-2-2-20000002200-2-2000022-2-200000000000002000000000
χ252-22-22-22-222-2-2-2-2222i2i−2i−2i2-20000002i−2i2i−2i002i−2i000000000000000002-20000000000
χ262-22-22-22-222-2-2-2-2222i2i−2i−2i2-20000002i−2i−2i2i00−2i2i00000000000000000-220000000000
χ272-22-22-22-222-2-2-2-222−2i−2i2i2i2-2000000−2i2i2i−2i002i−2i00000000000000000-220000000000
χ282-22-22-22-222-2-2-2-222−2i−2i2i2i2-2000000−2i2i−2i2i00−2i2i000000000000000002-20000000000
χ292-22-22-22-22-2-2-2222-20000-22000000002i−2i00−2i2i00000022-2-2000002i−2i000000000000
χ302-22-22-22-22-2-2-2222-20000-22000000002i−2i00−2i2i000000-2-22200000−2i2i000000000000
χ312-22-22-22-22-2-2-2222-20000-2200000000−2i2i002i−2i00000022-2-200000−2i2i000000000000
χ322-22-22-22-22-2-2-2222-20000-2200000000−2i2i002i−2i000000-2-222000002i−2i000000000000
χ332-22-22-22-2-2222-2-2-222i2i−2i−2i-22000000−2i2i000000000000000000000000002i−2i00002-20
χ342-22-22-22-2-2222-2-2-222i2i−2i−2i-22000000−2i2i00000000000000000000000000−2i2i0000-220
χ352-22-22-22-2-2222-2-2-22−2i−2i2i2i-220000002i−2i000000000000000000000000002i−2i0000-220
χ362-22-22-22-2-2222-2-2-22−2i−2i2i2i-220000002i−2i00000000000000000000000000−2i2i00002-20
χ372-2-222-2-2202002-20-22i−2i2i−2i0022−2−20000002-2002−22i−2i00i2−i2i2−i2i2i2−i2−i2000000002−200000
χ382-2-222-2-2202002-20-22i−2i2i−2i0022−2−2000000-22002−2−2i2i00i2−i2i2−i2−i2−i2i2i200000000−2200000
χ392-2-222-2-2202002-20-22i−2i2i−2i00−2−2220000002-200−222i−2i00−i2i2−i2i2−i2−i2i2i200000000−2200000
χ402-2-222-2-2202002-20-22i−2i2i−2i00−2−222000000-2200−22−2i2i00−i2i2−i2i2i2i2−i2−i2000000002−200000
χ412-2-222-2-2202002-20-2−2i2i−2i2i0022−2−20000002-2002−2−2i2i00−i2i2−i2i2−i2−i2i2i2000000002−200000
χ422-2-222-2-2202002-20-2−2i2i−2i2i0022−2−2000000-22002−22i−2i00−i2i2−i2i2i2i2−i2−i200000000−2200000
χ432-2-222-2-2202002-20-2−2i2i−2i2i00−2−2220000002-200−22−2i2i00i2−i2i2−i2i2i2−i2−i200000000−2200000
χ442-2-222-2-2202002-20-2−2i2i−2i2i00−2−222000000-2200−222i−2i00i2−i2i2−i2−i2−i2i2i2000000002−200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-44404-400-400000004-44-4000000000000000000000000000000000000000
χ47444-4-4-4-44404-400-40000000-44-44000000000000000000000000000000000000000
χ48444-4-4-4-44-40-4400400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ49444-4-4-4-44-40-440040000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5044-4-444-4-40400-440-44-4-44000000000000000000000000000000000000000000000
χ5144-4-444-4-40400-440-4-444-4000000000000000000000000000000000000000000000
χ5244-4-444-4-40-4004-404000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5344-4-444-4-40-4004-40400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ544-444-44-4-440-4400-4000000000004-40000000000000000000000000000000000000
χ554-444-44-4-440-4400-400000000000-440000000000000000000000000000000000000
χ564-444-44-4-4-404-40040000000000000000000000000000000000000000000002i2−2i2000
χ574-444-44-4-4-404-4004000000000000000000000000000000000000000000000−2i22i2000
χ584-44-44-44-4-4-44444-4-400004-40000000000000000000000000000000000000000000
χ594-4-444-4-440-400-44040000002222−22−220000000000−2222000000000000000000000000000
χ604-4-444-4-440-400-4404000000−22−222222000000000022−22000000000000000000000000000
χ614-4-4-4-44440000000000000022−22−22220000000000000022−2200002-2-22000000000000000
χ624-4-4-4-44440000000000000022−22−222200000000000000−22220000-222-2000000000000000
χ634-4-4-4-444400000000000000−222222−220000000000000022−220000-222-2000000000000000
χ644-4-4-4-444400000000000000−222222−2200000000000000−222200002-2-22000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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