Finite Group Databasebeta

← Group #72266237

Character table — Group #72266237

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244448888888888888888888816161616161616161616161616161616161616163232323232323232323232323232323264646464646464646464646464646464
order12222222222222222222222222444444442222222222444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111-1-1-1-11111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-11-111-1-111-1-1iiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-11-111-1-111-1-1−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii−i−iii
χ111111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-1111-1-1-1-111-11-111-1-1-1-111iiii−i−i−i−i11-1-1-1-111-1-111ii−i−i−i−iii−i−iii
χ121111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-1111-1-1-1-111-11-111-1-1-1-111−i−i−i−iiiii11-1-1-1-111-1-111−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-11-1-11111-1-1-11-1-1-11111-1-1iiii−i−i−i−i-1-11111-1-1-1-111−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-11-1-11111-1-1-11-1-1-11111-1-1−i−i−i−iiiii-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i
χ151111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-11-1-111-1-111-11-1-1-111-1-111iiii−i−i−i−i-1-111-1-11111-1-1−i−iii−i−iiiii−i−i
χ161111-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-11-1-111-1-111-11-1-1-111-1-111−i−i−i−iiiii-1-111-1-11111-1-1ii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-200000000-2220000000022-2-222-2-2000000000000000000000000
χ18222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-200000000-22200000000-2-222-2-222000000000000000000000000
χ192222222222222222-2-2222222-2-222-2-222-2-2-200002222-2-2-200002222000000000000-2-2-2-20000000000000000
χ202222222222222222-2-2222222-2-222-2-222-2-2-20000-2-2-2-2-2-2-20000-2-2-2-200000000000022220000000000000000
χ212222222222222222-2-2-2-2-2-222-2-2-2-222-2-2222000000002-2-2000000000000000000000000000000002-22-20000
χ222222222222222222-2-2-2-2-2-222-2-2-2-222-2-2222000000002-2-200000000000000000000000000000000-22-220000
χ2322222222222222-2-2222222-2-222-2-222-2-222-222220000-2-2-22222000000000000-2-2-2-200000000000000000000
χ2422222222222222-2-2222222-2-222-2-222-2-222-2-2-2-2-20000-2-2-2-2-2-2-2000000000000222200000000000000000000
χ2522222222222222-2-222-2-2-2-2-2-22222-2-222-2-22000000002-2-200000000000000000000000000002-22-200000000
χ2622222222222222-2-222-2-2-2-2-2-22222-2-222-2-22000000002-2-20000000000000000000000000000-22-2200000000
χ2722222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22000000002220000000000000000000000002-22-2000000000000
χ2822222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2200000000222000000000000000000000000-22-22000000000000
χ2922222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-200000000-2220000000000000000000000000000000000002i−2i2i−2i
χ3022222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-200000000-222000000000000000000000000000000000000−2i2i−2i2i
χ312222-2-2-2-2-2-22-222222222-2-2-2-2-2-2-2-2-2-22222-20000000022-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322222-2-2-2-2-2-22-222222222-2-2-2-2-2-2-2-2-2-22222-20000000022-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332222-2-2-2-2-2-22-22222-2-222-2-2-2-222-2-22222-2-2200000000-2-22000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-2-2-22-22222-2-222-2-2-2-222-2-22222-2-2200000000-2-2200000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-2-2-22-22222-2-2-2-222-2-22222-2-2-2-222-2000022-2-22-22000022-2-2000000000000-2-2220000000000000000
χ362222-2-2-2-2-2-22-22222-2-2-2-222-2-22222-2-2-2-222-20000-2-2222-220000-2-22200000000000022-2-20000000000000000
χ372222-2-2-2-2-2-22-222-2-22222-2-222-2-222-2-2-2-222200000000-2-2200000000000000000000000000002i−2i−2i2i00000000
χ382222-2-2-2-2-2-22-222-2-22222-2-222-2-222-2-2-2-222200000000-2-220000000000000000000000000000−2i2i2i−2i00000000
χ392222-2-2-2-2-2-22-222-2-222-2-22222-2-2-2-22222-2-2-222-2-200002-2222-2-2000000000000-2-22200000000000000000000
χ402222-2-2-2-2-2-22-222-2-222-2-22222-2-2-2-22222-2-2-2-2-22200002-22-2-22200000000000022-2-200000000000000000000
χ412222-2-2-2-2-2-22-222-2-2-2-222-2-222222222-2-2-2-2-20000000022-20000000000000000000000000000000000002-2-22
χ422222-2-2-2-2-2-22-222-2-2-2-222-2-222222222-2-2-2-2-20000000022-2000000000000000000000000000000000000-222-2
χ432222-2-2-2-2-2-22-222-2-2-2-2-2-2222222-2-2-2-22222200000000-22-20000000000000000000000002-2-22000000000000
χ442222-2-2-2-2-2-22-222-2-2-2-2-2-2222222-2-2-2-22222200000000-22-2000000000000000000000000-222-2000000000000
χ4544444444-4-4-4-44-4004-40000004-4000000000000022220000000-2-2-2-20000000000002-22-20000000000000000
χ4644444444-4-4-4-44-4004-40000004-40000000000000-2-2-2-200000002222000000000000-22-220000000000000000
χ4744444444-4-4-4-44-400-44000000-44000000000000022220000000-2-2-2-2000000000000-22-220000000000000000
χ4844444444-4-4-4-44-400-44000000-440000000000000-2-2-2-2000000022220000000000002-22-20000000000000000
χ49444444-4-444-4-4-444-40000004-40000000000022220000000-2-2-2-20000000000002-22-200000000000000000000
χ50444444-4-444-4-4-444-40000004-400000000000-2-2-2-200000002222000000000000-22-2200000000000000000000
χ51444444-4-444-4-4-44-44000000-440000000000022220000000-2-2-2-2000000000000-22-2200000000000000000000
χ52444444-4-444-4-4-44-44000000-4400000000000-2-2-2-2000000022220000000000002-22-200000000000000000000
χ53444444-4-4-4-444-4-400004-44-4000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ54444444-4-4-4-444-4-400004-44-400000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ55444444-4-4-4-444-4-40000-44-44000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ56444444-4-4-4-444-4-40000-44-4400000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ574444-4-444444-4-4-400004-4-44000000000000000000000000000000002-2-22-222-2000000000000000000000000
χ584444-4-444444-4-4-400004-4-4400000000000000000000000000000000-222-22-2-22000000000000000000000000
χ594444-4-444444-4-4-40000-444-4000000000000000000000000000000002-22-2-22-22000000000000000000000000
χ604444-4-444444-4-4-40000-444-400000000000000000000000000000000-22-222-22-2000000000000000000000000
χ614444-4-444-4-4-44-444-4000000-440000000000022-2-20000000-2-2220000000000002-2-2200000000000000000000
χ624444-4-444-4-4-44-444-4000000-4400000000000-2-222000000022-2-2000000000000-222-200000000000000000000
χ634444-4-444-4-4-44-44-440000004-40000000000022-2-20000000-2-222000000000000-222-200000000000000000000
χ644444-4-444-4-4-44-44-440000004-400000000000-2-222000000022-2-20000000000002-2-2200000000000000000000
χ654444-4-4-4-444-444-4004-4000000-44000000000000022-2-20000000-2-2220000000000002-2-220000000000000000
χ664444-4-4-4-444-444-4004-4000000-440000000000000-2-222000000022-2-2000000000000-222-20000000000000000
χ674444-4-4-4-444-444-400-440000004-4000000000000022-2-20000000-2-222000000000000-222-20000000000000000
χ684444-4-4-4-444-444-400-440000004-40000000000000-2-222000000022-2-20000000000002-2-220000000000000000
χ698-88-800008-800000000000000004-4004-40000000004-400000004-40000000000000000000000000000000000
χ708-88-800008-800000000000000004-4004-4000000000-440000000-440000000000000000000000000000000000
χ718-88-800008-80000000000000000-4400-4400000004-4000000000004-400000000000000000000000000000000
χ728-88-800008-80000000000000000-4400-440000000-4400000000000-4400000000000000000000000000000000
χ738-88-80000-8800000000000000004-400-440000000004-40000000-440000000000000000000000000000000000
χ748-88-80000-8800000000000000004-400-44000000000-4400000004-40000000000000000000000000000000000
χ758-88-80000-880000000000000000-44004-400000004-400000000000-4400000000000000000000000000000000
χ768-88-80000-880000000000000000-44004-40000000-44000000000004-400000000000000000000000000000000
χ778-8-88008-8000000000000000000004-4004-40004-400000004-400000000000000000000000000000000000000
χ788-8-88008-8000000000000000000004-4004-4000-440000000-4400000000000000000000000000000000000000
χ798-8-88008-800000000000000000000-4400-4404-4000000000004-4000000000000000000000000000000000000
χ808-8-88008-800000000000000000000-4400-440-4400000000000-44000000000000000000000000000000000000
χ818-8-8800-88000000000000000000004-400-440004-40000000-4400000000000000000000000000000000000000
χ828-8-8800-88000000000000000000004-400-44000-4400000004-400000000000000000000000000000000000000
χ838-8-8800-8800000000000000000000-44004-404-400000000000-44000000000000000000000000000000000000
χ848-8-8800-8800000000000000000000-44004-40-44000000000004-4000000000000000000000000000000000000
χ851616-16-1616-1600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ861616-16-16-161600000000000000000000000000000000000000000000000000000000000000000000000000000000

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