Finite Group Databasebeta

← Group #72262389

Character table — Group #72262389

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111122224444488888888888888888816161616161616161616161616323232323232323232323232323232323232323264646464646464646464646464646464
order12222222222222222222222444444442222222444444244444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-111-1-1111-1-1-111-1-1ii−i−i11-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ101111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-111-1-1111-1-1-111-1-1−i−iii11-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ111111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-111-1-1111-1-1-1-1-111ii−i−i11-1-1-1-111ii−i−iii−i−i-1-111−i−iii−i−iii
χ121111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-111-1-1111-1-1-1-1-111−i−iii11-1-1-1-111−i−iii−i−iii-1-111ii−i−iii−i−i
χ131111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-111-111-1-1ii−i−i-1-11111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ141111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-111-111-1-1−i−iii-1-11111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ151111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-111-1-1-111ii−i−i-1-111-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ161111-1-1-1-11-111-1111111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-111-1-1-111−i−iii-1-111-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222222222-2-22222-2-222-2-222-2-2-22222-22222-200000000-2-2-2-2000000000000000000000000
χ1822222222222222222-2-22222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ19222222222222222-2-22222-2-2-2-2-2-2-2-2-2-22220000-20000-2000000000000000000000000000000002i−2i2i−2i
χ20222222222222222-2-22222-2-2-2-2-2-2-2-2-2-22220000-20000-200000000000000000000000000000000−2i2i−2i2i
χ21222222222222222-2-2-2-222-2-222-2-222-2-2-2-2-2000020000200000000000000000000000000002-22-20000
χ22222222222222222-2-2-2-222-2-222-2-222-2-2-2-2-200002000020000000000000000000000000000-22-220000
χ232222222222222-2-22222-2-222-2-2-2-2-2-2-2-2-22-20000200002000000000000000000002-22-2000000000000
χ242222222222222-2-22222-2-222-2-2-2-2-2-2-2-2-22-2000020000200000000000000000000-22-22000000000000
χ252222222222222-2-222-2-2-2-22222-2-222-2-22-220000-20000-20000222200000000-2-2-2-20000000000000000
χ262222222222222-2-222-2-2-2-22222-2-222-2-22-220000-20000-20000-2-2-2-20000000022220000000000000000
χ272222222222222-2-2-2-222-2-2-2-222222222-22-20000-20000-2222200000000-2-2-2-200000000000000000000
χ282222222222222-2-2-2-222-2-2-2-222222222-22-20000-20000-2-2-2-2-200000000222200000000000000000000
χ292222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222-2200002000020000000000000000000000002-22-200000000
χ302222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222-220000200002000000000000000000000000-22-2200000000
χ312222-2-2-2-22-222-22222-2-2-2-2-2-2-2-2-2-22222-22222-2-2-222-2-2200000000-2-222000000000000000000000000
χ322222-2-2-2-22-222-22222-2-2-2-2-2-2-2-2-2-22222-222-2-222-2-2-22220000000022-2-2000000000000000000000000
χ332222-2-2-2-22-222-222-2-222-2-222-2-22222-2-22-2-20000-200002000000000000000000000000000000002-2-22
χ342222-2-2-2-22-222-222-2-222-2-222-2-22222-2-22-2-20000-20000200000000000000000000000000000000-222-2
χ352222-2-2-2-22-222-222-2-2-2-2-2-2222222-2-2-2-2-222000020000-200000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-22-222-222-2-2-2-2-2-2222222-2-2-2-2-222000020000-20000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-22-222-2-2-2222222-2-2-2-22222-2-2-2-22000020000-2000000000000000000002i−2i−2i2i000000000000
χ382222-2-2-2-22-222-2-2-2222222-2-2-2-22222-2-2-2-22000020000-200000000000000000000−2i2i2i−2i000000000000
χ392222-2-2-2-22-222-2-2-222-2-222-2-22222-2-2-2-222-20000-20000200002i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ402222-2-2-2-22-222-2-2-222-2-222-2-22222-2-2-2-222-20000-2000020000−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ412222-2-2-2-22-222-2-2-2-2-222222222-2-2-2-222-2-220000-20000222-2-200000000-2-22200000000000000000000
χ422222-2-2-2-22-222-2-2-2-2-222222222-2-2-2-222-2-220000-200002-2-2220000000022-2-200000000000000000000
χ432222-2-2-2-22-222-2-2-2-2-2-2-22222-2-2-2-2222222-2000020000-20000000000000000000000002-2-2200000000
χ442222-2-2-2-22-222-2-2-2-2-2-2-22222-2-2-2-2222222-2000020000-2000000000000000000000000-222-200000000
χ4544444444-4-44-4-400000000004-4004-40000022220-2-2-2-20000000002-22-2000000000000000000000000
χ4644444444-4-44-4-400000000004-4004-400000-2-2-2-202222000000000-22-22000000000000000000000000
χ4744444444-4-44-4-40000000000-4400-440000022220-2-2-2-2000000000-22-22000000000000000000000000
χ4844444444-4-44-4-40000000000-4400-4400000-2-2-2-2022220000000002-22-2000000000000000000000000
χ49444444-4-444-4-4-40000000000004-4004-4000000000000000002i−2i2i−2i000000002i−2i2i−2i0000000000000000
χ50444444-4-444-4-4-40000000000004-4004-400000000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000000000
χ51444444-4-444-4-4-4000000000000-4400-44000000000000000002i−2i2i−2i00000000−2i2i−2i2i0000000000000000
χ52444444-4-444-4-4-4000000000000-4400-4400000000000000000−2i2i−2i2i000000002i−2i2i−2i0000000000000000
χ53444444-4-4-4-4-444004-400004-40000000000000000000002-22-2000000002-22-200000000000000000000
χ54444444-4-4-4-4-444004-400004-4000000000000000000000-22-2200000000-22-2200000000000000000000
χ55444444-4-4-4-4-44400-440000-440000000000000000000002-22-200000000-22-2200000000000000000000
χ56444444-4-4-4-4-44400-440000-44000000000000000000000-22-22000000002-22-200000000000000000000
χ574444-4-4444-4-4-440000000000004-400-44000000000000000002-2-2200000000-222-20000000000000000
χ584444-4-4444-4-4-440000000000004-400-4400000000000000000-222-2000000002-2-220000000000000000
χ594444-4-4444-4-4-44000000000000-44004-4000000000000000002-2-22000000002-2-220000000000000000
χ604444-4-4444-4-4-44000000000000-44004-400000000000000000-222-200000000-222-20000000000000000
χ614444-4-444-44-44-4004-40000-440000000000000000000002-2-22000000002-2-2200000000000000000000
χ624444-4-444-44-44-4004-40000-44000000000000000000000-222-200000000-222-200000000000000000000
χ634444-4-444-44-44-400-4400004-40000000000000000000002-2-2200000000-222-200000000000000000000
χ644444-4-444-44-44-400-4400004-4000000000000000000000-222-2000000002-2-2200000000000000000000
χ654444-4-4-4-4-444-4400000000004-400-440000022-2-20-2-2220000000002-2-22000000000000000000000000
χ664444-4-4-4-4-444-4400000000004-400-4400000-2-222022-2-2000000000-222-2000000000000000000000000
χ674444-4-4-4-4-444-440000000000-44004-40000022-2-20-2-222000000000-222-2000000000000000000000000
χ684444-4-4-4-4-444-440000000000-44004-400000-2-222022-2-20000000002-2-22000000000000000000000000
χ698-8-88008-8000004-400004-40000000000000000004-44-40000000000000000000000000000000000000
χ708-8-88008-8000004-400004-4000000000000000000-44-440000000000000000000000000000000000000
χ718-8-88008-800000-440000-4400000000000004-44-4000000000000000000000000000000000000000000
χ728-8-88008-800000-440000-440000000000000-44-44000000000000000000000000000000000000000000
χ738-8-8800-88000004-40000-440000000000000000004-4-440000000000000000000000000000000000000
χ748-8-8800-88000004-40000-44000000000000000000-444-40000000000000000000000000000000000000
χ758-8-8800-8800000-4400004-400000000000004-4-44000000000000000000000000000000000000000000
χ768-8-8800-8800000-4400004-40000000000000-444-4000000000000000000000000000000000000000000
χ771616-16-1600000000000008-80000000000000000000000000000000000000000000000000000000000000
χ781616-16-160000000000000-880000000000000000000000000000000000000000000000000000000000000
χ7916-1616-1616-1600000000000000000000000000000000000000000000000000000000000000000000000000
χ8016-1616-16-161600000000000000000000000000000000000000000000000000000000000000000000000000

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