Finite Group Databasebeta

← Group #123779

Character table — Group #123779

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12224444222222222222224444444444444444444444444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ101111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ121111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ131111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ1711-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ1811-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii
χ1911-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ2011-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i
χ2111-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ2211-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i
χ2311-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ2411-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii
χ2511-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-1
χ2611-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-111
χ2711-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111
χ2811-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1
χ2911-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii11-1-1-1-111
χ3011-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-1
χ3111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1
χ3211-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111
χ3322222222222-2-2-2222-2-2-2-2-2222-2-2222-2-2-2-2-2-22-22-22-22-2000000000000000000000000000000000000000000000000
χ3422222222222-2-2-2222-2-2-2-2-2222-2-2222-2-2-2-2-2-2-22-22-22-22000000000000000000000000000000000000000000000000
χ35222222222-2-222-22-2-222-2-2-22-2-22-22-2-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ36222222222-2-222-22-2-222-2-2-22-2-22-22-2-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ37222222222-2-2-2-222-2-2-2-22222-2-2-222-2-2-22-22-2200000000000000002-22-22-22-200000000000000000000000000000000
χ38222222222-2-2-2-222-2-2-2-22222-2-2-222-2-2-22-22-220000000000000000-22-22-22-2200000000000000000000000000000000
χ3922222222-22-22-22-22-22-2-2-22-22-22-2-22-2-2-2-222200000000000000000000000000000000000000002-22-22-22-200000000
χ4022222222-22-22-22-22-22-2-2-22-22-22-2-22-2-2-2-22220000000000000000000000000000000000000000-22-22-22-2200000000
χ4122222222-22-2-22-2-22-2-2222-2-22-2-22-22-2222-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ4222222222-22-2-22-2-22-2-2222-2-22-2-22-22-2222-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
χ4322222222-2-222-2-2-2-222-222-2-2-2222-2-22-22-2-22-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4422222222-2-222-2-2-2-222-222-2-2-2222-2-22-22-2-22-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4522222222-2-22-222-2-22-22-2-22-2-22-2-2-2-222-222-22000000000000000000000000000000002-22-22-22-20000000000000000
χ4622222222-2-22-222-2-22-22-2-22-2-22-2-2-2-222-222-2200000000000000000000000000000000-22-22-22-220000000000000000
χ472222-2-2-2-2222-2-2-2222-2-2-2-2-2-2-2-222-2-2-22222222-22-2-22-22000000000000000000000000000000000000000000000000
χ482222-2-2-2-2222-2-2-2222-2-2-2-2-2-2-2-222-2-2-2222222-22-222-22-2000000000000000000000000000000000000000000000000
χ492222-2-2-2-22-2-222-22-2-222-2-2-2-222-22-222-22-22-22000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ502222-2-2-2-22-2-222-22-2-222-2-2-2-222-22-222-22-22-2200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ512222-2-2-2-22-2-2-2-222-2-2-2-2222-2222-2-2222-22-22-200000000000000002-22-2-22-2200000000000000000000000000000000
χ522222-2-2-2-22-2-2-2-222-2-2-2-2222-2222-2-2222-22-22-20000000000000000-22-222-22-200000000000000000000000000000000
χ532222-2-2-2-2-22-22-22-22-22-2-2-222-22-222-22222-2-2-200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ542222-2-2-2-2-22-22-22-22-22-2-2-222-22-222-22222-2-2-20000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ552222-2-2-2-2-22-2-22-2-22-2-2222-22-222-22-22-2-2-22220000000000000000000000000000000000000000000000002-22-2-22-22
χ562222-2-2-2-2-22-2-22-2-22-2-2222-22-222-22-22-2-2-2222000000000000000000000000000000000000000000000000-22-222-22-2
χ572222-2-2-2-2-2-222-2-2-2-222-222-222-2-2-222-22-222-220000000000000000000000002-22-2-22-22000000000000000000000000
χ582222-2-2-2-2-2-222-2-2-2-222-222-222-2-2-222-22-222-22000000000000000000000000-22-222-22-2000000000000000000000000
χ592222-2-2-2-2-2-22-222-2-22-22-2-2222-22222-2-22-2-22-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ602222-2-2-2-2-2-22-222-2-22-22-2-2222-22222-2-22-2-22-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ6122-2-222-2-2222-2-2-2-2-2-2222-22222-2-2-2-2-222-2-2222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ6222-2-222-2-2222-2-2-2-2-2-2222-22222-2-2-2-2-222-2-222−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ6322-2-222-2-22-2-222-2-222-2-22-222-2-22-2-222-222-2-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ6422-2-222-2-22-2-222-2-222-2-22-222-2-22-2-222-222-2-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ6522-2-222-2-22-2-2-2-22-22222-22-22-2-2-22-2222-2-222-200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ6622-2-222-2-22-2-2-2-22-22222-22-22-2-2-22-2222-2-222-20000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ6722-2-222-2-2-22-22-222-22-222-2-2-22-22-22-2222-22-2-200000000000000000000000000000000000000002-2-222-2-2200000000
χ6822-2-222-2-2-22-22-222-22-222-2-2-22-22-22-2222-22-2-20000000000000000000000000000000000000000-222-2-222-200000000
χ6922-2-222-2-2-22-2-22-22-222-2-222-22-2-222-22-2-22-2220000000000000000000000000000000000000000000000002-2-222-2-22
χ7022-2-222-2-2-22-2-22-22-222-2-222-22-2-222-22-2-22-222000000000000000000000000000000000000000000000000-222-2-222-2
χ7122-2-222-2-2-2-222-2-222-2-22-222-2-222222-22-2-2-2-220000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ7222-2-222-2-2-2-222-2-222-2-22-222-2-222222-22-2-2-2-22000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ7322-2-222-2-2-2-22-22222-22-22-2-2-2-22-2-222-2-22222-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ7422-2-222-2-2-2-22-22222-22-22-2-2-2-22-2-222-2-22222-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ7522-2-2-2-222222-2-2-2-2-2-2222-22-2-2-222222-2-222-2-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ7622-2-2-2-222222-2-2-2-2-2-2222-22-2-2-222222-2-222-2-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ7722-2-2-2-2222-2-222-2-222-2-22-22-222-222-2-22-2-222-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000
χ7822-2-2-2-2222-2-222-2-222-2-22-22-222-222-2-22-2-222-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000
χ7922-2-2-2-2222-2-2-2-22-22222-22-2-2222-22-2-2-222-2-2200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ8022-2-2-2-2222-2-2-2-22-22222-22-2-2222-22-2-2-222-2-220000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ8122-2-2-2-222-22-22-222-22-222-2-22-22-22-22-2-2-22-22200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ8222-2-2-2-222-22-22-222-22-222-2-22-22-22-22-2-2-22-2220000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ8322-2-2-2-222-22-2-22-22-222-2-2222-222-2-22-222-22-2-20000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i
χ8422-2-2-2-222-22-2-22-22-222-2-2222-222-2-22-222-22-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i
χ8522-2-2-2-222-2-222-2-222-2-22-22222-2-2-2-2-22-22222-20000000000000000000000002-2-22-222-2000000000000000000000000
χ8622-2-2-2-222-2-222-2-222-2-22-22222-2-2-2-2-22-22222-2000000000000000000000000-222-22-2-22000000000000000000000000
χ8722-2-2-2-222-2-22-22222-22-22-2-222-222-2-222-2-2-2-22000000000000000000000000000000002-2-22-222-20000000000000000
χ8822-2-2-2-222-2-22-22222-22-22-2-222-222-2-222-2-2-2-2200000000000000000000000000000000-222-22-2-220000000000000000
χ898-88-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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