Finite Group Databasebeta

← Group #123780

Character table — Group #123780

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12224444222222222222224444444444444444444444444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ91111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1
χ101111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111
χ111111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111
χ121111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1
χ131111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111
χ141111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1
χ151111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1
χ161111-1-1-1-111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111
χ171-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1
χ181-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1ii−i−iii−i−i11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111
χ191-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111
χ201-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1
χ211-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111
χ221-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1
χ231-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1
χ241-1-1111-1-1111-1-1111-1-1-1-11-1111-1-1-1111-1-1-11-1−i−iii−i−iii-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111
χ251-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ261-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ271-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-11111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ281-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ291-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-11111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ301-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ311-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ321-1-11-1-111111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ332222222222222-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ342222222222222-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
χ35222222222-2-22-222-222-2-2-2-22-2-222-22-2-22-2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ36222222222-2-22-222-222-2-2-2-22-2-222-22-2-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ37222222222-2-22-2-2-22-2-22-222-222-2-222-2-22-2-2-2200000000000000000000000000000000000000002-22-22-22-200000000
χ38222222222-2-22-2-2-22-2-22-222-222-2-222-2-22-2-2-220000000000000000000000000000000000000000-22-22-22-2200000000
χ3922222222-22-2-222-222-2-2-2-2222-22-22-22-2-22-2-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ4022222222-22-2-222-222-2-2-2-2222-22-22-22-2-22-2-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ4122222222-22-2-22-22-2-222-22-2-2-22-22-2-22-2-22-222000000000000000000000000000000002-22-22-22-20000000000000000
χ4222222222-22-2-22-22-2-222-22-2-2-22-22-2-22-2-22-22200000000000000000000000000000000-22-22-22-220000000000000000
χ4322222222-2-22-2-22-2-22-2222-22-222-2-2-2-22-2-22-220000000000000000000000002-22-22-22-2000000000000000000000000
χ4422222222-2-22-2-22-2-22-2222-22-222-2-2-2-22-2-22-22000000000000000000000000-22-22-22-22000000000000000000000000
χ4522222222-2-22-2-2-222-22-22-22-22-2-222-2-22-2-222-200000000000000002-22-22-22-200000000000000000000000000000000
χ4622222222-2-22-2-2-222-22-22-22-22-2-222-2-22-2-222-20000000000000000-22-22-22-2200000000000000000000000000000000
χ472222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i
χ482222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ492222-2-2-2-22-2-22-222-222-2-2-2-2-222-2-22-222-222-2200000000000000000000000000000000000000002-22-2-22-2200000000
χ502222-2-2-2-22-2-22-222-222-2-2-2-2-222-2-22-222-222-220000000000000000000000000000000000000000-22-222-22-200000000
χ512222-2-2-2-22-2-22-2-2-22-2-22-2222-2-222-2-222-2222-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ522222-2-2-2-22-2-22-2-2-22-2-22-2222-2-222-2-222-2222-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ532222-2-2-2-2-22-2-222-222-2-2-2-22-2-22-22-22-222-2222000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ542222-2-2-2-2-22-2-222-222-2-2-2-22-2-22-22-22-222-222200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ552222-2-2-2-2-22-2-22-22-2-222-22-222-22-222-222-22-2-2000000002-22-2-22-220000000000000000000000000000000000000000
χ562222-2-2-2-2-22-2-22-22-2-222-22-222-22-222-222-22-2-200000000-22-222-22-20000000000000000000000000000000000000000
χ572222-2-2-2-2-2-22-2-22-2-22-2222-2-22-2-22222-222-22-200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ582222-2-2-2-2-2-22-2-22-2-22-2222-2-22-2-22222-222-22-20000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ592222-2-2-2-2-2-22-2-2-222-22-22-222-222-2-222-222-2-220000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ602222-2-2-2-2-2-22-2-2-222-22-22-222-222-2-222-222-2-22000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ612-2-2222-2-2222-2-2-2-2-2222-2-22-2-2-2222222-2-2-2-220000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i
χ622-2-2222-2-2222-2-2-2-2-2222-2-22-2-2-2222222-2-2-2-22000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i
χ632-2-2222-2-22-2-2-2222-2-2-222-222-2-2-2-222-2-2-222222-2-222-2-22000000000000000000000000000000000000000000000000
χ642-2-2222-2-22-2-2-2222-2-2-222-222-2-2-2-222-2-2-22222-222-2-222-2000000000000000000000000000000000000000000000000
χ652-2-2222-2-22-2-2-22-2-2222-222-2-22222-22-2-2-222-2-200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ662-2-2222-2-22-2-2-22-2-2222-222-2-22222-22-2-2-222-2-20000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ672-2-2222-2-2-22-22-22-22-2222-2-222-2-22-2-22-22-22-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ682-2-2222-2-2-22-22-22-22-2222-2-222-2-22-2-22-22-22-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ692-2-2222-2-2-22-22-2-22-22-2-2222-2-222-22-22-22-222-2000000000000000000000000000000002-2-222-2-220000000000000000
χ702-2-2222-2-2-22-22-2-22-22-2-2222-2-222-22-22-22-222-200000000000000000000000000000000-222-2-222-20000000000000000
χ712-2-2222-2-2-2-22222-2-2-22-2-2222-22-222-2-2222-2-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ722-2-2222-2-2-2-22222-2-2-22-2-2222-22-222-2-2222-2-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ732-2-2222-2-2-2-2222-2222-22-2-2-2-22-22-2-2-2-2222-22200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ742-2-2222-2-2-2-2222-2222-22-2-2-2-22-22-2-2-2-2222-2220000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ752-2-22-2-222222-2-2222-2-2-2-22-2-2-2-2222-2-2-2222-220000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i
χ762-2-22-2-222222-2-2222-2-2-2-22-2-2-2-2222-2-2-2222-22000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i
χ772-2-22-2-2222-2-2-2222-2-2-222-22-22222-2-2222-2-2-2-200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ782-2-22-2-2222-2-2-2222-2-2-222-22-22222-2-2222-2-2-2-20000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ792-2-22-2-2222-2-2-22-2-2222-222-22-2-2-2-22-2222-2-2222-2-22-222-2000000000000000000000000000000000000000000000000
χ802-2-22-2-2222-2-2-22-2-2222-222-22-2-2-2-22-2222-2-222-222-22-2-22000000000000000000000000000000000000000000000000
χ812-2-22-2-222-22-22-22-22-2222-2-2-2-222-222-22-22-22-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ822-2-22-2-222-22-22-22-22-2222-2-2-2-222-222-22-22-22-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ832-2-22-2-222-22-22-2-22-22-2-222222-2-22-22-22-22-2-22000000002-2-22-222-20000000000000000000000000000000000000000
χ842-2-22-2-222-22-22-2-22-22-2-222222-2-22-22-22-22-2-2200000000-222-22-2-220000000000000000000000000000000000000000
χ852-2-22-2-222-2-22222-2-2-22-2-222-22-22-2-222-2-2-222200000000000000002-2-22-222-200000000000000000000000000000000
χ862-2-22-2-222-2-22222-2-2-22-2-222-22-22-2-222-2-2-22220000000000000000-222-22-2-2200000000000000000000000000000000
χ872-2-22-2-222-2-2222-2222-22-2-2-22-22-22222-2-2-22-2-20000000000000000000000002-2-22-222-2000000000000000000000000
χ882-2-22-2-222-2-2222-2222-22-2-2-22-22-22222-2-2-22-2-2000000000000000000000000-222-22-2-22000000000000000000000000
χ8988-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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