Finite Group Databasebeta

← Group #190021

Character table — Group #190021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12224444222222444444444444444444444444444444444444444444444488888888888888888888888888888888
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
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ181111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ191111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ201111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ211111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ221111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ231111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ241111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ251111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ261111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ271111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ281111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ291111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ301111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ311111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ321111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ332222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ342222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ352222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ362222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ3722222222-2-222-2-2-2-222-2-222-2-222-2-222-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ3822222222-2-222-2-2-2-222-2-222-2-222-2-222-2-222-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ3922222222-2-222-2-2-2-222-2-2-2-222-2-222-2-222-2-222000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ4022222222-2-222-2-2-2-222-2-2-2-222-2-222-2-222-2-22200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ4122222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2222-22-22-22-2000000000000000000000000000000000000000000000000
χ4222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-222-22-22-22-22000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-22222-2-22-22-2-22-22000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-22222-2-2-22-222-22-2000000000000000000000000000000000000000000000000
χ452222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ462222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ482222-2-2-2-222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ492222-2-2-2-2-2-222-2-222-2-22222-2-222-2-2-2-222-2-222000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ502222-2-2-2-2-2-222-2-222-2-22222-2-222-2-2-2-222-2-22200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ512222-2-2-2-2-2-222-2-222-2-222-2-222-2-22222-2-222-2-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000
χ522222-2-2-2-2-2-222-2-222-2-222-2-222-2-22222-2-222-2-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-2-22222-2-22-2-222-2-22000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-2-22222-2-2-222-2-222-2000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-222-2-2-2-2222-2-22-222-2000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-222-2-2-2-222-222-22-2-22000000000000000000000000000000000000000000000000
χ572-22-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ
χ582-22-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ
χ592-22-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i-22-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3
χ602-22-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i-22-22-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3
χ612-22-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i2-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ622-22-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i2-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ632-22-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i-22-222-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000000000000000
χ642-22-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i-22-222-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000000000000000
χ652-22-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i2-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ662-22-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i2-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ672-22-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ0000000000000000
χ682-22-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i-222-2-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ0000000000000000
χ692-22-22i2i−2i−2i-22-222-2−2i2i−2i2i2i−2i2-2-22-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000
χ702-22-22i2i−2i−2i-22-222-2−2i2i−2i2i2i−2i2-2-22-222-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000
χ712-22-22i2i−2i−2i-22-222-2−2i2i−2i2i2i−2i-222-22-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00000000
χ722-22-22i2i−2i−2i-22-222-2−2i2i−2i2i2i−2i-222-22-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00000000
χ732-22-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3
χ742-22-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3
χ752-22-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i-22-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ
χ762-22-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i-22-22-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ
χ772-22-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ782-22-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ792-22-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i-22-222-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000000000000000
χ802-22-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i-22-222-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000000000000000
χ812-22-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i2-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ822-22-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i2-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ832-22-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ30000000000000000
χ842-22-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i-222-2-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ30000000000000000
χ852-22-2−2i−2i2i2i-22-222-22i−2i2i−2i−2i2i2-2-22-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000
χ862-22-2−2i−2i2i2i-22-222-22i−2i2i−2i−2i2i2-2-22-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000
χ872-22-2−2i−2i2i2i-22-222-22i−2i2i−2i−2i2i-222-22-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300000000
χ882-22-2−2i−2i2i2i-22-222-22i−2i2i−2i−2i2i-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300000000
χ8988-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.