Finite Group Databasebeta

← Group #367674

Character table — Group #367674

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111111111111111111111111444444444444444444444444444444444444444444444444888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444488888888888888888888888888888888224444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ181111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ191111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ201111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ211111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-111-1-111-1-111-1-1-1-111−i−iii−i−iii−i−iiiii−i−i
χ221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111-1-11111-1-1−i−iii−i−iiiii−i−i−i−iii
χ231111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111-1-11111-1-1ii−i−iii−i−i−i−iiiii−i−i
χ241111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-111-1-111-1-1-1-111ii−i−iii−i−iii−i−i−i−iii
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1-1-11111-1-1ii−i−i−i−iii−i−iii−i−iii
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−iii−i−i
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iii−i−iii
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1-1-11111-1-1−i−iiiii−i−iii−i−iii−i−i
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-111-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-1111111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-1111111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-111-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ332222-2-2-2222-2-2-2-22-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i0000000000000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000002i−2i2-200000000000000000000000000
χ342222-2-2-2222-2-2-2-22-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i0000000000000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000−2i2i-2200000000000000000000000000
χ352222-2-2-2222-2-2-2-22-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i000000000000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000−2i2i-2200000000000000000000000000
χ362222-2-2-2222-2-2-2-22-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i000000000000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000002i−2i2-200000000000000000000000000
χ372222-2-2-2222-2-2-2-22-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i0000000000000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000−2i2i2-200000000000000000000000000
χ382222-2-2-2222-2-2-2-22-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i0000000000000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000002i−2i-2200000000000000000000000000
χ392222-2-2-2222-2-2-2-22-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000002i−2i-2200000000000000000000000000
χ402222-2-2-2222-2-2-2-22-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000−2i2i2-200000000000000000000000000
χ4122-2-222-222-22-2-2-2-222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i−2i22-2-22i2i−2i−2i000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4222-2-222-222-22-2-2-2-222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i−2i22-2-22i2i−2i−2i00000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4322-2-222-222-22-2-2-2-222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i−2i-2-222−2i−2i2i2i000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4422-2-222-222-22-2-2-2-222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i−2i-2-222−2i−2i2i2i00000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4522-2-222-222-22-2-2-2-22−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i22-2-2−2i−2i2i2i000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4622-2-222-222-22-2-2-2-22−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i22-2-2−2i−2i2i2i00000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4722-2-222-222-22-2-2-2-22−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i-2-2222i2i−2i−2i000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4822-2-222-222-22-2-2-2-22−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i-2-2222i2i−2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4922-2-222-2-2-22-222-22-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i−2i−2i2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000002i−2i2-200000000000000000000
χ5022-2-222-2-2-22-222-22-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i−2i−2i2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000−2i2i-2200000000000000000000
χ5122-2-222-2-2-22-222-22-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i−2i−2i2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000−2i2i-2200000000000000000000
χ5222-2-222-2-2-22-222-22-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i−2i−2i2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000002i−2i2-200000000000000000000
χ5322-2-222-2-2-22-222-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2i2i−2i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000−2i2i2-200000000000000000000
χ5422-2-222-2-2-22-222-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2i2i−2i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000002i−2i-2200000000000000000000
χ5522-2-222-2-2-22-222-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2i2i−2i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000002i−2i-2200000000000000000000
χ5622-2-222-2-2-22-222-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2i2i−2i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000−2i2i2-200000000000000000000
χ5722-2-2-2-2222-2-2222-2-22-2-2222-2-2-2-2222-2-22000000000000000022-2-222-2-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000002i−2i2i−2i0000000000000000
χ5822-2-2-2-2222-2-2222-2-22-2-2222-2-2-2-2222-2-22000000000000000022-2-222-2-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000−2i2i−2i2i0000000000000000
χ5922-2-2-2-2222-2-2222-2-22-2-2222-2-2-2-2222-2-220000000000000000-2-222-2-22200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000−2i2i−2i2i0000000000000000
χ6022-2-2-2-2222-2-2222-2-22-2-2222-2-2-2-2222-2-220000000000000000-2-222-2-2220000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000002i−2i2i−2i0000000000000000
χ6122-2-2-2-2222-2-2222-2-2-222-2-2-22222-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000002-2-222-2-220000000000000000−2i2i2i−2i0000000000000000
χ6222-2-2-2-2222-2-2222-2-2-222-2-2-22222-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000-222-2-222-200000000000000002i−2i−2i2i0000000000000000
χ6322-2-2-2-2222-2-2222-2-2-222-2-2-22222-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000002-2-222-2-2200000000000000002i−2i−2i2i0000000000000000
χ6422-2-2-2-2222-2-2222-2-2-222-2-2-22222-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000-222-2-222-20000000000000000−2i2i2i−2i0000000000000000
χ6522-2-2-2-22-2-222-2-222222222-22-2-22-22-2-2-2-20000000022-2-222-2-2000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002i−2i2i−2i00000000
χ6622-2-2-2-22-2-222-2-222222222-22-2-22-22-2-2-2-20000000022-2-222-2-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000−2i2i−2i2i00000000
χ6722-2-2-2-22-2-222-2-222222222-22-2-22-22-2-2-2-200000000-2-222-2-222000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000−2i2i−2i2i00000000
χ6822-2-2-2-22-2-222-2-222222222-22-2-22-22-2-2-2-200000000-2-222-2-22200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000002i−2i2i−2i00000000
χ6922-2-2-2-22-2-222-2-2222-2-2-2-2-22-222-22-222220000000022-2-2-2-222000000002-2-222-2-2200000000000000000000000000000000000000002-2-2200000000
χ7022-2-2-2-22-2-222-2-2222-2-2-2-2-22-222-22-222220000000022-2-2-2-22200000000-222-2-222-20000000000000000000000000000000000000000-222-200000000
χ7122-2-2-2-22-2-222-2-2222-2-2-2-2-22-222-22-2222200000000-2-22222-2-2000000002-2-222-2-220000000000000000000000000000000000000000-222-200000000
χ7222-2-2-2-22-2-222-2-2222-2-2-2-2-22-222-22-2222200000000-2-22222-2-200000000-222-2-222-200000000000000000000000000000000000000002-2-2200000000
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χ1114-44-4-44-44-4-4-4-444444444-4-4-4-4-4-4-4-44444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1154-4-44-444-44-44-44-44-44i4i−4i−4i−4i4i−4i4i−4i4i−4i4i−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-444-44-44-44-44-4−4i−4i4i4i4i−4i4i−4i4i−4i4i−4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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