Finite Group Databasebeta

← Group #72231932

Character table — Group #72231932

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size11112222222222222222224444444444444444444444444444448888888888888888888888888888888888888888888832323232323232323232323232323232
order1222444444444488888888248888888888881616161616161616161616161616161688881616161616161616323232323232323232323232323232323232323232323232323232323232323216161616161616161616161616161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ101111111111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ111111111111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ121111111111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ131111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ141111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ151111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ161111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ171111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-11-11-1
χ181111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-11-11-11-11
χ191111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-11-11-1-11-11-11-11
χ201111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-11-111-11-11-11-1
χ211111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii
χ221111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i
χ231111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1i−ii−i−ii−ii−ii−iii−ii−i
χ241111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−ii−iii−ii−ii−ii−i−ii−ii
χ251111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiζ−ζ−ζζζ3−ζ3−ζ3ζ3ζ−ζ−ζζζ3−ζ3−ζ3ζ3
χ261111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−ζζζ−ζ−ζ3ζ3ζ3−ζ3−ζζζ−ζ−ζ3ζ3ζ3−ζ3
χ271111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iζ−ζ−ζζζ3−ζ3−ζ3ζ3−ζζζ−ζ−ζ3ζ3ζ3−ζ3
χ281111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−ζζζ−ζ−ζ3ζ3ζ3−ζ3ζ−ζ−ζζζ3−ζ3−ζ3ζ3
χ291111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iζ3−ζ3−ζ3ζ3ζ−ζ−ζζζ3−ζ3−ζ3ζ3ζ−ζ−ζζ
χ301111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−ζ3ζ3ζ3−ζ3−ζζζ−ζ−ζ3ζ3ζ3−ζ3−ζζζ−ζ
χ311111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiζ3−ζ3−ζ3ζ3ζ−ζ−ζζ−ζ3ζ3ζ3−ζ3−ζζζ−ζ
χ321111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−ζ3ζ3ζ3−ζ3−ζζζ−ζζ3−ζ3−ζ3ζ3ζ−ζ−ζζ
χ33222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ3522222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-200000000000000002-22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3622222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-200000000000000002-22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3722222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-2220000000000000000-22-2200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-2220000000000000000-22-2200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ392222222222-2-2-2-222222222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-2-22222-2-2-2-222222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ402222222222-2-2-2-222222222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2-22222-2-2-2-22222−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ412222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2−222−2−22222−2−222−2−20000000000000000
χ422222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i222−2−222−2−2−2−222−2−2220000000000000000
χ432222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i222−2−222−2−2−2−222−2−2220000000000000000
χ442222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2−222−2−22222−2−222−2−20000000000000000
χ452222-2-2-2-22222222222-2-2-2-2-2-222-2-222-2-222-2-20000000000000000-22-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ462222-2-2-2-22222222222-2-2-2-2-2-222-2-222-2-222-2-20000000000000000-22-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ472222-2-2-2-22222222222-2-2-2-2-2-222-2-2-2-222-2-22200000000000000002-22-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ482222-2-2-2-22222222222-2-2-2-2-2-222-2-2-2-222-2-22200000000000000002-22-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ492222-2-2-2-2222222-2-2-2-22222-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ502222-2-2-2-2222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-222-2-2000000000000000000000000000000000000000000000000
χ512222-2-2-2-222-2-2-2-22222-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−2−22222−2−222−2−2−2−2220000000000000000
χ522222-2-2-2-222-2-2-2-22222-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i222−2−2−2−222−2−22222−2−20000000000000000
χ532222-2-2-2-222-2-2-2-22222-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2−22222−2−20000000000000000
χ542222-2-2-2-222-2-2-2-22222-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−2−22222−2−222−2−2−2−2220000000000000000
χ552222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-22i2i2i2i−2i−2i−2i−2i2222-2-2-2-2-2-2-2-22222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ562222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2−2i−2i−2i−2i2i2i2i2i2222-2-2-2-2-2-2-2-222222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ5722-2-200002-22i2i−2i−2i000022-2-200002i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000022-2-22i2i−2i−2i00002ζ−2ζ002ζ3−2ζ30000002i−2i2i−2i00002-22-200002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ0000000000000000
χ5822-2-200002-22i2i−2i−2i000022-2-200002i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000022-2-22i2i−2i−2i00002ζ−2ζ002ζ3−2ζ3000000−2i2i−2i2i0000-22-220000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ0000000000000000
χ5922-2-200002-22i2i−2i−2i000022-2-200002i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000-2-222−2i−2i2i2i0000−2ζ2ζ00−2ζ32ζ3002i−2i2i−2i00002-22-200002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ00000000000000000000
χ6022-2-200002-22i2i−2i−2i000022-2-200002i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000-2-222−2i−2i2i2i0000−2ζ2ζ00−2ζ32ζ300−2i2i−2i2i0000-22-220000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ00000000000000000000
χ6122-2-200002-22i2i−2i−2i000022-2-200002i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000022-2-22i2i−2i−2i0000−2ζ2ζ00−2ζ32ζ30000002i−2i2i−2i00002-22-20000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ0000000000000000
χ6222-2-200002-22i2i−2i−2i000022-2-200002i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000022-2-22i2i−2i−2i0000−2ζ2ζ00−2ζ32ζ3000000−2i2i−2i2i0000-22-2200002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ0000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.