Finite Group Databasebeta

← Group #197588

Character table — Group #197588

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444222222444444444444448888888888888888222244444444444444448888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ9111111111-1-1-1-1111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ10111111111-1-1-1-1111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ11111111111-1-1-1-1111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-1-1-111
χ12111111111-1-1-1-1111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-11111-1-1
χ13111111111-1-1-1-1111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-11111-1-1
χ14111111111-1-1-1-1111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1111-1-111-1-1-1-111
χ15111111111-1-1-1-1111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111-1-111
χ16111111111-1-1-1-1111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-11111-1-111-1-1
χ171111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11111-11-111-1-111-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-11i−ii−ii−ii−i1-11-1
χ181111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11111-11-111-1-111-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-111-1−ii−ii−ii−ii-11-11
χ191111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11-11-1-1-111-1-1111111ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-11−ii−iii−ii−i-11-11
χ201111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11-11-1-1-111-1-1111111ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1i−ii−i−ii−ii1-11-1
χ211111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11111-11-111-1-111-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1-11−ii−ii−ii−ii1-11-1
χ221111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11111-11-111-1-111-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-111-1i−ii−ii−ii−i-11-11
χ231111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11-11-1-1-111-1-1111111−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-1-11i−ii−i−ii−ii-11-11
χ241111-1-1-1-1-111-1-1-11111-1-1111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11-11-1-1-111-1-1111111−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-111-1−ii−iii−ii−i1-11-1
χ251111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11iiii−i−i−i−i−i−i−i−iiiii11-1-11-1-1111-1-1-1-111-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1i−i−iii−i−ii1-1-11
χ261111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11iiii−i−i−i−i−i−i−i−iiiii11-1-11-1-1111-1-1-1-111-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111−iii−i−iii−i-111-1
χ271111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1111-1-11-1-11111-1-111-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i11-1-1−iii−ii−i−ii-111-1
χ281111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11iiii−i−i−i−i−i−i−i−iiiii-1-1111-1-11-1-11111-1-111-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111i−i−ii−iii−i1-1-11
χ291111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-1111-1-1-1-111-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1−iii−i−iii−i1-1-11
χ301111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-1111-1-1-1-111-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111i−i−iii−i−ii-111-1
χ311111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1-11-1-11111-1-111-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1i−i−ii−iii−i-111-1
χ321111-1-1-1-1-1-1-111-111-1-1111-1-111-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1-11-1-11111-1-111-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−iii−ii−i−ii1-1-11
χ3322222222222222-2-2-2-2-2-222222-2-2200000000000000002222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ3422222222222222-2-2-2-2-2-222222-2-220000000000000000-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ35222222222-2-2-2-22-2-222222-2-2-2-2-2-22000000000000000022-2-2-2-222-2-2-2-2222222-2-20000000000000000000000000000000000000000
χ36222222222-2-2-2-22-2-222222-2-2-2-2-2-220000000000000000-2-222-2-2222222-2-2-2-2-2-2220000000000000000000000000000000000000000
χ3722222222-222-2-2-2222222-2-2-22222-222222222222222220000-2-2-2-2000000000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ3822222222-222-2-2-2222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222222200000000000000000000000000000000
χ3922222222-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2000000000000000000002222000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4022222222-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-200000000000000000000222200000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4122222222-2-2-222-222-2-2-2-2-222-2-222-222222222-2-2-2-2-2-2-2-20000-2-222000000000000-2-2-2-2222200000000000000000000000000000000
χ4222222222-2-2-222-222-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2222222220000-2-2220000000000002222-2-2-2-200000000000000000000000000000000
χ4322222222-2-2-222-2-2-22222-222-2-2-2-2-20000000000000000000022-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4422222222-2-2-222-2-2-22222-222-2-2-2-2-20000000000000000000022-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ452222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000-22-22000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i0000-22-220000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-2-2-2222222-2-2-2-222-2-2-2-2-222-2000000000000000000002-22-20000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ482222-2-2-2-2222222-2-2-2-222-2-2-2-2-222-2000000000000000000002-22-200000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ492222-2-2-2-22-2-2-2-2222-2-222-22222-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000-222-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ502222-2-2-2-22-2-2-2-2222-2-222-22222-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000-222-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ512222-2-2-2-22-2-2-2-22-2-222-2-2-2222222-2000000000000000000002-2-220000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ522222-2-2-2-22-2-2-2-22-2-222-2-2-2222222-2000000000000000000002-2-2200000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ532222-2-2-2-2-222-2-2-2-2-2-2-222222-2-222200000000000000002222-22-22-2-222-2-222-2-2-2-20000000000000000000000000000000000000000
χ542222-2-2-2-2-222-2-2-2-2-2-2-222222-2-22220000000000000000-2-2-2-2-22-2222-2-222-2-222220000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-222-2-2-222-2-22-2-222222000000000000000022-2-2-222-2-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-222-2-2-222-2-22-2-2222220000000000000000-2-222-222-222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ572-2-2222-2-222-22-2-2000000-22-22-2002i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-20000000000002-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ582-2-2222-2-222-22-2-2000000-22-22-2002i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-22-22000000000000-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ592-2-2222-2-222-22-2-2000000-22-22-2002−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-20000000000002-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ602-2-2222-2-222-22-2-2000000-22-22-2002−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-22-22000000000000-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ612-2-2222-2-22-22-22-2000000-2-22-22002i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-2-220000000000002-2-22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ622-2-2222-2-22-22-22-2000000-2-22-22002i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-222-2000000000000-222-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ632-2-2222-2-22-22-22-2000000-2-22-22002−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-2-220000000000002-2-22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ642-2-2222-2-22-22-22-2000000-2-22-22002−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-222-2000000000000-222-2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ652-2-2222-2-2-22-2-2220000002-222-200-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000002i−2i2i−2i2i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i22−2−222−2−222−2−222−2−220000000000000000
χ662-2-2222-2-2-22-2-2220000002-222-200-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000−2i2i−2i2i−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2−222−2−222−2−222−2−222−20000000000000000
χ672-2-2222-2-2-22-2-2220000002-222-200-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000002i−2i2i−2i2i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i2−222−2−222−2−222−2−222−20000000000000000
χ682-2-2222-2-2-22-2-2220000002-222-200-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000−2i2i−2i2i−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i22−2−222−2−222−2−222−2−220000000000000000
χ692-2-2222-2-2-2-222-2200000022-2-2200-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000002i−2i2i−2i−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i22−2−222−2−22−222−2−222−20000000000000000
χ702-2-2222-2-2-2-222-2200000022-2-2200-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000−2i2i−2i2i2i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i2−222−2−222−22−2−222−2−220000000000000000
χ712-2-2222-2-2-2-222-2200000022-2-2200-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000002i−2i2i−2i−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i2−222−2−222−22−2−222−2−220000000000000000
χ722-2-2222-2-2-2-222-2200000022-2-2200-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000−2i2i−2i2i2i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i22−2−222−2−22−222−2−222−20000000000000000
χ732-2-22-2-22222-22-2-20000002-22-2200-222−2−2−2−22222−2−2−2−222000000002i−2i−2i2i2i−2i−2i2i0000−222−2−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ742-2-22-2-22222-22-2-20000002-22-2200-222−2−2−2−22222−2−2−2−22200000000−2i2i2i−2i−2i2i2i−2i0000−222−2−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
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χ974-44-44i−4i−4i4i0000004-40000000004i−4i0000000004ζ−4ζ−4ζ4ζ4ζ3−4ζ3−4ζ34ζ3000000000000000000000000000000000000000000000000000000000000
χ984-44-44i−4i−4i4i0000004-40000000004i−4i000000000−4ζ4ζ4ζ−4ζ−4ζ34ζ34ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000
χ994-44-44i−4i−4i4i000000-44000000000−4i4i04ζ3−4ζ3−4ζ34ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-44i−4i−4i4i000000-44000000000−4i4i0−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-4−4i4i4i−4i0000004-4000000000−4i4i0000000004ζ3−4ζ3−4ζ34ζ34ζ−4ζ−4ζ4ζ000000000000000000000000000000000000000000000000000000000000
χ1024-44-4−4i4i4i−4i0000004-4000000000−4i4i000000000−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ000000000000000000000000000000000000000000000000000000000000
χ1034-44-4−4i4i4i−4i000000-440000000004i−4i04ζ−4ζ−4ζ4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000000000
χ1044-44-4−4i4i4i−4i000000-440000000004i−4i0−4ζ4ζ4ζ−4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000000000

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