Finite Group Databasebeta

← Group #72227022

Character table — Group #72227022

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size112222222222244444444444444444444444488888888888888888888888888888888888888888888816161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232323232326464646464646464
order122224444888844444488888888881616161616161616224444488888816161616161616161616161616161616323232323232323232323232323232324488161616161616323232323232323232323232323232323232323232323232888888881616161616161616224416161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ51111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111111iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111ii−i−i
χ10111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111111iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii
χ11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111111−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i
χ12111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111111−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-1-111−i−iii
χ13111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i1111-1-1-1-111-1-1−i−iii
χ14111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i
χ15111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii
χ16111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii1111-1-1-1-111-1-1ii−i−i
χ17111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i1-11-1-1i−ii−i11-1-1iiii−i−i−i−iii−i−i11-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3i−ii−i1-111-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζii−i−i11-1-11-1i−iζ3−ζ3ζ−ζ
χ18111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i1-11-1-1i−ii−i11-1-1iiii−i−i−i−iii−i−i11-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3i−ii−i1-111-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−i−iii-1-111-11−ii−ζ3ζ3−ζζ
χ19111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i1-11-1-1i−ii−i11-1-1iiii−i−i−i−iii−i−i11-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3i−ii−i1-111-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−i−iii-1-111-11−iiζ3−ζ3ζ−ζ
χ20111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i1-11-1-1i−ii−i11-1-1iiii−i−i−i−iii−i−i11-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3i−ii−i1-111-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζii−i−i11-1-11-1i−i−ζ3ζ3−ζζ
χ21111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i-11-11-1i−ii−i-1-111−i−i−i−iiiiiii−i−i11-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ii−ii1-1-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζii−i−i11-1-1-11−ii−ζ3ζ3−ζζ
χ22111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i-11-11-1i−ii−i-1-111−i−i−i−iiiiiii−i−i11-1-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ii−ii1-1-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−i−iii-1-1111-1i−iζ3−ζ3ζ−ζ
χ23111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i-11-11-1i−ii−i-1-111−i−i−i−iiiiiii−i−i11-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ii−ii1-1-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−i−iii-1-1111-1i−i−ζ3ζ3−ζζ
χ24111-1-11-11-1-1-1-1-111ii−i−i1-1i−i1-111i−iii−i−iii−i−i-11-11-1i−ii−i-1-111−i−i−i−iiiiiii−i−i11-1-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ii−ii1-1-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζii−i−i11-1-1-11−iiζ3−ζ3ζ−ζ
χ25111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii1-11-1-1−ii−ii11-1-1−i−i−i−iiiii−i−iii11-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ii−ii1-111-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3−i−iii11-1-11-1−iiζ−ζζ3−ζ3
χ26111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii1-11-1-1−ii−ii11-1-1−i−i−i−iiiii−i−iii11-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ii−ii1-111-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ii−i−i-1-111-11i−i−ζζ−ζ3ζ3
χ27111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii1-11-1-1−ii−ii11-1-1−i−i−i−iiiii−i−iii11-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ii−ii1-111-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3ii−i−i-1-111-11i−iζ−ζζ3−ζ3
χ28111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii1-11-1-1−ii−ii11-1-1−i−i−i−iiiii−i−iii11-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ii−ii1-111-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−i−iii11-1-11-1−ii−ζζ−ζ3ζ3
χ29111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii-11-11-1−ii−ii-1-111iiii−i−i−i−i−i−iii11-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζi−ii−i1-1-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−i−iii11-1-1-11i−i−ζζ−ζ3ζ3
χ30111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii-11-11-1−ii−ii-1-111iiii−i−i−i−i−i−iii11-1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζi−ii−i1-1-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ii−i−i-1-1111-1−iiζ−ζζ3−ζ3
χ31111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii-11-11-1−ii−ii-1-111iiii−i−i−i−i−i−iii11-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζi−ii−i1-1-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ii−i−i-1-1111-1−ii−ζζ−ζ3ζ3
χ32111-1-11-11-1-1-1-1-111−i−iii1-1−ii1-111−ii−i−iii−i−iii-11-11-1−ii−ii-1-111iiii−i−i−i−i−i−iii11-1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζi−ii−i1-1-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−i−iii11-1-1-11i−iζ−ζζ3−ζ3
χ3322222222222222222222222222222-2-2-2-2-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3422222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ35222222222222222-2-2-2-222-2-22222-2-22222222222222-2-2-2-22222222222222222-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ36222222222222222-2-2-2-222-2-22222-2-222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-2-22222000000000000000000000000000000000000000000000000
χ3722222222222-2-2-2-22222-2-222222-222222222220000-2-2-2-2-2000000000000-2-2-2-2222222222222222222220000-2-20000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3822222222222-2-2-2-22222-2-222222-222222222220000-2-2-2-2-2000000000000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000222222220000000000000000000000000000000000000000
χ3922222222222-2-2-2-22222-2-222222-222-2-2-2-2-2-2-2-20000-2-2-2-2-20000000000002222-2-2-2-200000000000000000000220000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ4022222222222-2-2-2-22222-2-222222-222-2-2-2-2-2-2-2-20000-2-2-2-2-20000000000002222-2-2-2-20000000000000000000022000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ4122222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2222222220000-22222000000000000-2-2-2-2-2-2-2-2000000000000000000002200000000000022-2-222-2-2-2-222-2-222000000000000000000000000
χ4222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2222222220000-22222000000000000-2-2-2-2-2-2-2-20000000000000000000022000000000000-2-222-2-22222-2-222-2-2000000000000000000000000
χ4322222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-20000-22222000000000000222222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i0000-2-20000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ4422222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-20000-2222200000000000022222222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i0000-2-200002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ45222222222-2-222-2-2222222-2-2-2-2-22-2-2000000002222-2-2-222-2-2-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i222-2-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ46222222222-2-222-2-2222222-2-2-2-2-22-2-2000000002222-2-2-222-2-2-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i222-2-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ47222222222-2-222-2-2222222-2-2-2-2-22-2-200000000-2-2-2-2-2-2-22222220000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-2-222000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ48222222222-2-222-2-2222222-2-2-2-2-22-2-200000000-2-2-2-2-2-2-22222220000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-2-222000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ49222222222-2-222-2-2-2-2-2-22222-2-2-2222000000002222-222-2-2-2-2-2-2000000000000000022−2−222−2−2−2−222−2−222-2-2220000002−22−2−22−222−22−22−22−2−22−22−22−22000000000000000000000000
χ50222222222-2-222-2-2-2-2-2-22222-2-2-2222000000002222-222-2-2-2-2-2-20000000000000000−2−222−2−22222−2−222−2−2-2-222000000−22−222−22−2−22−22−22−222−22−22−22−2000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.