Finite Group Databasebeta

← Group #72225522

Character table — Group #72225522

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size111122222222222222222222224444444444444444444444444444444488888888888888888888888888888888888888888832323232323232323232323232323232323232323232323232323232323232326464646464646464
order1222224444444488888888888844888888888888888888888816161616161616164444888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616163232323232323232323232323232323222448888
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
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1
χ1011111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111
χ1111111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11-1-111
χ1211111111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1
χ1311111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111
χ1411111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1
χ1511111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1
χ1611111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111
χ171111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1ii−i−i1111-1-1-1-111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-111-1-1i−ii−i
χ181111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1ii−i−i1111-1-1-1-111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111-1-111-1-111−ii−ii
χ191111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1ii−i−i1111-1-1-1-111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1-1-111−ii−ii
χ201111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1ii−i−i1111-1-1-1-111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii-1-111-1-11111-1-1i−ii−i
χ211111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1−i−iii1111-1-1-1-111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i-1-111-1-11111-1-1−ii−ii
χ221111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1−i−iii1111-1-1-1-111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1-1-111i−ii−i
χ231111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1−i−iii1111-1-1-1-111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111-1-111-1-111i−ii−i
χ241111-1-11111-1-1-1-1111111-1-1-1-111-1111-1-1−i−iii1111-1-1-1-111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-111-1-1−ii−ii
χ251111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111ii−i−i-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−i−iii-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1-11i−i−ii
χ261111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111ii−i−i-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−i−iii-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii-111-1−iii−i
χ271111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111ii−i−i-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−i−iii-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-111-1−iii−i
χ281111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111ii−i−i-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−i−iii-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii1-1-11i−i−ii
χ291111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111−i−iii-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iiii−i−i-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1-11−iii−i
χ301111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111−i−iii-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iiii−i−i-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-111-1i−i−ii
χ311111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111−i−iii-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iiii−i−i-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-111-1i−i−ii
χ321111-1-11111-1-1-1-1-1-111111111-1-1-11-1-111−i−iii-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iiii−i−i-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i1-1-11−iii−i
χ3322222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222222222222222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222220000000000000000000000000000000000000000
χ352222222222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000002−22−22−22−22−22−22−22−200000000
χ362222222222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-222222200000000000000000000000000000000000000000000−22−22−22−22−22−22−22−2200000000
χ372222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222222-2-2-2-2-2-2000000000000000000000000000000000000000000002−22−22−22−2−22−22−22−2200000000
χ382222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222222-2-2-2-2-2-200000000000000000000000000000000000000000000−22−22−22−222−22−22−22−200000000
χ3922222222222222-2-22222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-222222222222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ4022222222222222-2-22222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ4122222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222222222-2-2-2-2-2-2000000002222-2-2-2-222-2-2-2-200000000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ4222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222222222-2-2-2-2-2-2000000002222-2-2-2-222-2-2-2-200000000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ4322222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-200000000-2-2-2-22222-2-2222200000000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ4422222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-200000000-2-2-2-22222-2-2222200000000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ4522222222-2-2-2-2-2-20022220000002-200002i2i−2i−2i00000000-2-222-2-22222-2-2-2-200002i−2i2i−2i−2i2i0000-2-22200000000000000002i2i−2i−2i2i2i−2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000000000000000
χ4622222222-2-2-2-2-2-20022220000002-200002i2i−2i−2i00000000-2-222-2-22222-2-2-2-200002i−2i2i−2i−2i2i0000-2-22200000000000000002i2i−2i−2i2i2i−2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000000000000000
χ4722222222-2-2-2-2-2-20022220000002-200002i2i−2i−2i00000000-2-222-2-2-2-2-2-2222200002i−2i2i−2i−2i2i000022-2-20000000000000000−2i−2i2i2i−2i−2i2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ4822222222-2-2-2-2-2-20022220000002-200002i2i−2i−2i00000000-2-222-2-2-2-2-2-2222200002i−2i2i−2i−2i2i000022-2-20000000000000000−2i−2i2i2i−2i−2i2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ4922222222-2-2-2-2-2-20022220000002-20000−2i−2i2i2i00000000-2-222-2-22222-2-2-2-20000−2i2i−2i2i2i−2i0000-2-2220000000000000000−2i−2i2i2i−2i−2i2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000000000000000
χ5022222222-2-2-2-2-2-20022220000002-20000−2i−2i2i2i00000000-2-222-2-22222-2-2-2-20000−2i2i−2i2i2i−2i0000-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000000000000000
χ5122222222-2-2-2-2-2-20022220000002-20000−2i−2i2i2i00000000-2-222-2-2-2-2-2-222220000−2i2i−2i2i2i−2i000022-2-200000000000000002i2i−2i−2i2i2i−2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ5222222222-2-2-2-2-2-20022220000002-20000−2i−2i2i2i00000000-2-222-2-2-2-2-2-222220000−2i2i−2i2i2i−2i000022-2-200000000000000002i2i−2i−2i2i2i−2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ532222-2-22222-2-2-2-2222222-2-2-2-222-2222-2-22i2i−2i−2i2222-2-2-2-222-2-2-2-2-2-2-2-222222i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i-2-222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ542222-2-22222-2-2-2-2222222-2-2-2-222-2222-2-2−2i−2i2i2i2222-2-2-2-222-2-2-2-2-2-2-2-22222−2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i-2-222-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ552222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222-2222-2-22i2i−2i−2i-2-2-2-22222-2-2222200000000−2i−2i2i2i−2i−2i2i2i2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i22−2−222−2−2200000000
χ562222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222-2222-2-22i2i−2i−2i-2-2-2-22222-2-2222200000000−2i−2i2i2i−2i−2i2i2i2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−2−222−200000000
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χ1358-8-888-800000000−424242−42−4242−424242−4242−420000000000-444-4-444-40042−4200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1368-8-888-800000000−4242−424242−42−424242−4242−4200000000004-4-444-4-4400−424200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1378-8-88-880000000042−4242−42−4242−424242−42−424200000000004-4-44-444-400−424200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1388-8-88-880000000042−42−424242−42−424242−42−42420000000000-444-44-4-440042−4200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1398-8-88-8800000000−424242−42−424242−42−424242−420000000000-444-44-4-4400−424200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1408-8-88-8800000000−4242−424242−4242−42−424242−4200000000004-4-44-444-40042−4200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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