Finite Group Databasebeta

← Group #10798407

Character table — Group #10798407

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size111111111111111122222222222222222222222244444444444444444444444444444444444444446666666688888888888888888888121212121212121212121212121212121212121224242424
order122244444444444422344444466612121212121212121212121222444444444444446612121212121212121212121212121212121212121212888888886688881212121212122424242424242424888888888888888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11ii−i−i11-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii11ii−i−i11-1-1-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii-1-1-1-11111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i11−i−iii11-1-1-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i-1-1-1-11111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11−i−iii11-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-1−i−iii-1-11111−i−i−i−iiiiiii−i−i−i−i−i−iiiii1111-1-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1−i−iii-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1ii−i−i-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-1ii−i−i-1-11111iiii−i−i−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-111
χ171111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11i−ii−i-1-111-1-1ii−i−iii−i−ii−ii−iii−i−iii−i−i11-1-111-1-11-11-1
χ181111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11i−ii−i-1-111-1-1ii−i−iii−i−i−ii−ii−i−iii−i−iii-1-111-1-111-11-11
χ191111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11−ii−ii-1-111-1-1−i−iii−i−iiii−ii−iii−i−iii−i−i-1-111-1-111-11-11
χ201111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11−ii−ii-1-111-1-1−i−iii−i−iii−ii−ii−i−iii−i−iii11-1-111-1-11-11-1
χ211111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-1-1−ii−ii11-1-111−i−iii−i−iiii−ii−i−i−iii−i−iii11-1-111-1-1-11-11
χ221111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-1−ii−ii11-1-111−i−iii−i−iii−ii−iiii−i−iii−i−i-1-111-1-1111-11-1
χ231111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iii-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-1i−ii−i11-1-111ii−i−iii−i−ii−ii−i−i−iii−i−iii-1-111-1-1111-11-1
χ241111-1-1-1-11111-1-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iii-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii-1-1i−ii−i11-1-111ii−i−iii−i−i−ii−iiii−i−iii−i−i11-1-111-1-1-11-11
χ251111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111-1-11
χ261111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-11-1-1-1-11111-1-1-1-111-111-1-1-11111-1-1-1-11111-1-1-111-1
χ271111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-111-1-1-1-1-111-1-11111-1-11-1-1111-1-1-1-111-1-11111-1-1-111-1
χ281111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-111-1-1-1-1-111-1-11111-1-1-111-1-1-11111-1-111-1-1-1-1111-1-11
χ291111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11111-1-1-1-11111-1-11-1-11-1-11111-1-111-1-1-1-111-111-1
χ301111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11111-1-1-1-11111-1-1-111-111-1-1-1-111-1-11111-1-11-1-11
χ311111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11-1-111111-1-111-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-11-1-11
χ321111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11-1-111111-1-111-1-1-1-111-111-111-1-1-1-11111-1-1-1-111-111-1
χ33222222222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ34222222222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000000000000000
χ35222222222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011-2-2-2-211111111111111000000000000000000000000
χ36222222222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000112222111111-1-1-1-1-1-1-1-1000000000000000000000000
χ372222222222222222-2-22-2-2-2-2-2-22222222222222220000000000000000-2-2-2-2-2-2-2-200000000000000002222222200000000000000000000-2-2-2-200000000000000000000
χ382222222222222222-2-22-2-2-2-2-2-22222222222222220000000000000000-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-200000000000000000000222200000000000000000000
χ3922222222-2-2-2-2-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-22200000000000000002i2i2i2i−2i−2i−2i−2i00000000000000000000−2i−2i2i2i00000000000000000000
χ4022222222-2-2-2-2-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-2220000000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000002i2i−2i−2i00000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-1-1-1-1-1111111112222-2-2-2-22i2i2i2i−2i−2i−2i−2i11-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii00000000-1-12i2i−2i−2i-1-11111−i−i−i−iiiii000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-1-1-1-1-1111111112222-2-2-2-2−2i−2i−2i−2i2i2i2i2i11-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i00000000-1-1−2i−2i2i2i-1-11111iiii−i−i−i−i000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-1-1-1-1-111111111-2-2-2-222222i2i2i2i−2i−2i−2i−2i11-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii0000000011−2i−2i2i2i11-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-1-1-1-1-111111111-2-2-2-22222−2i−2i−2i−2i2i2i2i2i11-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i00000000112i2i−2i−2i11-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ452222-2-2-2-22222-2-2-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-2000000000000000022-2-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−2i2i−2i2i00000000000000000000
χ462222-2-2-2-22222-2-2-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-2000000000000000022-2-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000002i−2i2i−2i00000000000000000000
χ472222-2-2-2-22222-2-2-2-2-2-2-1-2-22222-1-1-11111-1-1-1-1111122-2-222-2-22i2i−2i−2i2i2i−2i−2i11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii00000000-1-12i−2i2i−2i11-1-111−i−iii−i−iii000000000000000000000000
χ482222-2-2-2-22222-2-2-2-2-2-2-1-2-22222-1-1-11111-1-1-1-1111122-2-222-2-2−2i−2i2i2i−2i−2i2i2i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i00000000-1-1−2i2i−2i2i11-1-111ii−i−iii−i−i000000000000000000000000
χ492222-2-2-2-22222-2-2-2-2-2-2-1-2-22222-1-1-11111-1-1-1-11111-2-222-2-2222i2i−2i−2i2i2i−2i−2i11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii0000000011−2i2i−2i2i-1-111-1-1ii−i−iii−i−i000000000000000000000000
χ502222-2-2-2-22222-2-2-2-2-2-2-1-2-22222-1-1-11111-1-1-1-11111-2-222-2-222−2i−2i2i2i−2i−2i2i2i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i00000000112i−2i2i−2i-1-111-1-1−i−iii−i−iii000000000000000000000000
χ512222-2-2-2-2-2-2-2-2222222-1-2-2-2-222-1-1-111111111-1-1-1-122-2-2-2-22222-2-2-2-222-1-1-1-11111-1-1-1-111111111-1-1-1-100000000-1-12-2-221111-1-1-1-11111-1-1000000000000000000000000
χ522222-2-2-2-2-2-2-2-2222222-1-2-2-2-222-1-1-111111111-1-1-1-122-2-2-2-222-2-22222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111100000000-1-1-222-21111-1-111-1-1-1-111000000000000000000000000
χ532222-2-2-2-2-2-2-2-2222222-1-2-2-2-222-1-1-111111111-1-1-1-1-2-22222-2-222-2-2-2-222-1-1-1-11111-1-1-1-111111111-1-1-1-10000000011-222-2-1-1-1-11111-1-1-1-111000000000000000000000000
χ542222-2-2-2-2-2-2-2-2222222-1-2-2-2-222-1-1-111111111-1-1-1-1-2-22222-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111100000000112-2-22-1-1-1-111-1-11111-1-1000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-222222-2-2222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-22222000000000000000022-2-2-2-22200000000000000000000-222-200000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-222222-2-2222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-222220000000000000000-2-22222-2-2000000000000000000002-2-2200000000000000000000
χ5722-2-222-2-22i2i−2i−2i2i2i−2i−2i0020000002-2-222-2-22i2i−2i−2i2i2i−2i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000002−22−2−i2i2−i2i20000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.