Finite Group Databasebeta

← Group #10798405

Character table — Group #10798405

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11111111111111112222222222222222222222222222222244444444444444444444444444448888888888888888888888881212121212121212121212121212121212121212121212121212121212121212
order122244444444444422344444466688888888121212121212121212121212668888121212121212242424242424242424242424242424242444668888121212121212242424242424242422444444444444448888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ911111111-1-1-1-1-1-1-1-1-1-1111-1-111111iiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111ii−i−i11-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1111-1-111111iiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111ii−i−i11-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-1-1-1111-1-111111iiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1−i−iii-1-11111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111
χ1211111111-1-1-1-1-1-1-1-1-1-1111-1-111111iiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1−i−iii-1-11111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111-1-111111−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111−i−iii11-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1111-1-111111−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111−i−iii11-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111
χ1511111111-1-1-1-1-1-1-1-1-1-1111-1-111111−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1ii−i−i-1-11111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111
χ1611111111-1-1-1-1-1-1-1-1-1-1111-1-111111−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1ii−i−i-1-11111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1
χ171111-1-1-1-11111-1-1-1-1-1-11-1-11111111ii−i−iii−i−i-1-1-1-11111-1-1-1-1-1-1i−ii−i11-1-111iiii−i−i−i−iiiii−i−i−i−i1-11-111i−ii−i-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ181111-1-1-1-11111-1-1-1-1-1-11-1-11111111ii−i−iii−i−i-1-1-1-11111-1-1-1-1-1-1i−ii−i11-1-111iiii−i−i−i−iiiii−i−i−i−i1-11-111i−ii−i-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-111
χ191111-1-1-1-11111-1-1-1-1-1-11-1-11111111ii−i−iii−i−i-1-1-1-11111-1-1-1-1-1-1i−ii−i11-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11-1-1−ii−ii11-1-111−i−iii−i−iii11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ201111-1-1-1-11111-1-1-1-1-1-11-1-11111111ii−i−iii−i−i-1-1-1-11111-1-1-1-1-1-1i−ii−i11-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11-1-1−ii−ii11-1-111−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1
χ211111-1-1-1-11111-1-1-1-1-1-11-1-11111111−i−iii−i−iii-1-1-1-11111-1-1-1-1-1-1−ii−ii11-1-111−i−i−i−iiiii−i−i−i−iiiii1-11-111−ii−ii-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ221111-1-1-1-11111-1-1-1-1-1-11-1-11111111−i−iii−i−iii-1-1-1-11111-1-1-1-1-1-1−ii−ii11-1-111−i−i−i−iiiii−i−i−i−iiiii1-11-111−ii−ii-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-111
χ231111-1-1-1-11111-1-1-1-1-1-11-1-11111111−i−iii−i−iii-1-1-1-11111-1-1-1-1-1-1−ii−ii11-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11-1-1i−ii−i11-1-111ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ241111-1-1-1-11111-1-1-1-1-1-11-1-11111111−i−iii−i−iii-1-1-1-11111-1-1-1-1-1-1−ii−ii11-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11-1-1i−ii−i11-1-111ii−i−iii−i−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1
χ251111-1-1-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ261111-1-1-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11111-1-11-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ271111-1-1-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-111-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ281111-1-1-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-111-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ291111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-111-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ301111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-111-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ311111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11-1-111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ321111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11-1-111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ33222222222222222222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ34222222222222222222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-21111111111111100000000000000000000000000000000
χ35222222222222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111111111112222-1-1-2-2-2-2-1-1-1-1-1-11111111100000000000000000000000000000000
χ36222222222222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2112222111111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ372222222222222222-2-22-2-2-2-2-2-222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ382222222222222222-2-22-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222222222-2-22222-2-2-2-2-2-2-2-222-2-222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ392222222222222222-2-2-1-2-2-2-2-2-2-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111-1-111-1-111-1-111-1-1110000−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000000000000000000000
χ402222222222222222-2-2-1-2-2-2-2-2-2-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111-1-111-1-111-1-111-1-1110000i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000000000000000000000
χ412222222222222222-2-2-1-2-2-2-2-2-2-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111222211111111-1-111-1-111-1-111-1-10000−i3i30000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000000000000000000000
χ422222222222222222-2-2-1-2-2-2-2-2-2-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111222211111111-1-111-1-111-1-111-1-10000i3−i30000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2222-2-222-2-22222i2i2i2i−2i−2i−2i−2i2222-2-2-2-2-2-2-2-222−2i−2i2i2i-2-2-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2222-2-222-2-2222−2i−2i−2i−2i2i2i2i2i2222-2-2-2-2-2-2-2-2222i2i−2i−2i-2-2-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ4522222222-2-2-2-2-2-2-2-222-1-2-222-2-2-1-1-12i2i2i2i−2i−2i−2i−2i-1-1-1-111111111-1-1−2i−2i2i2i1111-1-1−i−iii−i−iiiii−i−iii−i−i0000−i3i30000−i3i3i3−i3i3−i33−33−3−33−3300000000000000000000000000000000
χ4622222222-2-2-2-2-2-2-2-222-1-2-222-2-2-1-1-12i2i2i2i−2i−2i−2i−2i-1-1-1-111111111-1-1−2i−2i2i2i1111-1-1−i−iii−i−iiiii−i−iii−i−i0000i3−i30000i3−i3−i3i3−i3i3−33−333−33−300000000000000000000000000000000
χ4722222222-2-2-2-2-2-2-2-222-1-2-222-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i-1-1-1-111111111-1-12i2i−2i−2i1111-1-1ii−i−iii−i−i−i−iii−i−iii0000−i3i30000−i3i3i3−i3i3−i3−33−333−33−300000000000000000000000000000000
χ4822222222-2-2-2-2-2-2-2-222-1-2-222-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i-1-1-1-111111111-1-12i2i−2i−2i1111-1-1ii−i−iii−i−i−i−iii−i−iii0000i3−i30000i3−i3−i3i3−i3i33−33−3−33−3300000000000000000000000000000000
χ4922222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-12i2i2i2i−2i−2i−2i−2i-1-1-1-111111111112i2i−2i−2i-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-2-1-12i2i−2i−2i-1-11111−i−i−i−iiiii00000000000000000000000000000000
χ5022222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-12i2i2i2i−2i−2i−2i−2i-1-1-1-111111111112i2i−2i−2i-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-2-22211−2i−2i2i2i11-1-1-1-1iiii−i−i−i−i00000000000000000000000000000000
χ5122222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-1−2i−2i−2i−2i2i2i2i2i-1-1-1-11111111111−2i−2i2i2i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i22-2-2-1-1−2i−2i2i2i-1-11111iiii−i−i−i−i00000000000000000000000000000000
χ5222222222-2-2-2-2-2-2-2-2-2-2-122-2-222-1-1-1−2i−2i−2i−2i2i2i2i2i-1-1-1-11111111111−2i−2i2i2i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-2-222112i2i−2i−2i11-1-1-1-1−i−i−i−iiiii00000000000000000000000000000000
χ532222-2-2-2-22222-2-2-2-222222-2-2-2-22222i2i−2i−2i2i2i−2i−2i-2-2-2-22222-2-2-2-222−2i2i−2i2i-2-222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ542222-2-2-2-22222-2-2-2-222222-2-2-2-2222−2i−2i2i2i−2i−2i2i2i-2-2-2-22222-2-2-2-2222i−2i2i−2i-2-222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ552222-2-2-2-22222-2-2-2-222-122-2-2-2-2-1-1-12i2i−2i−2i2i2i−2i−2i1111-1-1-1-11111-1-1−2i2i−2i2i11-1-111−i−iiiii−i−i−i−iiiii−i−i0000−i3i30000i3−i3−i3i3i3−i33−3−333−3−3300000000000000000000000000000000
χ562222-2-2-2-22222-2-2-2-222-122-2-2-2-2-1-1-12i2i−2i−2i2i2i−2i−2i1111-1-1-1-11111-1-1−2i2i−2i2i11-1-111−i−iiiii−i−i−i−iiiii−i−i0000i3−i30000−i3i3i3−i3−i3i3−333−3−333−300000000000000000000000000000000
χ572222-2-2-2-22222-2-2-2-222-122-2-2-2-2-1-1-1−2i−2i2i2i−2i−2i2i2i1111-1-1-1-11111-1-12i−2i2i−2i11-1-111ii−i−i−i−iiiii−i−i−i−iii0000−i3i30000i3−i3−i3i3i3−i3−333−3−333−300000000000000000000000000000000
χ582222-2-2-2-22222-2-2-2-222-122-2-2-2-2-1-1-1−2i−2i2i2i−2i−2i2i2i1111-1-1-1-11111-1-12i−2i2i−2i11-1-111ii−i−i−i−iiiii−i−i−i−iii0000i3−i30000−i3i3i3−i3−i3i33−3−333−3−3300000000000000000000000000000000
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χ1174-44-4−4i4i−4i4i4i−4i4i−4i-44-444-4-24i−4i−4i4i-442-22000000002i−2i2i−2i−2i2i−2i2i2-22-2-2200002-2−2i2i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000
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χ1304-4-44−4i4i4i−4i-444-4−4i4i4i−4i004000000-4-4400000000−4i4i4i−4i-444-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1314-4-44−4i4i4i−4i-444-4−4i4i4i−4i00-200000022-2000000002i−2i−2i2i2-2-222i−2i−2i2i00000000000000−2ζ7+2ζ232ζ7−2ζ2300−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23002ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000000000000000000000000000
χ1324-4-44−4i4i4i−4i-444-4−4i4i4i−4i00-200000022-2000000002i−2i−2i2i2-2-222i−2i−2i2i000000000000002ζ7−2ζ23−2ζ7+2ζ23002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.