Finite Group Databasebeta

← Group #10762165

Character table — Group #10762165

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111111122222222222222222222222244444444444444444444444444444444446666666688888888888888888888888812121212121212121212121212121212242424242424
order1222444434444444444444444666121212122224448888121212121212121212121212121212122424242424242424888888886668888881212122424242424242424242424242244888888888888444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ6111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ7111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1
χ911111111111-1-1-1-11111-1-1-1-1111111111-11-1-11-111111111-1-1-1-11111-1-1-1-11111111111111111-11-1-1-111-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1
χ1011111111111-1-1-1-11111-1-1-1-1111111111-11-1-11-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111
χ1111111111111-1-1-1-11111-1-1-1-1111111111-11-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111-1-111-11-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ1211111111111-1-1-1-11111-1-1-1-1111111111-11-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-11-11111-1-1-1-1111111111111-1-1-1-11111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-111111111111111111111-1-11-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ1411111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ1511111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1611111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ171111-1-1-1-111111-1-111-1-111-1-1-1-1111-1-1-1-111-1-1-11ii−i−i11-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1i−ii−ii−i-1-11ii−i−iii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−i1-11-11-1
χ181111-1-1-1-111111-1-111-1-111-1-1-1-1111-1-1-1-111-1-1-11ii−i−i11-1-111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1i−ii−ii−i-1-11ii−i−iii−i−iii−i−i-1-111−i−iii−i−iii−i−iii-11-11-11
χ191111-1-1-1-111111-1-111-1-111-1-1-1-1111-1-1-1-111-1-1-11−i−iii11-1-111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1−ii−ii−ii-1-11−i−iii−i−iii−i−iii-1-111ii−i−iii−i−iii−i−i-11-11-11
χ201111-1-1-1-111111-1-111-1-111-1-1-1-1111-1-1-1-111-1-1-11−i−iii11-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1−ii−ii−ii-1-11−i−iii−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii1-11-11-1
χ211111-1-1-1-111111-1-1-1-111-1-111-1-1111-1-1-1-11-11-11-1ii−i−i11-1-111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1-11i−i−ii−ii-11-1ii−i−i−i−iii−i−iii11-1-1ii−i−i−i−iii−i−iii1-1-11-11
χ221111-1-1-1-111111-1-1-1-111-1-111-1-1111-1-1-1-11-11-11-1ii−i−i11-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-11i−i−ii−ii-11-1ii−i−i−i−iii−i−iii-1-111−i−iiiii−i−iii−i−i-111-11-1
χ231111-1-1-1-111111-1-1-1-111-1-111-1-1111-1-1-1-11-11-11-1−i−iii11-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11−iii−ii−i-11-1−i−iiiii−i−iii−i−i-1-111ii−i−i−i−iii−i−iii-111-11-1
χ241111-1-1-1-111111-1-1-1-111-1-111-1-1111-1-1-1-11-11-11-1−i−iii11-1-111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1-11−iii−ii−i-11-1−i−iiiii−i−iii−i−i11-1-1−i−iiiii−i−iii−i−i1-1-11-11
χ251111-1-1-1-1111-1-11111-1-1-1-111-1-1111-1-1-1-1-1111-1-1ii−i−i11-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-111−iii−i−ii1-1-1−i−iiiii−i−i−i−iii11-1-1−i−iiiii−i−i−i−iii-111-1-11
χ261111-1-1-1-1111-1-11111-1-1-1-111-1-1111-1-1-1-1-1111-1-1ii−i−i11-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111−iii−i−ii1-1-1−i−iiiii−i−i−i−iii-1-111ii−i−i−i−iiiii−i−i1-1-111-1
χ271111-1-1-1-1111-1-11111-1-1-1-111-1-1111-1-1-1-1-1111-1-1−i−iii11-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111i−i−iii−i1-1-1ii−i−i−i−iiiii−i−i-1-111−i−iiiii−i−i−i−iii1-1-111-1
χ281111-1-1-1-1111-1-11111-1-1-1-111-1-1111-1-1-1-1-1111-1-1−i−iii11-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-111i−i−iii−i1-1-1ii−i−i−i−iiiii−i−i11-1-1ii−i−i−i−iiiii−i−i-111-1-11
χ291111-1-1-1-1111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-1111ii−i−i11-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1−ii−iii−i111−i−iii−i−iiiii−i−i11-1-1−i−iii−i−iiiii−i−i-11-111-1
χ301111-1-1-1-1111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-1111ii−i−i11-1-1-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1−ii−iii−i111−i−iii−i−iiiii−i−i-1-111ii−i−iii−i−i−i−iii1-11-1-11
χ311111-1-1-1-1111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-1111−i−iii11-1-1-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1i−ii−i−ii111ii−i−iii−i−i−i−iii-1-111−i−iii−i−iiiii−i−i1-11-1-11
χ321111-1-1-1-1111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-1111−i−iii11-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1i−ii−i−ii111ii−i−iii−i−i−i−iii11-1-1ii−i−iii−i−i−i−iii-11-111-1
χ33222222222-2-2222222222222-2-22222222-2-2-2-2-2-20000-2-2-2-22222222222220000000000000000-2-2-2000000-2-2-20000000000000000000000000000000000
χ34222222222-2-22222-2-2-2-2-2-2-2-2-2-22222222-222-2220000-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-222000000-2220000000000000000000000000000000000
χ35222222222-2-2-2-2-2-22222-2-2-2-2-2-222222222-222-220000-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002-220000002-220000000000000000000000000000000000
χ36222222222-2-2-2-2-2-2-2-2-2-22222-2-2222222222-222-20000-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-200000022-20000000000000000000000000000000000
χ3722222222-12222222222222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3822222222-12222222222222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111100000000-1-1-1-2-2-2-2-2-2-1-1-11111111111110000000000000000000000
χ3922222222-1222222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12-2-22-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-100000000-11122-2-2-2-2-111-1-1-1-1111111110000000000000000000000
χ4022222222-1222222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000-111-2-22222-1111111-1-1-1-1-1-1-1-10000000000000000000000
χ4122222222-122-2-2-2-22222-2-2-2-222-1-1-1-1-1-1-1-22-2-22-22222-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1000000001-11-2-222-2-21-111111-1-1-1-111110000000000000000000000
χ4222222222-122-2-2-2-22222-2-2-2-222-1-1-1-1-1-1-1-22-2-22-2-2-2-2-2-1-1-1-11111-1-1-1-1111111111111000000001-1122-2-2221-11-1-1-1-11111-1-1-1-10000000000000000000000
χ4322222222-122-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-2-22-2-222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-10000000011-1-2-2-2-22211-111111111-1-1-1-10000000000000000000000
χ4422222222-122-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-2-22-2-22-2-2-2-2-1-1-1-111111111-1-1-1-1111111110000000011-12222-2-211-1-1-1-1-1-1-1-1-111110000000000000000000000
χ4522222222-1-2-2222222222222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000111000000111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000000000
χ4622222222-1-2-2222222222222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-1-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000111000000111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000000000
χ4722222222-1-2-22222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-222-22200001111-1-1-1-111111111−i3−i3i3i3−i3−i3i3i3000000001-1-10000001-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000000000
χ4822222222-1-2-22222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-222-22200001111-1-1-1-111111111i3i3−i3−i3i3i3−i3−i3000000001-1-10000001-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000000000
χ4922222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-12-222-22000011111111-1-1-1-11111−i3−i3i3i3−i3−i3i3i300000000-11-1000000-11-1i3−i3i3−i3−i3i3−i3i3i3−i3i3−i30000000000000000000000
χ5022222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-12-222-22000011111111-1-1-1-11111i3i3−i3−i3i3i3−i3−i300000000-11-1000000-11-1−i3i3−i3i3i3−i3i3−i3−i3i3−i3i30000000000000000000000
χ5122222222-1-2-2-2-2-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-122-222-20000111111111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000-1-11000000-1-11i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000000000
χ5222222222-1-2-2-2-2-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-122-222-20000111111111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000-1-11000000-1-11−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000000000
χ532222-2-2-2-22-2-222-2-222-2-222-2-222222-2-2-2-2-2-2222-20000-2-22222-2-222-2-222-2-20000000000000000-2-2200000022-20000000000000000000000000000000000
χ542222-2-2-2-22-2-222-2-2-2-222-2-22222222-2-2-2-2-22-22-220000-2-22222-2-2-2-222-2-2220000000000000000-22-20000002-220000000000000000000000000000000000
χ552222-2-2-2-22-2-2-2-22222-2-2-2-22222222-2-2-2-22-2-2-2220000-2-222-2-22222-2-2-2-22200000000000000002-2-2000000-2220000000000000000000000000000000000
χ562222-2-2-2-22-2-2-2-222-2-22222-2-222222-2-2-2-2222-2-2-20000-2-222-2-222-2-22222-2-20000000000000000222000000-2-2-20000000000000000000000000000000000
χ572222-2-2-2-2-12222-2-222-2-222-2-2-2-2-1-1-1111122-2-2-222i2i−2i−2i-1-111-1-111-1-111-1-111−i−i−i−iiiii00000000-1-112i−2i2i−2i2i−2i11-1−i−iii−i−iii−i−iii0000000000000000000000
χ582222-2-2-2-2-12222-2-222-2-222-2-2-2-2-1-1-1111122-2-2-22−2i−2i2i2i-1-111-1-111-1-111-1-111iiii−i−i−i−i00000000-1-11−2i2i−2i2i−2i2i11-1ii−i−iii−i−iii−i−i0000000000000000000000
χ592222-2-2-2-2-12222-2-2-2-222-2-222-2-2-1-1-111112-22-22-22i2i−2i−2i-1-111-1-11111-1-111-1-1−i−i−i−iiiii00000000-11-12i−2i−2i2i−2i2i1-11−i−iiiii−i−iii−i−i0000000000000000000000
χ602222-2-2-2-2-12222-2-2-2-222-2-222-2-2-1-1-111112-22-22-2−2i−2i2i2i-1-111-1-11111-1-111-1-1iiii−i−i−i−i00000000-11-1−2i2i2i−2i2i−2i1-11ii−i−i−i−iii−i−iii0000000000000000000000
χ612222-2-2-2-2-122-2-22222-2-2-2-222-2-2-1-1-11111-2222-2-22i2i−2i−2i-1-11111-1-1-1-11111-1-1−i−i−i−iiiii000000001-1-1−2i2i2i−2i−2i2i-111ii−i−i−i−iiiii−i−i0000000000000000000000
χ622222-2-2-2-2-122-2-22222-2-2-2-222-2-2-1-1-11111-2222-2-2−2i−2i2i2i-1-11111-1-1-1-11111-1-1iiii−i−i−i−i000000001-1-12i−2i−2i2i2i−2i-111−i−iiiii−i−i−i−iii0000000000000000000000
χ632222-2-2-2-2-122-2-222-2-22222-2-2-2-2-1-1-11111-2-2-22222i2i−2i−2i-1-11111-1-111-1-1-1-111−i−i−i−iiiii00000000111−2i2i−2i2i2i−2i-1-1-1ii−i−iii−i−i−i−iii0000000000000000000000
χ642222-2-2-2-2-122-2-222-2-22222-2-2-2-2-1-1-11111-2-2-2222−2i−2i2i2i-1-11111-1-111-1-1-1-111iiii−i−i−i−i000000001112i−2i2i−2i−2i2i-1-1-1−i−iii−i−iiiii−i−i0000000000000000000000
χ652222-2-2-2-2-1-2-222-2-222-2-222-2-222-1-1-11111-2-2222-2000011-1-1-1-111-1-111-1-11133−3−3−3−3330000000011-1000000-1-113−3−333−3−333−3−330000000000000000000000
χ662222-2-2-2-2-1-2-222-2-222-2-222-2-222-1-1-11111-2-2222-2000011-1-1-1-111-1-111-1-111−3−33333−3−30000000011-1000000-1-11−333−3−333−3−333−30000000000000000000000
χ672222-2-2-2-2-1-2-222-2-2-2-222-2-22222-1-1-11111-22-22-22000011-1-1-1-11111-1-111-1-133−3−3−3−333000000001-11000000-11-13−3−33−333−3−333−30000000000000000000000
χ682222-2-2-2-2-1-2-222-2-2-2-222-2-22222-1-1-11111-22-22-22000011-1-1-1-11111-1-111-1-1−3−33333−3−3000000001-11000000-11-1−333−33−3−333−3−330000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.