Finite Group Databasebeta

← Group #10800210

Character table — Group #10800210

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222233333333444444444444444444444444446666666688888888888888888888881212121212121212121212121212121212121616161624242424
order1222444422223444466612121212444444442444444444666688888888121212124444444424446121212121212121212242424242424242444444444448888888861212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-111111-1-1111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-111
χ1011111111-1-111111-1-1111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-111-1-1
χ1111111111-1-111111-1-1111111111111111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1
χ1211111111-1-111111-1-1111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111
χ1311111111-1-111111-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1111-1-1
χ1411111111-1-111111-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-111-1-1-111
χ1511111111-1-111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-111
χ1611111111-1-111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11-1-1111-1-1
χ171111-1-1-1-111-1-1111-1-1111-1-1-1-11111-1-1-1-1-11ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-111-1-111-1-11-11-1-11ii−i−iii−i−iii−i−iii−i−i1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-11-1
χ181111-1-1-1-111-1-1111-1-1111-1-1-1-11111-1-1-1-1-11ii−i−iii−i−i11-1-1−i−iii−i−iii11-1-111-1-111-1-1-11-11-11ii−i−iii−i−i−i−iii−i−iii1-1ii−i−iii−i−i−i−iii−i−iii-1-111-11-11
χ191111-1-1-1-111-1-1111-1-1111-1-1-1-11111-1-1-1-1-11−i−iii−i−iii11-1-1ii−i−iii−i−i11-1-111-1-111-1-1-11-11-11−i−iii−i−iiiii−i−iii−i−i1-1−i−iii−i−iiiii−i−iii−i−i-1-111-11-11
χ201111-1-1-1-111-1-1111-1-1111-1-1-1-11111-1-1-1-1-11−i−iii−i−iii11-1-1−i−iii−i−iii11-1-111-1-111-1-11-11-1-11−i−iii−i−iii−i−iii−i−iii1-1−i−iii−i−iii−i−iii−i−iii11-1-11-11-1
χ211111-1-1-1-111-1-1111-1-1111-1-1-1-1-1-1-1-11111-11ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1-1-111-1-1111-11-1-11ii−i−iii−i−iii−i−iii−i−i-11−i−iii−i−iii−i−iii−i−iii11-1-1-11-11
χ221111-1-1-1-111-1-1111-1-1111-1-1-1-1-1-1-1-11111-11ii−i−iii−i−i11-1-1−i−iii−i−iii11-1-1-1-111-1-111-11-11-11ii−i−iii−i−i−i−iii−i−iii-11−i−iii−i−iiiii−i−iii−i−i-1-1111-11-1
χ231111-1-1-1-111-1-1111-1-1111-1-1-1-1-1-1-1-11111-11−i−iii−i−iii11-1-1ii−i−iii−i−i11-1-1-1-111-1-111-11-11-11−i−iii−i−iiiii−i−iii−i−i-11ii−i−iii−i−i−i−iii−i−iii-1-1111-11-1
χ241111-1-1-1-111-1-1111-1-1111-1-1-1-1-1-1-1-11111-11−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1-1-111-1-1111-11-1-11−i−iii−i−iii−i−iii−i−iii-11ii−i−iii−i−iii−i−iii−i−i11-1-1-11-11
χ251111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1ii−i−i−i−iii-1-1-1-1ii−i−i−i−iii111111-1-1-1-1111-1-111-1ii−i−i−i−iiiii−i−i−i−iii-11ii−i−i−i−iiiii−i−i−i−iii1-11-1-111-1
χ261111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1ii−i−i−i−iii-1-1-1-1−i−iiiii−i−i111111-1-1-1-111-111-11-1ii−i−i−i−iii−i−iiiii−i−i-11ii−i−i−i−iii−i−iiiii−i−i-11-111-1-11
χ271111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1−i−iiiii−i−i-1-1-1-1ii−i−i−i−iii111111-1-1-1-111-111-11-1−i−iiiii−i−iii−i−i−i−iii-11−i−iiiii−i−iii−i−i−i−iii-11-111-1-11
χ281111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-1−i−iiiii−i−i-1-1-1-1−i−iiiii−i−i111111-1-1-1-1111-1-111-1−i−iiiii−i−i−i−iiiii−i−i-11−i−iiiii−i−i−i−iiiii−i−i1-11-1-111-1
χ291111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii-1-1-1-1ii−i−i−i−iii1111-1-11111-1-11-1-111-1ii−i−i−i−iiiii−i−i−i−iii1-1−i−iiiii−i−i−i−iiiii−i−i1-11-11-1-11
χ301111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii-1-1-1-1−i−iiiii−i−i1111-1-11111-1-1-111-11-1ii−i−i−i−iii−i−iiiii−i−i1-1−i−iiiii−i−iii−i−i−i−iii-11-11-111-1
χ311111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i-1-1-1-1ii−i−i−i−iii1111-1-11111-1-1-111-11-1−i−iiiii−i−iii−i−i−i−iii1-1ii−i−i−i−iii−i−iiiii−i−i-11-11-111-1
χ321111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i-1-1-1-1−i−iiiii−i−i1111-1-11111-1-11-1-111-1−i−iiiii−i−i−i−iiiii−i−i1-1ii−i−i−i−iiiii−i−i−i−iii1-11-11-1-11
χ33222222222222-12222-1-1-1-1-1-1-1000000002222222222-1-1-1-122222222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-1-1-1-10000
χ34222222222222-12222-1-1-1-1-1-1-1000000002222222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000000011110000
χ35222222222222-12222-1-1-1-1-1-1-10000000022-2-2-2-2-2-2-2-2-1-1-1-122222222-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-100000000000000000011110000
χ36222222222222-12222-1-1-1-1-1-1-10000000022-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1000000002222-1-11111111111111111000000000000000000-1-1-1-10000
χ372222222222-2-22-2-222222222222222222-2-20000000022-2-200000000-2-222-2-2-2-222220000-2-20000000000000000-2-2000000000000000000000000
χ382222222222-2-22-2-2222222222-2-2-2-2-2-2-2-2-2-20000000022-2-200000000-2-2222222-2-2-2-20000-2-2000000000000000022000000000000000000000000
χ3922222222-2-222-122-2-2-1-1-1-1-1-1-100000000-2-22222-2-2-2-211-1-12222-2-2-2-2-1-1110000000022-2-211-1-1-1-11111-1-1-1-11111000000000000000000-111-10000
χ4022222222-2-222-122-2-2-1-1-1-1-1-1-100000000-2-22222-2-2-2-211-1-1-2-2-2-22222-1-11100000000-2-22211-1-1-1-111111111-1-1-1-10000000000000000001-1-110000
χ4122222222-2-222-122-2-2-1-1-1-1-1-1-100000000-2-2-2-2-2-2222211-1-12222-2-2-2-2-1-11100000000-2-222111111-1-1-1-1-1-1-1-111110000000000000000001-1-110000
χ4222222222-2-222-122-2-2-1-1-1-1-1-1-100000000-2-2-2-2-2-2222211-1-1-2-2-2-22222-1-1110000000022-2-2111111-1-1-1-11111-1-1-1-1000000000000000000-111-10000
χ4322222222-2-2-2-22-2-2-2-22222222222222222200000000-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2000022000000000000000022000000000000000000000000
χ4422222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-200000000-2-2-2-2222222220000220000000000000000-2-2000000000000000000000000
χ452222-2-2-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-22-200000000222200000000-2-2-2-2-2-22222-2-200002-20000000000000000-22000000000000000000000000
χ462222-2-2-2-222222-2-2-2-2222-2-2-2-2-2-2-2-222222-200000000222200000000-2-2-2-222-2-2-2-22200002-200000000000000002-2000000000000000000000000
χ472222-2-2-2-222-2-2-122-2-2-1-1-1111100000000-222i2i−2i−2i2i2i−2i−2i-1-1112i2i−2i−2i2i2i−2i−2i-1-111000000002-22-21-1−i−iii−i−iii−i−iii−i−iii000000000000000000-1-1110000
χ482222-2-2-2-222-2-2-122-2-2-1-1-1111100000000-222i2i−2i−2i2i2i−2i−2i-1-111−2i−2i2i2i−2i−2i2i2i-1-11100000000-22-221-1−i−iii−i−iiiii−i−iii−i−i00000000000000000011-1-10000
χ492222-2-2-2-222-2-2-122-2-2-1-1-1111100000000-22−2i−2i2i2i−2i−2i2i2i-1-1112i2i−2i−2i2i2i−2i−2i-1-11100000000-22-221-1ii−i−iii−i−i−i−iii−i−iii00000000000000000011-1-10000
χ502222-2-2-2-222-2-2-122-2-2-1-1-1111100000000-22−2i−2i2i2i−2i−2i2i2i-1-111−2i−2i2i2i−2i−2i2i2i-1-111000000002-22-21-1ii−i−iii−i−iii−i−iii−i−i000000000000000000-1-1110000
χ512222-2-2-2-2-2-2222-2-222222-2-2-2-22222-2-2-2-2-2200000000-2-22200000000-2-222-2-222-2-2220000-2200000000000000002-2000000000000000000000000
χ522222-2-2-2-2-2-2222-2-222222-2-2-2-2-2-2-2-22222-2200000000-2-22200000000-2-22222-2-222-2-20000-220000000000000000-22000000000000000000000000
χ532222-2-2-2-2-2-2-2-2-12222-1-1-11111000000002-22i2i−2i−2i−2i−2i2i2i11112i2i−2i−2i−2i−2i2i2i-1-1-1-1000000002-2-22-11−i−iiiii−i−i−i−iiiii−i−i000000000000000000-11-110000
χ542222-2-2-2-2-2-2-2-2-12222-1-1-11111000000002-22i2i−2i−2i−2i−2i2i2i1111−2i−2i2i2i2i2i−2i−2i-1-1-1-100000000-222-2-11−i−iiiii−i−iii−i−i−i−iii0000000000000000001-11-10000
χ552222-2-2-2-2-2-2-2-2-12222-1-1-11111000000002-2−2i−2i2i2i2i2i−2i−2i11112i2i−2i−2i−2i−2i2i2i-1-1-1-100000000-222-2-11ii−i−i−i−iii−i−iiiii−i−i0000000000000000001-11-10000
χ562222-2-2-2-2-2-2-2-2-12222-1-1-11111000000002-2−2i−2i2i2i2i2i−2i−2i1111−2i−2i2i2i2i2i−2i−2i-1-1-1-1000000002-2-22-11ii−i−i−i−iiiii−i−i−i−iii000000000000000000-11-110000
χ5722-2-222-2-2002-222-200-2-22-2-2222i2i−2i−2i2i2i−2i−2i0000000000002-22-22-200002-2002i−2i2i−2i0000000000000000002-22-2000000000000002i−2i2i−2i000000000000
χ5822-2-222-2-2002-222-200-2-22-2-2222i2i−2i−2i2i2i−2i−2i0000000000002-2-22-2200002-2002i−2i2i−2i000000000000000000-22-2200000000000000−2i2i−2i2i000000000000
χ5922-2-222-2-2002-222-200-2-22-2-222−2i−2i2i2i−2i−2i2i2i0000000000002-22-22-200002-200−2i2i−2i2i0000000000000000002-22-200000000000000−2i2i−2i2i000000000000
χ6022-2-222-2-2002-222-200-2-22-2-222−2i−2i2i2i−2i−2i2i2i0000000000002-2-22-2200002-200−2i2i−2i2i000000000000000000-22-22000000000000002i−2i2i−2i000000000000
χ6122-2-222-2-200-222-2200-2-22-2-2222i2i−2i−2i2i2i−2i−2i000000000000-2200002-22-2-2200−2i2i−2i2i00000000000000000000002-22-2000000000000002i−2i2i−2i00000000
χ6222-2-222-2-200-222-2200-2-22-2-2222i2i−2i−2i2i2i−2i−2i000000000000-220000-22-22-2200−2i2i−2i2i0000000000000000000000-22-2200000000000000−2i2i−2i2i00000000
χ6322-2-222-2-200-222-2200-2-22-2-222−2i−2i2i2i−2i−2i2i2i000000000000-2200002-22-2-22002i−2i2i−2i00000000000000000000002-22-200000000000000−2i2i−2i2i00000000
χ6422-2-222-2-200-222-2200-2-22-2-222−2i−2i2i2i−2i−2i2i2i000000000000-220000-22-22-22002i−2i2i−2i0000000000000000000000-22-22000000000000002i−2i2i−2i00000000
χ6522-2-2-2-222002-22-2200-2-2222-2-22i2i−2i−2i−2i−2i2i2i0000000000002-200002i−2i−2i2i-2200−2i2i2i−2i00000000000000000000002i−2i−2i2i00000000000000-222-200000000
χ6622-2-2-2-222002-22-2200-2-2222-2-22i2i−2i−2i−2i−2i2i2i0000000000002-20000−2i2i2i−2i-2200−2i2i2i−2i0000000000000000000000−2i2i2i−2i000000000000002-2-2200000000
χ6722-2-2-2-222002-22-2200-2-2222-2-2−2i−2i2i2i2i2i−2i−2i0000000000002-200002i−2i−2i2i-22002i−2i−2i2i00000000000000000000002i−2i−2i2i000000000000002-2-2200000000
χ6822-2-2-2-222002-22-2200-2-2222-2-2−2i−2i2i2i2i2i−2i−2i0000000000002-20000−2i2i2i−2i-22002i−2i−2i2i0000000000000000000000−2i2i2i−2i00000000000000-222-200000000
χ6922-2-2-2-22200-2222-200-2-2222-2-22i2i−2i−2i−2i−2i2i2i000000000000-222i−2i−2i2i00002-2002i−2i−2i2i0000000000000000002i−2i−2i2i00000000000000-222-2000000000000
χ7022-2-2-2-22200-2222-200-2-2222-2-22i2i−2i−2i−2i−2i2i2i000000000000-22−2i2i2i−2i00002-2002i−2i−2i2i000000000000000000−2i2i2i−2i000000000000002-2-22000000000000
χ7122-2-2-2-22200-2222-200-2-2222-2-2−2i−2i2i2i2i2i−2i−2i000000000000-222i−2i−2i2i00002-200−2i2i2i−2i0000000000000000002i−2i−2i2i000000000000002-2-22000000000000
χ7222-2-2-2-22200-2222-200-2-2222-2-2−2i−2i2i2i2i2i−2i−2i000000000000-22−2i2i2i−2i00002-200−2i2i2i−2i000000000000000000−2i2i2i−2i00000000000000-222-2000000000000
χ732-22-22i−2i2i−2i2-2002002i−2i2-2-22i−2i2i−2i2-22-22i−2i2i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i2-20000000000002i−2i00002-22i−2i0000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000000000
χ742-22-22i−2i2i−2i2-2002002i−2i2-2-22i−2i2i−2i2-22-22i−2i2i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i2-20000000000002i−2i00002-22i−2i000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000000000
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χ1138-8-888i−8i−8i8i0000-400004-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88−8i8i8i−8i0000-400004-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).