Finite Group Databasebeta

← Group #13155665

Character table — Group #13155665

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11112222222222222222224444444444444444444444446666666666666666666666668888888888999912121212121212121212121212121212121212121212121212121818181818181818181824242424242424243636363672727272108108
order1222333446666666661212121233366666666612121212121212121212121288888888242424242424242424242424242424243666121212121212444444242424242424242424242424242424242424242424242424441212121212121212121212121212121244441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1
χ91-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-111-111-1-1ii−i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−iiiii−i−i−i−ii−ii−iii−i−ii−i1-11-1i−i1-1
χ101-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-111-111-1-1ii−i−i−ii111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−iiiii−i−i−i−i−ii−ii−i−iii−ii-11-11−ii-11
χ111-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-111-111-1-1−i−iiii−i111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−i−i−iiiiii−ii−iii−i−ii−i-11-11i−i-11
χ121-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-111-111-1-1−i−iii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−i−i−iiiii−ii−ii−i−iii−ii1-11-1−ii1-1
χ131-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1-111-111-1-1−i−iiii−i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−i−i−i−iiiiii−ii−iii−i−i−ii1-11-1−ii-11
χ141-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1-111-111-1-1−i−iii−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−i−i−i−iiiii−ii−ii−i−iiii−i-11-11i−i1-1
χ151-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1-111-111-1-1ii−i−ii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−iiiii−i−i−i−ii−ii−iii−i−i−ii-11-11−ii1-1
χ161-1-111111-1-1-111-1-1-11-111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1-111-111-1-1ii−i−i−ii-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−iiiii−i−i−i−i−ii−ii−i−iiii−i1-11-1i−i-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-2222200000000000000000000000000-2-222-2-222-2-2000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-2-2-2-2-20000000000000000000000000022-2-222-2-222000000000000000000
χ19222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122220022-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000
χ20222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-1-2-2-2-20022-1-1-1-122-1-1-1-1-2-21111-2-21111-2-211111111000000000000000000
χ21222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-200-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-211111111000000000000000000
χ22222222-122222-12-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1222200-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-1-1-1-1000000000000000000
χ23222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-211110000000033−3−333−3−333−3−333−3−3-1-1-1-1-2-211112222000033−3−30033−3−30033−3−30033−3−3-2-2-1-111-1-111000000000000000000
χ24222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-211110000000033−3−333−3−3−3−333−3−333-1-1-1-1-2-21111-2-2-2-2000033−3−30033−3−300−3−33300−3−3332211-1-111-1-1000000000000000000
χ25222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-2111100000000−3−333−3−33333−3−333−3−3-1-1-1-1-2-21111-2-2-2-20000−3−33300−3−3330033−3−30033−3−32211-1-111-1-1000000000000000000
χ26222222-1-2-2222-12-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-2111100000000−3−333−3−333−3−333−3−333-1-1-1-1-2-2111122220000−3−33300−3−33300−3−33300−3−333-2-2-1-111-1-111000000000000000000
χ2722222-12222-122-122-122222-12-1-122-1-1-12-1-12-1-1-1222-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000022000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000-1-122-1-1-1-10022-1-10000
χ2822222-12222-122-122-122222-12-1-122-1-1-12-1-12-1-1-1222-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-10000-2-2000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000011-2-2111100-2-2110000
χ2922222-12222-122-122-122222-12-1-122-1-1-12-1-12-1-1-1222-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000220000000000001111111111110000000000-1-122-1-1-1-100-2-2110000
χ3022222-12222-122-122-122222-12-1-122-1-1-12-1-12-1-1-1222-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2000000000000111111111111000000000011-2-211110022-1-10000
χ312222-12222-12-122222-12222-1-12-1-1-122-1-12-1-1222-1-1-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000022-1-1-1-1-1-1220000-1-100
χ322222-12222-12-122222-12222-1-12-1-1-122-1-12-1-1222-1-1-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-10000-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000-2-2111111-2-200001100
χ332222-12222-12-122222-12222-1-12-1-1-122-1-12-1-1222-1-1-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1000022111111111111000000000000000000000022-1-1-1-1-1-1-2-200001100
χ342222-12222-12-122222-12222-1-12-1-1-122-1-12-1-1222-1-1-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-10000-2-21111111111110000000000000000000000-2-2111111220000-1-100
χ3522-2-22220022-2-2-22-2-2-2000022222-22-2-2-2-2-20000000000002−22−22−22−22−22−22−22−22−22−22−22−222-2-20000002-22-2002−22−22−22−22−22−22−22−22−22−22−22−2002-2002-200000000000000000000
χ3622-2-22220022-2-2-22-2-2-2000022222-22-2-2-2-2-20000000000002−22−2−22−222−22−22−22−2−22−22−22−2222-2-2000000-22-22002−22−22−22−22−22−2−22−22−22−22−22−2200-2200-2200000000000000000000
χ3722-2-22220022-2-2-22-2-2-2000022222-22-2-2-2-2-2000000000000−22−222−22−2−22−22−22−222−22−22−22−222-2-2000000-22-2200−22−22−22−22−22−222−22−22−22−22−22−200-2200-2200000000000000000000
χ3822-2-22220022-2-2-22-2-2-2000022222-22-2-2-2-2-2000000000000−22−22−22−22−22−22−22−22−22−22−22−2222-2-20000002-22-200−22−22−22−22−22−22−22−22−22−22−22−22002-2002-200000000000000000000
χ3922-2-222-10022-21-2-11-2-23−33−32-1-12-11-11-211-2003−33−3003−33−32−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-1-111003−33−32-22-2002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300-113−3-113−3000000000000000000
χ4022-2-222-10022-21-2-11-2-23−33−32-1-12-11-11-211-2003−33−3003−33−32−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23-1-111003−33−3-22-22002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23001-1−331-1−33000000000000000000
χ4122-2-222-10022-21-2-11-2-23−33−32-1-12-11-11-211-2003−33−3003−33−3−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-1-111003−33−3-22-2200−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23001-1−331-1−33000000000000000000
χ4222-2-222-10022-21-2-11-2-23−33−32-1-12-11-11-211-2003−33−3003−33−3−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23-1-111003−33−32-22-200−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300-113−3-113−3000000000000000000
χ4322-2-222-10022-21-2-11-2-2−33−332-1-12-11-11-211-200−33−3300−33−332−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7-1-11100−33−332-22-2002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700-11−33-11−33000000000000000000
χ4422-2-222-10022-21-2-11-2-2−33−332-1-12-11-11-211-200−33−3300−33−332−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7-1-11100−33−33-22-22002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7001-13−31-13−3000000000000000000
χ4522-2-222-10022-21-2-11-2-2−33−332-1-12-11-11-211-200−33−3300−33−33−22−222−22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7-1-11100−33−33-22-2200−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7001-13−31-13−3000000000000000000
χ4622-2-222-10022-21-2-11-2-2−33−332-1-12-11-11-211-200−33−3300−33−33−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7-1-11100−33−332-22-200−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700-11−33-11−33000000000000000000
χ472-22-222200-2-2-2-22-22-220000222-2-22-22-2-2-220000000000002−2−22−i2i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i22-22-2000000−2i2i2i−2i002−22−22−2−22−22−22−i2i2−i2i2−i2i2i2−i2i2−i2i2−i200−2i2i002i−2i00000000000000000000
χ482-22-222200-2-2-2-22-22-220000222-2-22-22-2-2-220000000000002−2−22i2−i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i22-22-20000002i−2i−2i2i002−22−22−2−22−22−22i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2002i−2i00−2i2i00000000000000000000
χ492-22-222200-2-2-2-22-22-220000222-2-22-22-2-2-22000000000000−222−2−i2i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i22-22-20000002i−2i−2i2i00−22−22−222−22−22−2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2002i−2i00−2i2i00000000000000000000
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χ1388-8-88-4-4-4-8844-4-4444-4444-4-4222-2-2-2-2-2222-2-44-2-2224-4-2-222000000000000000000000000-111-1-2211-1-10000000000000000000000000000000000000000000000000000000000

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