Finite Group Databasebeta

← Group #13155648

Character table — Group #13155648

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11112222222222222222224444444444444444444444446666666666666666666666668888888888999912121212121212121212121212121212121212121212121212121818181818181818181824242424242424243636363672727272108108
order12223334466666666612121212333666666666121212121212121212121212888888882424242424242424242424242424242436661212121212124444442424242424242424242424242424242424242424242424244412121212121212121212121212121212224466121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
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
χ91-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1-111-111-1-1ii−i−ii−iiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1i−iiiii−i−i−i−iii−i−iii−i−i1-1i−i1-1i−i1-1
χ101-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1-111-111-1-1ii−i−i−iiiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1i−iiiii−i−i−i−i−i−iii−i−iii-11−ii-11−ii-11
χ111-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1ii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1-111-111-1-1−i−iiii−iiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−ii−i−i−i−iiiiiii−i−iii−i−i1-1−ii1-1−ii-11
χ121-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1ii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1-111-111-1-1−i−iii−iiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−ii−i−i−i−iiiii−i−iii−i−iii-11i−i-11i−i1-1
χ131-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1-111-111-1-1−i−iiii−i−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−ii−i−i−i−iiiiiii−i−iii−i−i-11i−i-11i−i-11
χ141-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1-111-111-1-1−i−iii−ii−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−ii−i−i−i−iiiii−i−iii−i−iii1-1−ii1-1−ii1-1
χ151-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-111-111-1-1ii−i−ii−i−i−i−i−i−i−iiiiiii-1-1-1-1-1-1111111i−iiiii−i−i−i−iii−i−iii−i−i-11−ii-11−ii1-1
χ161-1-111111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-1−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-111-111-1-1ii−i−i−ii−i−i−i−i−i−iiiiiii-1-1-1-1-1-1111111i−iiiii−i−i−i−i−i−iii−i−iii1-1i−i1-1i−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
χ19222222-122-122-12-122222222-1-122-1-1-12-1-1-1-12-1-1222-122-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000002-12-1-1-1-1-12200-1-10000
χ20222222-122-122-12-122222222-1-122-1-1-12-1-1-1-12-1-1222-122-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-10000-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000-21-211111-2-200110000
χ21222222-122-122-12-122222222-1-122-1-1-12-1-1-1-12-1-1222-122-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-100002211111111111100000000000000000000002-12-1-1-1-1-1-2-200110000
χ22222222-122-122-12-122222222-1-122-1-1-12-1-1-1-12-1-1222-122-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-10000-2-21111111111110000000000000000000000-21-2111112200-1-10000
χ2322222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122220022-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000
χ2422222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-1-2-2-2-20022-1-1-1-122-1-1-1-1-2-21111-2-21111-2-211111111000000000000000000
χ2522222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-200-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-211111111000000000000000000
χ2622222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1222200-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-1-1-1-1000000000000000000
χ2722222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-211110000000033−3−333−3−333−3−333−3−3-1-1-1-1-2-211112222000033−3−30033−3−30033−3−30033−3−3-2-2-1-111-1-111000000000000000000
χ2822222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-211110000000033−3−333−3−3−3−333−3−333-1-1-1-1-2-21111-2-2-2-2000033−3−30033−3−300−3−33300−3−3332211-1-111-1-1000000000000000000
χ2922222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-2111100000000−3−333−3−33333−3−333−3−3-1-1-1-1-2-21111-2-2-2-20000−3−33300−3−3330033−3−30033−3−32211-1-111-1-1000000000000000000
χ3022222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-2111100000000−3−333−3−333−3−333−3−333-1-1-1-1-2-2111122220000−3−33300−3−33300−3−33300−3−333-2-2-1-111-1-111000000000000000000
χ312222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-122000022220000000022222222-1-1-1-1-1-1-1-1-1-1000022000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000-12-12-1-1-1-1002200-1-100
χ322222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-122000022220000000022222222-1-1-1-1-1-1-1-1-1-10000-2-2000000000000-1-1-1-1-1-1-1-1-1-1-1-100000000001-21-2111100-2-2001100
χ332222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-1220000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000220000000000001111111111110000000000-12-12-1-1-1-100-2-2001100
χ342222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-1220000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-200000000000011111111111100000000001-21-21111002200-1-100
χ3522-2-222200-2-2-2-2222-2-200002222-2-22-2-2-2-220000000000002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i222-2-20000002i−2i2i−2i002−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i00000000000000000000
χ3622-2-222200-2-2-2-2222-2-200002222-2-22-2-2-2-220000000000002−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i222-2-2000000−2i2i−2i2i002−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i00000000000000000000
χ3722-2-222200-2-2-2-2222-2-200002222-2-22-2-2-2-22000000000000−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i222-2-2000000−2i2i−2i2i00−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i00000000000000000000
χ3822-2-222200-2-2-2-2222-2-200002222-2-22-2-2-2-22000000000000−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i222-2-20000002i−2i2i−2i00−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i00000000000000000000
χ3922-2-22-1200-2-21-222-11-23−33−3-12-1-11-2-111-212003−33−3003−33−32−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-1-111003−33−32i−2i2i−2i002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700−ii−i3i3−ii−i3i3000000000000000000
χ4022-2-22-1200-2-21-222-11-23−33−3-12-1-11-2-111-212003−33−3003−33−32−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-1-111003−33−3−2i2i−2i2i002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700i−ii3−i3i−ii3−i3000000000000000000
χ4122-2-22-1200-2-21-222-11-23−33−3-12-1-11-2-111-212003−33−3003−33−3−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-1-111003−33−3−2i2i−2i2i00−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700i−ii3−i3i−ii3−i3000000000000000000
χ4222-2-22-1200-2-21-222-11-23−33−3-12-1-11-2-111-212003−33−3003−33−3−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-1-111003−33−32i−2i2i−2i00−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700−ii−i3i3−ii−i3i3000000000000000000
χ4322-2-22-1200-2-21-222-11-2−33−33-12-1-11-2-111-21200−33−3300−33−332−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23-1-11100−33−332i−2i2i−2i002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300−iii3−i3−iii3−i3000000000000000000
χ4422-2-22-1200-2-21-222-11-2−33−33-12-1-11-2-111-21200−33−3300−33−332−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23-1-11100−33−33−2i2i−2i2i002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300i−i−i3i3i−i−i3i3000000000000000000
χ4522-2-22-1200-2-21-222-11-2−33−33-12-1-11-2-111-21200−33−3300−33−33−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23-1-11100−33−33−2i2i−2i2i00−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300i−i−i3i3i−i−i3i3000000000000000000
χ4622-2-22-1200-2-21-222-11-2−33−33-12-1-11-2-111-21200−33−3300−33−33−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23-1-11100−33−332i−2i2i−2i00−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300−iii3−i3−iii3−i3000000000000000000
χ472-22-2222002-2-2-2-2-2-2220000222-222-22-2-2-2-2000000000000−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22-22-20000002-2-2200−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2002-200-2200000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.