Finite Group Databasebeta

← Group #13155001

Character table — Group #13155001

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11112222222222444444444444444444444444444466666666666666666666666688888888889999121212121212121212121212121212121212121212121212181818181818181818183636363672727272108108108108
order12442346661212121233336666666666121212121212121212121212121288888888242424242424242424242424242424243666612121212122244242424242424242424242424242424242424242424242424246666121212128888242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ51111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-1-11-111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1111-1-111-1-111-1-111-1-1ii−i−i
χ61111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-1-11-111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1111-1-111-1-1-1-111-1-111−i−iii
χ71111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1-1-1-11-111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1111-1-111-1-111-1-111-1-1−i−iii
χ81111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1-1-1-11-111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1111-1-111-1-1-1-111-1-111ii−i−i
χ911-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-1-1-111iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-11-1-1-1-11111i−ii−ii−ii−i1-11-1
χ1011-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-1-1-111iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-11-1-1-1-11111−ii−ii−ii−ii-11-11
χ1111-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111-1-1-1-1-1-1-111−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-11-1-1-1-11111i−ii−ii−ii−i-11-11
χ1211-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111-1-1-1-1-1-1-111−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-11-1-1-1-11111−ii−ii−ii−ii1-11-1
χ1311-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11111-1-1i−i−iii−i−ii−iii−i
χ1411-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11111-1-1−iii−i−iii−ii−i−ii
χ1511-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-1-11111-1-1i−i−iii−i−iii−i−ii
χ1611-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-1-11111-1-1−iii−i−iii−i−iii−i
χ172222222222222222222222222222222222222222220000000000000000000000002222222222-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2000000000000
χ1822222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-12200000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-12-1-1-12-1-1-1-1-2-2-2-200−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-211111111000000000000
χ1922222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-12200000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-12-1-1-12-1-1-1-1-2-2-2-200i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-211111111000000000000
χ2022222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ2122222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-2-2-2-2-2-2-2-21111111111111111-12-1-1-12-1-1-1-12222-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-1-1-1-1000000000000
χ222222-22-2-2-2222-2-22222-2-2-2-2-2-22222222222-2-2-2-2-2-2220000000000000000000000002-2-2-22-222-2-22222000000000000000000000000-2-2-2-222-2-222000000000000
χ232222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-21111220000000033−3−333−3−3−3−333−3−333-1-211-1-2-1-11122220033−3−30033−3−300−3−33300−3−333-2-211-1-111-1-1000000000000
χ242222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-211112200000000−3−333−3−33333−3−333−3−3-1-211-1-2-1-111222200−3−33300−3−3330033−3−30033−3−3-2-211-1-111-1-1000000000000
χ252222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-21111222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii-1-211-1-2-1-111-2-2-2-22i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii22-1-111-1-111000000000000
χ262222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i-1-211-1-2-1-111-2-2-2-2−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i22-1-111-1-111000000000000
χ2722-2-222-2222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000022222-2-2-2-2-222-2-20000000000000000000000002-22222-2-2-2-2000000000000
χ2822-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-20000000033−3−3−3−33333−3−3−3−333-12-1-1-1-2111122-2-20033−3−300−3−3330033−3−300−3−3332-2-1-1-1-11111000000000000
χ2922-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-200000000−3−33333−3−3−3−33333−3−3-12-1-1-1-2111122-2-200−3−3330033−3−300−3−3330033−3−32-2-1-1-1-11111000000000000
χ3022-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-22i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii-12-1-1-1-21111-2-2222i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii-221111-1-1-1-1000000000000
χ3122-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i-12-1-1-1-21111-2-222−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i-221111-1-1-1-1000000000000
χ3222-2-2-222-2-22-2-2222222-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-20000000000000000000000002-2-2-222-2-222-2-2220000000000000000000000002-222-2-2-2-222000000000000
χ3322-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-200000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-211-1211-1-1-2-22200−i3−i3i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i32-2-1-11111-1-1000000000000
χ3422-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-200000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-211-1211-1-1-2-22200i3i3−i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i32-2-1-11111-1-1000000000000
χ3522-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-222-2-2-2-222-1-1-1-111111111-1-1-1-1-1-211-1211-1-122-2-222-1-1-1-1-2-21111-2-2111122-1-1-1-1-2211-1-1-1-111000000000000
χ3622-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-2-22222-2-21111-1-1-1-1-1-1-1-11111-1-211-1211-1-122-2-2-2-2111122-1-1-1-122-1-1-1-1-2-21111-2211-1-1-1-111000000000000
χ372-22i−2i02000-22i−2i002222000000-2-2-2-22i−2i2i2i−2i−2i0000002i−2i2−2−i2i2−i2i22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22000-202i−2i002-22i−2i2−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22−22−22−200002-2002i−2i000000000000
χ382-22i−2i02000-22i−2i002222000000-2-2-2-22i−2i2i2i−2i−2i0000002i−2i−i2i2−222−2i2−i2−i2i2−i2i2−22−222−22−2i2−i2i2−i22000-202i−2i00-22−2i2i−i2i2−i2i2−i2i2−22−22−222−22−22−2i2−i2i2−i2i2−i20000-2200−2i2i000000000000
χ392-22i−2i02000-22i−2i002222000000-2-2-2-22i−2i2i2i−2i−2i0000002i−2ii2−i22−2−22−i2i2i2−i2i2−i22−22−2−22−22−i2i2−i2i22000-202i−2i00-22−2i2ii2−i2i2−i2i2−i22−22−22−2−22−22−22−i2i2−i2i2−i2i20000-2200−2i2i000000000000
χ402-22i−2i02000-22i−2i002222000000-2-2-2-22i−2i2i2i−2i−2i0000002i−2i−22i2−i2i2−i2−22−22−22i2−i2i2−i2i2−i2i2−i2−22−222000-202i−2i002-22i−2i−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−22−22−2200002-2002i−2i000000000000
χ412-22i−2i0-10−i3i31−ii3−322-1-100−i3−i3i3i3-2-2112i−2i−i−iii0033−3−32i−2i2−2−i2i2−i2i22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7-10−i3i310−ii3−32-22i−2i2−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ232−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700−i3i3-113−3−ii000000000000
χ422-22i−2i0-10−i3i31−ii3−322-1-100−i3−i3i3i3-2-2112i−2i−i−iii0033−3−32i−2i−i2i2−222−2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7-10−i3i310−ii3−3-22−2i2i−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ72−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700i3−i31-1−33i−i000000000000
χ432-22i−2i0-10−i3i31−ii3−322-1-100−i3−i3i3i3-2-2112i−2i−i−iii0033−3−32i−2ii2−i22−2−22−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7-10−i3i310−ii3−3-22−2i2ii2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ232−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700i3−i31-1−33i−i000000000000
χ442-22i−2i0-10−i3i31−ii3−322-1-100−i3−i3i3i3-2-2112i−2i−i−iii0033−3−32i−2i−22i2−i2i2−i2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7-10−i3i310−ii3−32-22i−2i−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700−i3i3-113−3−ii000000000000
χ452-22i−2i0-10i3−i31−ii−3322-1-100i3i3−i3−i3-2-2112i−2i−i−iii00−3−3332i−2i2−2−i2i2−i2i22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-10i3−i310−ii−332-22i−2i2−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ72−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300i3−i3-11−33−ii000000000000
χ462-22i−2i0-10i3−i31−ii−3322-1-100i3i3−i3−i3-2-2112i−2i−i−iii00−3−3332i−2i−i2i2−222−2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23-10i3−i310−ii−33-22−2i2i−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ232−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300−i3i31-13−3i−i000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.