Finite Group Databasebeta

← Group #13155702

Character table — Group #13155702

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order1222333446666666663336666666661212121212121212121244441212121212121212366612121212121212124444121212121212121212121212121212121212121212121212121212121212121244448812121212121212122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1i−ii−iiiii−i−i−i−i1-1-111-11-111-1-1i−i1-111-1-1i−iii−i−ii−iiiii−i−i−i−ii−i1-1ii−i−i11-1-1i−i1-1i−i11-1-1ii−i−iii−i−i1-1
χ101-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1i−ii−iiiii−i−i−i−i1-1-111-11-111-1-1i−i-11-1-111i−iii−i−ii−iiiii−i−i−i−ii−i-11ii−i−i-1-111−ii1-1−ii11-1-1−i−iii−i−iii-11
χ111-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1i−ii−iiiii−i−i−i−i1-1-111-11-111-1-1−ii1-111-1-1i−i−i−iiii−iiiii−i−i−i−i−ii1-1−i−iii11-1-1i−i-11−ii-1-111ii−i−i−i−iii-11
χ121-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1i−ii−iiiii−i−i−i−i1-1-111-11-111-1-1−ii-11-1-111i−i−i−iiii−iiiii−i−i−i−i−ii-11−i−iii-1-111−ii-11i−i-1-111−i−iiiii−i−i1-1
χ131-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1−ii−ii−i−i−i−iiiii1-1-111-11-111-1-1i−i1-111-1-1−iiii−i−i−ii−i−i−i−iiiiii−i1-1ii−i−i11-1-1−ii-11i−i-1-111−i−iiiii−i−i-11
χ141-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1−ii−ii−i−i−i−iiiii1-1-111-11-111-1-1i−i-11-1-111−iiii−i−i−ii−i−i−i−iiiiii−i-11ii−i−i-1-111i−i-11−ii-1-111ii−i−i−i−iii1-1
χ151-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1−ii−ii−i−i−i−iiiii1-1-111-11-111-1-1−ii1-111-1-1−ii−i−iii−ii−i−i−i−iiiii−ii1-1−i−iii11-1-1−ii1-1−ii11-1-1−i−iii−i−iii1-1
χ161-1-11111-11-1-1-1-111-11-1111-1-1-111-1-1-1111-11-111-1-1-1−ii−ii−i−i−i−iiiii1-1-111-11-111-1-1−ii-11-1-111−ii−i−iii−ii−i−i−i−iiiii−ii-11−i−iii-1-111i−i1-1i−i11-1-1ii−i−iii−i−i-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-22222-2-2-2-2-2-2-2-200000000220000-2-222-2-222-2-200000000000000000000000000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2222222-2-2-2-2-2-2-2-200000000-2-2000022-2-222-2-22200000000000000000000000000000000
χ19222222-12222-1222-1-122-1-122-1-1-1-1-1-12222-1-1-1-1-1-12222222-1-122-1-1-1-1-1-1-1-122-1-1-1-122000000-1-1-1-1-1-122-1-1-1-1-1-1-1-12200-1-1-1-10000002200-1-1-1-10000000000
χ20222222-12222-1222-1-122-1-122-1-1-1-1-1-12222-1-1-1-1-1-12222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2000000-1-1111122-1-1-1-1-1-1-1-1-2-2001111000000-2-20011110000000000
χ21222222-12222-1222-1-122-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-2-2-2-2-2-211-2-211-1-1-1-1-1-122-1-1-1-12200000011-1-1-1-1-2-2111111112200-1-1-1-1000000-2-20011110000000000
χ22222222-12222-1222-1-122-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-2-2-2-2-2-211-2-211-1-1-1-1-1-122-1-1-1-1-2-2000000111111-2-211111111-2-20011110000002200-1-1-1-10000000000
χ23222222-1-2-222-1222-1-122-1-122-1-1-1-1-1-12-2-2-2111111-222-2-222112211-1-1-1-111-2-2111100000000-1-1−i3i3−i3i3-2-2-1-111-1-1110000−i3i3−i3i30000000000−i3i3−i3i30000000000
χ24222222-1-2-222-1222-1-122-1-122-1-1-1-1-1-12-2-2-2111111-222-2-222112211-1-1-1-111-2-2111100000000-1-1i3−i3i3−i3-2-2-1-111-1-1110000i3−i3i3−i30000000000i3−i3i3−i30000000000
χ25222222-1-2-222-1222-1-122-1-122-1-1-1-1-1-12-2-2-2111111-2-2-222-2-2-1-1-2-2-1-1-1-1-1-111-2-211110000000011−i3i3−i3i32211-1-111-1-10000−i3i3−i3i30000000000i3−i3i3−i30000000000
χ26222222-1-2-222-1222-1-122-1-122-1-1-1-1-1-12-2-2-2111111-2-2-222-2-2-1-1-2-2-1-1-1-1-1-111-2-211110000000011i3−i3i3−i32211-1-111-1-10000i3−i3i3−i30000000000−i3i3−i3i30000000000
χ2722222-12222-1222-122-1-12-1-1-122-1-1-12-12-1-122-1-1-1-122222-1-122-1-122-1-1-1-122-1-1-1-1-1-10022-1-1-1-1220000-1-1-1-1-1-1-1-1-1-100220000-1-1-1-12200000000-1-1-1-1000000
χ2822222-12222-1222-122-1-12-1-1-122-1-1-12-12-1-122-1-1-1-122222-1-122-1-122-1-1-1-122-1-1-1-1-1-100-2-21111220000-1-1-1-1-1-1-1-1-1-100-2-200001111-2-2000000001111000000
χ2922222-12222-1222-122-1-12-1-1-122-1-1-12-12-1-122-1-1-1-12-2-2-2-211-2-211-2-2-1-1-1-122-1-1-1-1-1-10022-1-1-1-1-2-20000111111111100220000-1-1-1-1-2-2000000001111000000
χ3022222-12222-1222-122-1-12-1-1-122-1-1-12-12-1-122-1-1-1-12-2-2-2-211-2-211-2-2-1-1-1-122-1-1-1-1-1-100-2-21111-2-20000111111111100-2-2000011112200000000-1-1-1-1000000
χ3122222-12-2-22-1222-122-1-12-1-1-122-1-1-12-1-211-2-21111-222-2-2-1-1-2-2-1-1-2-2-1-1-1-1-2-21111110000−i3i3−i3i322000011-1-111-1-11100000000−i3i3−i3i30000000000−i3i3−i3i3000000
χ3222222-12-2-22-1222-122-1-12-1-1-122-1-1-12-1-211-2-21111-222-2-2-1-1-2-2-1-1-2-2-1-1-1-1-2-21111110000i3−i3i3−i322000011-1-111-1-11100000000i3−i3i3−i30000000000i3−i3i3−i3000000
χ3322222-12-2-22-1222-122-1-12-1-1-122-1-1-12-1-211-2-21111-2-2-22211221122-1-1-1-1-2-21111110000−i3i3−i3i3-2-20000-1-111-1-111-1-100000000−i3i3−i3i30000000000i3−i3i3−i3000000
χ3422222-12-2-22-1222-122-1-12-1-1-122-1-1-12-1-211-2-21111-2-2-22211221122-1-1-1-1-2-21111110000i3−i3i3−i3-2-20000-1-111-1-111-1-100000000i3−i3i3−i30000000000−i3i3−i3i3000000
χ352222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1222222220022220000000000-1-1-1-1-1-1-1-1-1-1-1-100002200000000-1-1-1-100
χ362222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-20022220000000000-1-111-1-1-1-111110000-2-200000000111100
χ372222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-222222200-2-2-2-2000000000011-1-11111-1-1-1-10000-2-200000000111100
χ382222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-200-2-2-2-2000000000011111111111100002200000000-1-1-1-100
χ392-2-222222-2-2-2-2-222-22-2222-2-2-222-2-2-22-2-22-22-2-22222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2-2-22-22-22-2-222000000002i−2i0000−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-2-222222-2-2-2-2-222-22-2222-2-2-222-2-2-22-2-22-22-2-2222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22-22-22-2-22200000000−2i2i00002i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-2-2222-12-2-2-21-2221-1-22-1-1-2-21-1-11112-2-221-111-1-122i−2i−2i2i2i2iii−2i−2i−i−i-111-11-1-2211-1-100000000−ii3−3−33−2i2i−i−iiiii−i−i00003−3−330000000000−i3i3i3−i30000000000
χ422-2-2222-12-2-2-21-2221-1-22-1-1-2-21-1-11112-2-221-111-1-122i−2i−2i2i2i2iii−2i−2i−i−i-111-11-1-2211-1-100000000−ii−333−3−2i2i−i−iiiii−i−i0000−333−30000000000i3−i3−i3i30000000000
χ432-2-2222-12-2-2-21-2221-1-22-1-1-2-21-1-11112-2-221-111-1-12−2i2i2i−2i−2i−2i−i−i2i2iii-111-11-1-2211-1-100000000i−i3−3−332i−2iii−i−i−i−iii00003−3−330000000000i3−i3−i3i30000000000
χ442-2-2222-12-2-2-21-2221-1-22-1-1-2-21-1-11112-2-221-111-1-12−2i2i2i−2i−2i−2i−i−i2i2iii-111-11-1-2211-1-100000000i−i−333−32i−2iii−i−i−i−iii0000−333−30000000000−i3i3i3−i30000000000
χ452-2-2222-1-22-2-21-2221-1-22-1-1-2-21-1-1111222-2-11-1-111-22i−2i2i−2i2i2i−i−i−2i−2iii-111-1-112-2-1-1112i−2i000000−ii−i−iii2i−2i−i−i−i−iiiii2i−2i00−i−iii0000002-200-1-1110000000000
χ462-2-2222-1-22-2-21-2221-1-22-1-1-2-21-1-1111222-2-11-1-111-22i−2i2i−2i2i2i−i−i−2i−2iii-111-1-112-2-1-111−2i2i000000−iiii−i−i2i−2i−i−i−i−iiiii−2i2i00ii−i−i000000-220011-1-10000000000
χ472-2-2222-1-22-2-21-2221-1-22-1-1-2-21-1-1111222-2-11-1-111-2−2i2i−2i2i−2i−2iii2i2i−i−i-111-1-112-2-1-1112i−2i000000i−i−i−iii−2i2iiiii−i−i−i−i2i−2i00−i−iii000000-220011-1-10000000000
χ482-2-2222-1-22-2-21-2221-1-22-1-1-2-21-1-1111222-2-11-1-111-2−2i2i−2i2i−2i−2iii2i2i−i−i-111-1-112-2-1-111−2i2i000000i−iii−i−i−2i2iiiii−i−i−i−i−2i2i00ii−i−i0000002-200-1-1110000000000
χ492-2-222-122-2-21-2-22-1-221-12-111-22-111-2-1-21-1-2211-1-122i−2i−2i2i−i−i−2i−2iii2i2i-111-1-221-111-1-10000−i3i3i3−i32i−2i0000i−i−i−iiiii−i−i00000000−i3i3i3−i300000000003−3−33000000
χ502-2-222-122-2-21-2-22-1-221-12-111-22-111-2-1-21-1-2211-1-122i−2i−2i2i−i−i−2i−2iii2i2i-111-1-221-111-1-10000i3−i3−i3i32i−2i0000i−i−i−iiiii−i−i00000000i3−i3−i3i30000000000−333−3000000
χ512-2-222-122-2-21-2-22-1-221-12-111-22-111-2-1-21-1-2211-1-12−2i2i2i−2iii2i2i−i−i−2i−2i-111-1-221-111-1-10000−i3i3i3−i3−2i2i0000−iiii−i−i−i−iii00000000−i3i3i3−i30000000000−333−3000000
χ522-2-222-122-2-21-2-22-1-221-12-111-22-111-2-1-21-1-2211-1-12−2i2i2i−2iii2i2i−i−i−2i−2i-111-1-221-111-1-10000i3−i3−i3i3−2i2i0000−iiii−i−i−i−iii00000000i3−i3−i3i300000000003−3−33000000
χ532-2-222-12-22-21-2-22-1-221-12-111-22-111-2-12-112-2-1-111-22i−2i2i−2i−i−i2i2iii−2i−2i-111-12-2-11-1-111002-2-1-1112i−2i0000−ii−i−i−i−iiiii002-20000-1-1112i−2i00000000−i−iii000000
χ542-2-222-12-22-21-2-22-1-221-12-111-22-111-2-12-112-2-1-111-22i−2i2i−2i−i−i2i2iii−2i−2i-111-12-2-11-1-11100-2211-1-12i−2i0000−ii−i−i−i−iiiii00-22000011-1-1−2i2i00000000ii−i−i000000
χ552-2-222-12-22-21-2-22-1-221-12-111-22-111-2-12-112-2-1-111-2−2i2i−2i2iii−2i−2i−i−i2i2i-111-12-2-11-1-111002-2-1-111−2i2i0000i−iiiii−i−i−i−i002-20000-1-111−2i2i00000000ii−i−i000000
χ562-2-222-12-22-21-2-22-1-221-12-111-22-111-2-12-112-2-1-111-2−2i2i−2i2iii−2i−2i−i−i2i2i-111-12-2-11-1-11100-2211-1-1−2i2i0000i−iiiii−i−i−i−i00-22000011-1-12i−2i00000000−i−iii000000
χ572-2-22-122-221-2-21-12-22-2-1-12111-12-2-21-1-12-22-222-2-21000000000000-111-1-11-11-1-1112i−2i2-222-2-2002i2i−2i−2i0000000000−ii-11−i−iii-1-11100002i−2i00000000−i−iii00
χ582-2-22-122-221-2-21-12-22-2-1-12111-12-2-21-1-12-22-222-2-21000000000000-111-1-11-11-1-1112i−2i-22-2-222002i2i−2i−2i0000000000−ii1-1−i−iii11-1-10000−2i2i00000000ii−i−i00
χ592-2-22-122-221-2-21-12-22-2-1-12111-12-2-21-1-12-22-222-2-21000000000000-111-1-11-11-1-111−2i2i2-222-2-200−2i−2i2i2i0000000000i−i-11ii−i−i-1-1110000−2i2i00000000ii−i−i00
χ602-2-22-122-221-2-21-12-22-2-1-12111-12-2-21-1-12-22-222-2-21000000000000-111-1-11-11-1-111−2i2i-22-2-22200−2i−2i2i2i0000000000i−i1-1ii−i−i11-1-100002i−2i00000000−i−iii00
χ6144444-2-2444-2-244-2-2-2-2-2-21-2-2-2-2111-2-24-2-2-2-2111144444-2-2-2-2-2-2-2-21111-2-2-2-2111100000000-2-20000-2-21111111100000000000000000000000000000000
χ6244444-2-2444-2-244-2-2-2-2-2-21-2-2-2-2111-2-24-2-2-2-211114-4-4-4-4222222221111-2-2-2-211110000000022000022-1-1-1-1-1-1-1-100000000000000000000000000000000
χ6344444-2-2-4-44-2-244-2-2-2-2-2-21-2-2-2-2111-2-2-42222-1-1-1-1-444-4-4-2-222-2-22211112222-1-1-1-100000000-2-200002211-1-111-1-100000000000000000000000000000000
χ6444444-2-2-4-44-2-244-2-2-2-2-2-21-2-2-2-2111-2-2-42222-1-1-1-1-4-4-44422-2-222-2-211112222-1-1-1-100000000220000-2-2-1-111-1-11100000000000000000000000000000000
χ654444-244-4-4-244-2-24444-2-24-2-2-2-2444-2-22-4-4-4-4-4-4-4-42000000000000-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ664444-24-244-24-2-2-24-2-24-21-2-2-211-2-2-21-2-244-2-2-2-2-2-2-2000000000000111111-2-211114400000000-2-2-2-20000000000-2-2001111000000000000000000000000
χ674444-24-244-24-2-2-24-2-24-21-2-2-211-2-2-21-2-244-2-2-2-2-2-2-2000000000000111111-2-21111-4-400000000222200000000002200-1-1-1-1000000000000000000000000
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Here i is the imaginary unit (i² = −1).