Finite Group Databasebeta

← Group #13155679

Character table — Group #13155679

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order122233344666666666333666666666121212121212121212124444121212121212121236661212121212121212224466661212121212121212121212121212121266666612121212121244448812121212121212122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111
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
χ91-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-11-1i−i11-1-1i−ii−iii−i−iiiii−i−i−i−i1-111-1-1i−iii−i−i1-1i−ii−i11-1-1ii−i−iii−i−i1-1
χ101-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-11-1−ii11-1-1i−ii−i−i−iiiiiii−i−i−i−i1-111-1-1−ii−i−iii-11i−i−ii-1-111ii−i−i−i−iii-11
χ111-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-1-11i−i-1-111i−ii−iii−i−iiiii−i−i−i−i-11-1-111i−iii−i−i1-1−ii−ii11-1-1−i−iii−i−iii-11
χ121-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-1-11−ii-1-111i−ii−i−i−iiiiiii−i−i−i−i-11-1-111−ii−i−iii-11−iii−i-1-111−i−iiiii−i−i1-1
χ131-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-11-1i−i11-1-1−ii−iiii−i−i−i−i−i−iiiii1-111-1-1i−iii−i−i-11−iii−i-1-111−i−iiiii−i−i-11
χ141-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-11-1−ii11-1-1−ii−ii−i−iii−i−i−i−iiiii1-111-1-1−ii−i−iii1-1−ii−ii11-1-1−i−iii−i−iii1-1
χ151-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-1-11i−i-1-111−ii−iiii−i−i−i−i−i−iiiii-11-1-111i−iii−i−i-11i−i−ii-1-111ii−i−i−i−iii1-1
χ161-11-1111-11-111-1-1-1-11-1111-1-1-1111-1-1-111-11-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-1-11−ii-1-111−ii−ii−i−iii−i−i−i−iiiii-11-1-111−ii−i−iii1-1i−ii−i11-1-1ii−i−iii−i−i-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-2000022-2-222-2-200000000000000000000000000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-200000000-2-2220000-2-222-2-22200000000000000000000000000000000
χ19222222-12222-12-1222-12-1-12-1-12-1-1-1-122-1-122-1-1-1-1222222222-1-1-1-1-1-1-1-12-12-1-1-1-1-12200-1-1-1-1-1-1220000-1-1-1-1-1-1-1-122-1-1-1-10000000022000000-1-1-1-1000000
χ20222222-12222-12-1222-12-1-12-1-12-1-1-1-122-1-122-1-1-1-1222222222-1-1-1-1-1-1-1-12-12-1-1-1-1-1-2-2001111-1-1220000-1-1-1-1-1-1-1-1-2-2111100000000-2-20000001111000000
χ21222222-12222-12-1222-12-1-12-1-12-1-1-1-122-1-122-1-1-1-12-2-2-2-2-2-2-2-21111-1-1-1-12-12-1-1-1-1-12200-1-1-1-111-2-200001111111122-1-1-1-100000000-2-20000001111000000
χ22222222-12222-12-1222-12-1-12-1-12-1-1-1-122-1-122-1-1-1-12-2-2-2-2-2-2-2-21111-1-1-1-12-12-1-1-1-1-1-2-200111111-2-2000011111111-2-211110000000022000000-1-1-1-1000000
χ23222222-1-2-222-12-1222-12-1-12-1-12-1-1-1-12-211-2-21111-222-2-222221111-1-1-1-1-21-2111110000−i3i3−i3i3-1-1-2-20000-1-111-1-11100−i3i3−i3i30000000000000000−i3i3−i3i3000000
χ24222222-1-2-222-12-1222-12-1-12-1-12-1-1-1-12-211-2-21111-222-2-222221111-1-1-1-1-21-2111110000i3−i3i3−i3-1-1-2-20000-1-111-1-11100i3−i3i3−i30000000000000000i3−i3i3−i3000000
χ25222222-1-2-222-12-1222-12-1-12-1-12-1-1-1-12-211-2-21111-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-21-2111110000−i3i3−i3i31122000011-1-111-1-100−i3i3−i3i30000000000000000i3−i3i3−i3000000
χ26222222-1-2-222-12-1222-12-1-12-1-12-1-1-1-12-211-2-21111-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-21-2111110000i3−i3i3−i31122000011-1-111-1-100i3−i3i3−i30000000000000000−i3i3−i3i3000000
χ2722222-1222-1-1222-1222-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1222222220000222200000000-1-1-1-1-1-1-1-1-1-1-1-100002200000000-1-1-1-100
χ2822222-1222-1-1222-1222-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-122-2-222220000-2-2-2-200000000-1-1-1-1-1-11111110000-2-200000000111100
χ2922222-1222-1-1222-1222-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-20000222200000000111111-1-1-1-1-1-10000-2-200000000111100
χ3022222-1222-1-1222-1222-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-20000-2-2-2-20000000011111111111100002200000000-1-1-1-100
χ312222-12222222-122-1-12-1-12-122-1-12-1-1-1222-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-12-12-1-1-1-10022000022-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1220000-1-1-1-10000000000
χ322222-12222222-122-1-12-1-12-122-1-12-1-1-1222-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-12-12-1-1-1-100-2-2000022-1-11111-1-1-1-1-1-1-1-1000000-2-21111-2-2000011110000000000
χ332222-12222222-122-1-12-1-12-122-1-12-1-1-1222-1-1-1-1-1-12-2-2-2-21111-2-2-2-2-1-1-1-1-12-12-1-1-1-100220000-2-211-1-1-1-11111111100000022-1-1-1-1-2-2000011110000000000
χ342222-12222222-122-1-12-1-12-122-1-12-1-1-1222-1-1-1-1-1-12-2-2-2-21111-2-2-2-2-1-1-1-1-12-12-1-1-1-100-2-20000-2-211111111111111000000-2-21111220000-1-1-1-10000000000
χ352222-122-2-2222-122-1-12-1-12-122-1-12-1-1-1-2-2-2111111-222-2-2-1-1-1-1-2-2-2-2-1-1-1-11-21-21111000000002211−i3i3−i3i3-1-111-1-11100000000−i3i3−i3i3000000−i3i3−i3i30000000000
χ362222-122-2-2222-122-1-12-1-12-122-1-12-1-1-1-2-2-2111111-222-2-2-1-1-1-1-2-2-2-2-1-1-1-11-21-21111000000002211i3−i3i3−i3-1-111-1-11100000000i3−i3i3−i3000000i3−i3i3−i30000000000
χ372222-122-2-2222-122-1-12-1-12-122-1-12-1-1-1-2-2-2111111-2-2-22211112222-1-1-1-11-21-2111100000000-2-2-1-1−i3i3−i3i311-1-111-1-100000000−i3i3−i3i3000000i3−i3i3−i30000000000
χ382222-122-2-2222-122-1-12-1-12-122-1-12-1-1-1-2-2-2111111-2-2-22211112222-1-1-1-11-21-2111100000000-2-2-1-1i3−i3i3−i311-1-111-1-100000000i3−i3i3−i3000000−i3i3−i3i30000000000
χ392-22-22222-2-222-2-2-2-22-2222-2-2-2222-2-2-2-2-22-22-2-22222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2-2-22-2-222-2-222000000002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-22-22222-2-222-2-2-2-22-2222-2-2-2222-2-2-2-2-22-22-2-2222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22-2-222-2-22200000000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-22-222-12-2-22-1-21-2-2212-1-1-2112-1-111-2-21-1-2211-1-122i−2i−2i2i2i2i−2i−2iii−i−i-111-1-212-111-1-10000−i3i3i3−i3−ii−2i2i0000−i−iiiii−i−i00−i3i3i3−i300000000000000003−3−33000000
χ422-22-222-12-2-22-1-21-2-2212-1-1-2112-1-111-2-21-1-2211-1-122i−2i−2i2i2i2i−2i−2iii−i−i-111-1-212-111-1-10000i3−i3−i3i3−ii−2i2i0000−i−iiiii−i−i00i3−i3−i3i30000000000000000−333−3000000
χ432-22-222-12-2-22-1-21-2-2212-1-1-2112-1-111-2-21-1-2211-1-12−2i2i2i−2i−2i−2i2i2i−i−iii-111-1-212-111-1-10000−i3i3i3−i3i−i2i−2i0000ii−i−i−i−iii00−i3i3i3−i30000000000000000−333−3000000
χ442-22-222-12-2-22-1-21-2-2212-1-1-2112-1-111-2-21-1-2211-1-12−2i2i2i−2i−2i−2i2i2i−i−iii-111-1-212-111-1-10000i3−i3−i3i3i−i2i−2i0000ii−i−i−i−iii00i3−i3−i3i300000000000000003−3−33000000
χ452-22-222-1-22-22-1-21-2-2212-1-1-2112-1-111-22-112-2-1-111-22i−2i2i−2i2i2i−2i−2i−i−iii-111-12-1-21-1-1112-200-1-111−ii2i−2i0000−i−i−i−iiiii2-2-1-111000000002i−2i000000−i−iii000000
χ462-22-222-1-22-22-1-21-2-2212-1-1-2112-1-111-22-112-2-1-111-22i−2i2i−2i2i2i−2i−2i−i−iii-111-12-1-21-1-111-220011-1-1−ii2i−2i0000−i−i−i−iiiii-2211-1-100000000−2i2i000000ii−i−i000000
χ472-22-222-1-22-22-1-21-2-2212-1-1-2112-1-111-22-112-2-1-111-2−2i2i−2i2i−2i−2i2i2iii−i−i-111-12-1-21-1-1112-200-1-111i−i−2i2i0000iiii−i−i−i−i2-2-1-11100000000−2i2i000000ii−i−i000000
χ482-22-222-1-22-22-1-21-2-2212-1-1-2112-1-111-22-112-2-1-111-2−2i2i−2i2i−2i−2i2i2iii−i−i-111-12-1-21-1-111-220011-1-1i−i−2i2i0000iiii−i−i−i−i-2211-1-1000000002i−2i000000−i−iii000000
χ492-22-22-12-221-12-2-21-22-2-12-1111-12-1-2-21-12-22-222-2-21000000000000-111-1-1-111-1-1112-22i−2i22-2-200002i2i−2i−2i00000000-11-1-111−ii−i−iii00002i−2i00000000−i−iii00
χ502-22-22-12-221-12-2-21-22-2-12-1111-12-1-2-21-12-22-222-2-21000000000000-111-1-1-111-1-1112-2−2i2i22-2-20000−2i−2i2i2i00000000-11-1-111i−iii−i−i0000−2i2i00000000ii−i−i00
χ512-22-22-12-221-12-2-21-22-2-12-1111-12-1-2-21-12-22-222-2-21000000000000-111-1-1-111-1-111-222i−2i-2-22200002i2i−2i−2i000000001-111-1-1−ii−i−iii0000−2i2i00000000ii−i−i00
χ522-22-22-12-221-12-2-21-22-2-12-1111-12-1-2-21-12-22-222-2-21000000000000-111-1-1-111-1-111-22−2i2i-2-2220000−2i−2i2i2i000000001-111-1-1i−iii−i−i00002i−2i00000000−i−iii00
χ532-22-2-1222-2-2221-2-21-1-2-1-121-2-2-1-12111-2-221-111-1-122i−2i−2i2i−i−iii−2i−2i2i2i-111-11-2-1211-1-1000000002i−2ii−i3−3−33−i−iiiii−i−i000000003−3−33000000−i3i3i3−i30000000000
χ542-22-2-1222-2-2221-2-21-1-2-1-121-2-2-1-12111-2-221-111-1-122i−2i−2i2i−i−iii−2i−2i2i2i-111-11-2-1211-1-1000000002i−2ii−i−333−3−i−iiiii−i−i00000000−333−3000000i3−i3−i3i30000000000
χ552-22-2-1222-2-2221-2-21-1-2-1-121-2-2-1-12111-2-221-111-1-12−2i2i2i−2iii−i−i2i2i−2i−2i-111-11-2-1211-1-100000000−2i2i−ii3−3−33ii−i−i−i−iii000000003−3−33000000i3−i3−i3i30000000000
χ562-22-2-1222-2-2221-2-21-1-2-1-121-2-2-1-12111-2-221-111-1-12−2i2i2i−2iii−i−i2i2i−2i−2i-111-11-2-1211-1-100000000−2i2i−ii−333−3ii−i−i−i−iii00000000−333−3000000−i3i3i3−i30000000000
χ572-22-2-122-22-2221-2-21-1-2-1-121-2-2-1-1211122-2-11-1-111-22i−2i2i−2i−i−iii2i2i−2i−2i-111-1-121-2-1-111002i−2i00002i−2i−ii−i−iii−i−i−i−iiiii0000002i−2i−i−iii2-20000-1-1110000000000
χ582-22-2-122-22-2221-2-21-1-2-1-121-2-2-1-1211122-2-11-1-111-22i−2i2i−2i−i−iii2i2i−2i−2i-111-1-121-2-1-11100−2i2i00002i−2i−iiii−i−i−i−i−i−iiiii000000−2i2iii−i−i-22000011-1-10000000000
χ592-22-2-122-22-2221-2-21-1-2-1-121-2-2-1-1211122-2-11-1-111-2−2i2i−2i2iii−i−i−2i−2i2i2i-111-1-121-2-1-111002i−2i0000−2i2ii−i−i−iiiiiii−i−i−i−i0000002i−2i−i−iii-22000011-1-10000000000
χ602-22-2-122-22-2221-2-21-1-2-1-121-2-2-1-1211122-2-11-1-111-2−2i2i−2i2iii−i−i−2i−2i2i2i-111-1-121-2-1-11100−2i2i0000−2i2ii−iii−i−iiiii−i−i−i−i000000−2i2iii−i−i2-20000-1-1110000000000
χ6144444-24-4-4-2-2444-2444-24-2-2-2-2-24-244-22-4-4-4-4-4-4-4-42000000000000-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ6244444-2-244-2-2-24-2-244-2-2-21-211-2-21-2-2-2-2-2-244-2-2-2-2-20000000000001111-21-2111114400-2-2-2-20000000000000000-2-2111100000000000000000000000000
χ6344444-2-244-2-2-24-2-244-2-2-21-211-2-21-2-2-2-2-2-244-2-2-2-2-20000000000001111-21-211111-4-4002222000000000000000022-1-1-1-100000000000000000000000000
χ6444444-2-2-4-4-2-2-24-2-244-2-2-21-211-2-21-2-2-2222-4-42222200000000000011112-12-1-1-1-1-10000−2i32i3−2i32i3000000000000000000i3−i3i3−i300000000000000000000000000
χ6544444-2-2-4-4-2-2-24-2-244-2-2-21-211-2-21-2-2-2222-4-42222200000000000011112-12-1-1-1-1-100002i3−2i32i3−2i3000000000000000000−i3i3−i3i300000000000000000000000000
χ664444-24-24444-2-2-24-2-2-2-21-2-2-2-2-21-211-24-2-2-2-2111144444-2-2-2-2-2-2-2-21111-2-2-2-2111100000000-2-2-2-200001111111100000000000000000000000000000000
χ674444-24-24444-2-2-24-2-2-2-21-2-2-2-2-21-211-24-2-2-2-211114-4-4-4-4222222221111-2-2-2-211110000000022220000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ684444-24-2-4-444-2-2-24-2-2-2-21-2-2-2-2-21-211-2-42222-1-1-1-1-444-4-4-2-2-2-2222211112222-1-1-1-100000000-2-222000011-1-111-1-100000000000000000000000000000000
χ694444-24-2-4-444-2-2-24-2-2-2-21-2-2-2-2-21-211-2-42222-1-1-1-1-4-4-4442222-2-2-2-211112222-1-1-1-10000000022-2-20000-1-111-1-11100000000000000000000000000000000
χ704444-2-2444-2-24-24-2-2-241-2-21-2-21-2-2-2-21-244-2-2-2-2-2-2-200000000000011111-21-21111004400000000-2-2-2-200000000000000-2-2111100000000000000000000
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χ924-44-4-24-2-44-44-222-42-22-21-2222-21-2-1-124-22-2211-1-1-44i−4i4i−4i−2i−2i2i2i−2i−2i2i2i1-1-11-2-22211-1-100000000−2i2i−2i2i0000iiii−i−i−i−i00000000000000000000000000000000
χ934-44-4-24-2-44-44-222-42-22-21-2222-21-2-1-124-22-2211-1-1-4−4i4i−4i4i2i2i−2i−2i2i2i−2i−2i1-1-11-2-22211-1-1000000002i−2i2i−2i0000−i−i−i−iiiii00000000000000000000000000000000
χ944-44-4-2-244-42-242-422-2-41-2-2-1221-2-222-12-442-222-2-2-20000000000001-1-11-121-2-1-11100000000000023−23−23230000000000000000−333−300000000000000000000
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χ1108888-4-4-4-8-8-4-4-4-4-4-4-4-4-422222222222244444-2-2-2-24000000000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000
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χ1158-88-8-4-4-48-84-4-44444-44222-2-2-2222-2-2-244-44-4-2-222-4000000000000-111-1-2-22211-1-100000000000000000000000000000000000000000000000000000000
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χ1208-8-88-4-4-40044444-4-44-4222-2-22-2-2-2-22200000−6i6i6i−6i0000000000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

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