Finite Group Databasebeta

← Group #11777440

Character table — Group #11777440

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111111122222222222222222222444444444444444444448888888888888888888812121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636
order12224444334444666666121212121212121222344666121212121212121212121212666666661212121212121212121212128888888824242424242424242424242424242424888844881212121224242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111
χ71111111111111111111111111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ91111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i1-1i−i11-1-1ii−i−ii−iii−i−i
χ101111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii1-1−ii11-1-1−i−iii−ii−i−iii
χ111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−i−iii-11i−i-1-111ii−i−i−ii−i−iii
χ121111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiiiii−i−i-11−ii-1-111−i−iiii−iii−i−i
χ131111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i-11−ii-1-111−i−iiii−i−i−iii
χ141111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii-11i−i-1-111ii−i−i−iiii−i−i
χ151111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−i−iii1-1−ii11-1-1−i−iii−iiii−i−i
χ161111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-111−i−iii-1-1-1-11111−i−i−i−iiiiiii−i−i1-1i−i11-1-1ii−i−ii−i−i−iii
χ172222222222-2-2-2-22222222222222200200222-2-2-2-22222-2-2-2-2000000000000-2-2-2-200000000000000000000000000002222000000000000-2-20000
χ182222222222-2-2-2-22222222222222200200222-2-2-2-22222-2-2-2-2000000000000-2-2-2-20000000000000000000000000000-2-2-2-2000000000000220000
χ19222222222-12222222-1-1-122-1-1-1-12222-122-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000002200-1-1-1-10000000000
χ20222222222-12222222-1-1-122-1-1-1-12222-122-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000-2-20011110000000000
χ21222222222-12222222-1-1-122-1-1-1-122-2-2-1-2-2-1-1-122-1-1-1-1-1-122-1-1-2-2111111-2-211-1-1-1-1111122220000-1-1-1-1-1-1-1-1000000000000-2-20011110000000000
χ22222222222-12222222-1-1-122-1-1-1-122-2-2-1-2-2-1-1-122-1-1-1-1-1-122-1-1-2-2111111-2-211-1-1-1-11111-2-2-2-20000111111110000000000002200-1-1-1-10000000000
χ2322222222-122222-1-1-1222-1-12222-1-122-122-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000220000-1-1-1-1000000
χ2422222222-122222-1-1-1222-1-12222-1-122-122-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000-2-200001111000000
χ2522222222-122222-1-1-1222-1-12222-1-1-2-2-1-2-2-1-1-1-1-122-1-1-1-1-1-12211-2-2111111-2-2-1-1-1-111110000222200000000-1-1-1-1-1-1-1-1000000-2-200001111000000
χ2622222222-122222-1-1-1222-1-12222-1-1-2-2-1-2-2-1-1-1-1-122-1-1-1-1-1-12211-2-2111111-2-2-1-1-1-111110000-2-2-2-20000000011111111000000220000-1-1-1-1000000
χ272222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-200200222-2-222-2-2-2-222-2-2000000000000-2-22200000000000000000000000000002i2i−2i−2i000000000000−2i2i0000
χ282222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-200200222-2-222-2-2-2-222-2-2000000000000-2-2220000000000000000000000000000−2i−2i2i2i0000000000002i−2i0000
χ292222-2-2-2-22-122-2-2222-1-1-1-2-21111-2-222-1-2-2-1-1-122111111-2-2-1-122-1-1-1-1-1-1-2-211-1-111111122-2-20000-1-1-1-111110000000000002-200-1-1110000000000
χ302222-2-2-2-22-122-2-2222-1-1-1-2-21111-2-222-1-2-2-1-1-122111111-2-2-1-122-1-1-1-1-1-1-2-211-1-1111111-2-22200001111-1-1-1-1000000000000-220011-1-10000000000
χ312222-2-2-2-22-122-2-2222-1-1-1-2-21111-2-2-2-2-122-1-1-122111111-2-2-1-1-2-211111122-1-1-1-111-1-1-1-122-2-20000-1-1-1-11111000000000000-220011-1-10000000000
χ322222-2-2-2-22-122-2-2222-1-1-1-2-21111-2-2-2-2-122-1-1-122111111-2-2-1-1-2-211111122-1-1-1-111-1-1-1-1-2-22200001111-1-1-1-10000000000002-200-1-1110000000000
χ332222-2-2-2-2-1222-2-2-1-1-122211-2-2-2-21122-1-2-2-1-1-1-1-1-2-211111122-1-122-1-1-1-111-2-2-1-111111100002i2i−2i−2i00000000−i−i−i−iiiii0000002i−2i0000−i−iii000000
χ342222-2-2-2-2-1222-2-2-1-1-122211-2-2-2-21122-1-2-2-1-1-1-1-1-2-211111122-1-122-1-1-1-111-2-2-1-11111110000−2i−2i2i2i00000000iiii−i−i−i−i000000−2i2i0000ii−i−i000000
χ352222-2-2-2-2-1222-2-2-1-1-122211-2-2-2-211-2-2-122-1-1-1-1-1-2-21111112211-2-21111-1-122-1-111-1-1-1-100002i2i−2i−2i00000000−i−i−i−iiiii000000−2i2i0000ii−i−i000000
χ362222-2-2-2-2-1222-2-2-1-1-122211-2-2-2-211-2-2-122-1-1-1-1-1-2-21111112211-2-21111-1-122-1-111-1-1-1-10000−2i−2i2i2i00000000iiii−i−i−i−i0000002i−2i0000−i−iii000000
χ3722-2-222-2-2220000-2-222-2-2-2-222-2-22200200-2-22000022-2-2000000000000000000000000−i2i2−i2i22−22−2−i2−i2i2i2−i2−i2i2i222−2−222−2−22i−2i2i−2i000000000000000000
χ3822-2-222-2-2220000-2-222-2-2-2-222-2-22200200-2-22000022-2-2000000000000000000000000−i2i2−i2i2−22−22−i2−i2i2i2−i2−i2i2i2−2−222−2−222−2i2i−2i2i000000000000000000
χ3922-2-222-2-2220000-2-222-2-2-2-222-2-22200200-2-22000022-2-2000000000000000000000000i2−i2i2−i22−22−2i2i2−i2−i2i2i2−i2−i222−2−222−2−2−2i2i−2i2i000000000000000000
χ4022-2-222-2-2220000-2-222-2-2-2-222-2-22200200-2-22000022-2-2000000000000000000000000i2−i2i2−i2−22−22i2i2−i2−i2i2i2−i2−i2−2−222−2−2222i−2i2i−2i000000000000000000
χ4122-2-2-2-222220000-2-222-2-222-2-222-2-200200-2-220000-2-222000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2-22000000000000000000
χ4222-2-2-2-222220000-2-222-2-222-2-222-2-200200-2-220000-2-222000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-222-2000000000000000000
χ4322-2-2-2-222220000-2-222-2-222-2-222-2-200200-2-220000-2-222000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-222-2000000000000000000
χ4422-2-2-2-222220000-2-222-2-222-2-222-2-200200-2-220000-2-222000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2-22000000000000000000
χ452-22-22i−2i2i−2i222-22i−2i2-2-2-22-22i−2i2i−2i2i−2i2i−2i002002-2-22-22i−2i2i−2i2i−2i2i−2i2-20000000000002-22i−2i0000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ462-22-22i−2i2i−2i222-22i−2i2-2-2-22-22i−2i2i−2i2i−2i2i−2i002002-2-22-22i−2i2i−2i2i−2i2i−2i2-20000000000002-22i−2i00000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ472-22-22i−2i2i−2i22-22−2i2i2-2-2-22-22i−2i2i−2i2i−2i2i−2i2-222i−2i2-2-2-22−2i2i2i−2i2i−2i−2i2i-222-22-222-2-22i−2i2i−2i-22−2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ482-22-22i−2i2i−2i22-22−2i2i2-2-2-22-22i−2i2i−2i2i−2i2i−2i-222−2i2i2-2-2-22−2i2i2i−2i2i−2i−2i2i-22-22-22-2-222−2i2i−2i2i-22−2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ492-22-22i−2i2i−2i2-1-22−2i2i2-2-21-112i−2i−ii−ii2i−2i2-2-12i−2i-111-22i−i−ii−ii−2i2i1-12-2-11-1-1112i−2i−ii1-1i−i−i−iii000000003−33−3−i3i3−i3i300000000000000003−3−i3i30000000000
χ502-22-22i−2i2i−2i2-1-22−2i2i2-2-21-112i−2i−ii−ii2i−2i2-2-12i−2i-111-22i−i−ii−ii−2i2i1-12-2-11-1-1112i−2i−ii1-1i−i−i−iii00000000−33−33i3−i3i3−i30000000000000000−33i3−i30000000000
χ512-22-22i−2i2i−2i2-1-22−2i2i2-2-21-112i−2i−ii−ii2i−2i-22-1−2i2i-111-22i−i−ii−ii−2i2i1-1-221-111-1-1−2i2ii−i1-1i−iii−i−i000000003−33−3−i3i3−i3i30000000000000000−33i3−i30000000000
χ522-22-22i−2i2i−2i2-1-22−2i2i2-2-21-112i−2i−ii−ii2i−2i-22-1−2i2i-111-22i−i−ii−ii−2i2i1-1-221-111-1-1−2i2ii−i1-1i−iii−i−i00000000−33−33i3−i3i3−i300000000000000003−3−i3i30000000000
χ532-22-22i−2i2i−2i-12-22−2i2i-111-22-2−ii2i−2i2i−2i−ii2-2-12i−2i-1111-1−2i2i−ii−iii−i-22-112-2-1-111−ii2i−2i1-1i−i−i−iii0000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ542-22-22i−2i2i−2i-12-22−2i2i-111-22-2−ii2i−2i2i−2i−ii2-2-12i−2i-1111-1−2i2i−ii−iii−i-22-112-2-1-111−ii2i−2i1-1i−i−i−iii0000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ552-22-22i−2i2i−2i-12-22−2i2i-111-22-2−ii2i−2i2i−2i−ii-22-1−2i2i-1111-1−2i2i−ii−iii−i-221-1-2211-1-1i−i−2i2i1-1i−iii−i−i0000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ562-22-22i−2i2i−2i-12-22−2i2i-111-22-2−ii2i−2i2i−2i−ii-22-1−2i2i-1111-1−2i2i−ii−iii−i-221-1-2211-1-1i−i−2i2i1-1i−iii−i−i0000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ572-22-2−2i2i−2i2i222-2−2i2i2-2-2-22-2−2i2i−2i2i−2i2i−2i2i002002-2-22-2−2i2i−2i2i−2i2i−2i2i2-20000000000002-2−2i2i00000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ582-22-2−2i2i−2i2i222-2−2i2i2-2-2-22-2−2i2i−2i2i−2i2i−2i2i002002-2-22-2−2i2i−2i2i−2i2i−2i2i2-20000000000002-2−2i2i0000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ592-22-2−2i2i−2i2i22-222i−2i2-2-2-22-2−2i2i−2i2i−2i2i−2i2i2-22−2i2i2-2-2-222i−2i−2i2i−2i2i2i−2i-222-22-222-2-2−2i2i−2i2i-222i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ602-22-2−2i2i−2i2i22-222i−2i2-2-2-22-2−2i2i−2i2i−2i2i−2i2i-2222i−2i2-2-2-222i−2i−2i2i−2i2i2i−2i-22-22-22-2-2222i−2i2i−2i-222i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ612-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11−2i2ii−ii−i−2i2i2-2-1−2i2i-111-22−iii−ii−i2i−2i1-12-2-11-1-111−2i2ii−i1-1−iiii−i−i000000003−33−3i3−i3i3−i300000000000000003−3i3−i30000000000
χ622-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11−2i2ii−ii−i−2i2i2-2-1−2i2i-111-22−iii−ii−i2i−2i1-12-2-11-1-111−2i2ii−i1-1−iiii−i−i00000000−33−33−i3i3−i3i30000000000000000−33−i3i30000000000
χ632-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11−2i2ii−ii−i−2i2i-22-12i−2i-111-22−iii−ii−i2i−2i1-1-221-111-1-12i−2i−ii1-1−ii−i−iii000000003−33−3i3−i3i3−i30000000000000000−33−i3i30000000000
χ642-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11−2i2ii−ii−i−2i2i-22-12i−2i-111-22−iii−ii−i2i−2i1-1-221-111-1-12i−2i−ii1-1−ii−i−iii00000000−33−33−i3i3−i3i300000000000000003−3i3−i30000000000
χ652-22-2−2i2i−2i2i-12-222i−2i-111-22-2i−i−2i2i−2i2ii−i2-2-1−2i2i-1111-12i−2ii−ii−i−ii-22-112-2-1-111i−i−2i2i1-1−iiii−i−i0000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.