Finite Group Databasebeta

← Group #13155754

Character table — Group #13155754

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order1244233346666612121212121212123336666666661212121212121212121212128888242424243666612121212124488121212121212121212121212121212122424242424242424242424242424242424242424242424242244668812122424242461288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111-11-111-1-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-11-11-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1i−ii−iii−i−iiiiiii−i−i−i−i−i−iii−i−ii−iii−i−iiiii−i−i−i−ii−iii−i−i11-1-1111-1-1-111-1-11-1i−i
χ1011-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1i−i−iiii−i−iiiiiii−i−i−i−i−i−iii−i−ii−i−i−iiiiiii−i−i−i−i−ii−i−iii-1-111-1-11-11111-1-1-11−ii
χ1111-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1−iii−i−i−iii−i−i−i−i−i−iiiiiiiii−i−ii−iii−i−iiiii−i−i−i−ii−iii−i−i1-1-1111-11-1-1-1-111-11−ii
χ1211-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1−ii−ii−i−iii−i−i−i−i−i−iiiiiiiii−i−ii−i−i−iiiiiii−i−i−i−i−ii−i−iii-111-1-1-1-1111-1-1111-1i−i
χ1311-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1i−ii−iii−i−iiiiiii−i−i−i−i−i−i−i−iii−iiii−i−i−i−i−i−iiiiii−iii−i−i-111-1-1-1-1111-1-1111-1−ii
χ1411-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1i−i−iiii−i−iiiiiii−i−i−i−i−i−i−i−iii−ii−i−iii−i−i−i−iiiii−ii−i−iii1-1-1111-11-1-1-1-111-11i−i
χ1511-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1−iii−i−i−iii−i−i−i−i−i−iiiiiii−i−iii−iiii−i−i−i−i−i−iiiiii−iii−i−i-1-111-1-11-11111-1-1-11i−i
χ1611-1-1-111111-1-111-1-1-1-1-1-111111-1-1-1111-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1−ii−ii−i−iii−i−i−i−i−i−iiiiiii−i−iii−ii−i−iii−i−i−i−iiiii−ii−i−iii11-1-1111-1-1-111-1-11-1−ii
χ172222222-122222-12222-1-1222-1-1-1-1-12-1-12222-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12020-1-100-1-100000000
χ182222222-122222-12222-1-1222-1-1-1-1-12-1-12222-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-200000000000000002222-1-11111-1-1-1-1-1-1-1-1-2-21111-20-2011001100000000
χ192222222-122222-12222-1-1222-1-1-1-1-12-1-12222-122-1-122-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-100220000000000000000-2-2-2-211-1-1-1-11111111122-1-1-1-1-20-2011001100000000
χ202222222-122222-12222-1-1222-1-1-1-1-12-1-12222-122-1-122-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2-2-211111111111111-2-211112020-1-100-1-100000000
χ21222222-122222-1222-1-12222-12-1222-12-1-1-1-1-12-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000000222200000000-1-1-1-1-1-102020000000000-1-100
χ22222222-122222-1222-1-12222-12-1222-12-1-1-1-1-12-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-122-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-2000000001111110-20-200000000001100
χ23222222-122222-1222-1-12222-12-1222-12-1-1-1-1-12-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2111111111111000000222200000000-1-1-1-1-1-10-20-200000000001100
χ24222222-122222-1222-1-12222-12-1222-12-1-1-1-1-12-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111000000-2-2-2-20000000011111102020000000000-1-100
χ2522222-1222-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-12222222222-12-1-1-12-1-1-1-12200-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-10000000000002200-1-1-1-10000
χ2622222-1222-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-12222222222-12-1-1-12-1-1-1-1-2-2001111-2-21111-2-21111-1-1-1-1220000-1-1-1-1-1-1-1-1000000000000-2-20011110000
χ2722222-1222-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-12200-1-1-1-122-1-1-1-122-1-1-1-11111-2-2000011111111000000000000-2-20011110000
χ2822222-1222-1-1-122-1-12222-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-1-2-2001111-2-21111-2-211111111-2-20000111111110000000000002200-1-1-1-10000
χ292222-2222-22-2-222222222-2-2222-2-2-2222-2-2-2-2-2-2-2-2-22222222-22-222222-2-2-22-2-2-222000000000000000000002-22-2-2-2000022-2-222-2-2000000000000000000000000
χ302222-2222-22-2-222222222-2-2222-2-2-2222-2-2-2-2-2-2-2-2-2222222-22-22-2-2-2-22-2-2-22-2-2-22200000000000000000000-22-22220000-2-222-2-222000000000000000000000000
χ312222-222-1-22-2-22-12222-1-1-2-22-1-11112-1-1-2-2-2-21-2-21122-1-1-1-12-22-2-1-1-1-1-1111-1111-1-1000000000000000000002-22-211−i3i3−i3i3-1-111-1-11100−i3i3−i3i30000−i3i300−i3i300000000
χ322222-222-1-22-2-22-12222-1-1-2-22-1-11112-1-1-2-2-2-21-2-21122-1-1-1-12-22-2-1-1-1-1-1111-1111-1-1000000000000000000002-22-211i3−i3i3−i3-1-111-1-11100i3−i3i3−i30000i3−i300i3−i300000000
χ332222-222-1-22-2-22-12222-1-1-2-22-1-11112-1-1-2-2-2-21-2-21122-1-1-1-1-22-221111-1111-1111-1-100000000000000000000-22-22-1-1−i3i3−i3i311-1-111-1-100−i3i3−i3i30000i3−i300i3−i300000000
χ342222-222-1-22-2-22-12222-1-1-2-22-1-11112-1-1-2-2-2-21-2-21122-1-1-1-1-22-221111-1111-1111-1-100000000000000000000-22-22-1-1i3−i3i3−i311-1-111-1-100i3−i3i3−i30000−i3i300−i3i300000000
χ352222-2-122-2-11122-1-1222211-1-12-211-1-12-211-2-21111-1-1-1-1222-22-22222-1-211-1-211-1-100003−33−30033−3−30033−3−3-11-11-2-20000-1-111-1-11100000000000000003−33−30000
χ362222-2-122-2-11122-1-1222211-1-12-211-1-12-211-2-21111-1-1-1-1222-22-22222-1-211-1-211-1-10000−33−3300−3−33300−3−333-11-11-2-20000-1-111-1-1110000000000000000−33−330000
χ372222-2-122-2-11122-1-1222211-1-12-211-1-12-211-2-21111-1-1-1-122-22-22-2-2-2-2-1-211-1-211-1-100003−33−30033−3−30033−3−31-11-122000011-1-111-1-10000000000000000−33−330000
χ382222-2-122-2-11122-1-1222211-1-12-211-1-12-211-2-21111-1-1-1-122-22-22-2-2-2-2-1-211-1-211-1-10000−33−3300−3−33300−3−3331-11-122000011-1-111-1-100000000000000003−33−30000
χ3922-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22i−2i−2i2i2i2i−2i−2i22222-2-2-2-2-2000000000000000000002i−2i−2i2i−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4022-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2−2i2i2i−2i−2i−2i2i2i22222-2-2-2-2-200000000000000000000−2i2i2i−2i2i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4122-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12-1-1222-21-2-211-2-211112i−2i−2i2i−i−iii-1-1-1-1-111111000000000000000000002i−2i−2i2ii−i3−3−33−i−iiiii−i−i003−3−330000−i3i300i3−i300000000
χ4222-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12-1-1222-21-2-211-2-211112i−2i−2i2i−i−iii-1-1-1-1-111111000000000000000000002i−2i−2i2ii−i−333−3−i−iiiii−i−i00−333−30000i3−i300−i3i300000000
χ4322-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12-1-1222-21-2-211-2-21111−2i2i2i−2iii−i−i-1-1-1-1-11111100000000000000000000−2i2i2i−2i−ii3−3−33ii−i−i−i−iii003−3−330000i3−i300−i3i300000000
χ4422-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-1-12-1-1222-21-2-211-2-21111−2i2i2i−2iii−i−i-1-1-1-1-11111100000000000000000000−2i2i2i−2i−ii−333−3ii−i−i−i−iii00−333−30000−i3i300i3−i300000000
χ4522-2-22-122-2-1-1-12211-2-2-2-211-1-122-1-1-1-122-1-1-2-211111111-2-22i−2i−2i2i2i2i−2i−2i-12-1-1-1-211110000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3−iii−i−2i2i0000−i−iiiii−i−i0000000000000000−333−30000
χ4622-2-22-122-2-1-1-12211-2-2-2-211-1-122-1-1-1-122-1-1-2-211111111-2-22i−2i−2i2i2i2i−2i−2i-12-1-1-1-211110000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3−iii−i−2i2i0000−i−iiiii−i−i00000000000000003−3−330000
χ4722-2-22-122-2-1-1-12211-2-2-2-211-1-122-1-1-1-122-1-1-2-211111111-2-2−2i2i2i−2i−2i−2i2i2i-12-1-1-1-211110000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3i−i−ii2i−2i0000ii−i−i−i−iii00000000000000003−3−330000
χ4822-2-22-122-2-1-1-12211-2-2-2-211-1-122-1-1-1-122-1-1-2-211111111-2-2−2i2i2i−2i−2i−2i2i2i-12-1-1-1-211110000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3i−i−ii2i−2i0000ii−i−i−i−iii0000000000000000−333−30000
χ4922-2-2-222-122-2-22-1-2-2-2-211222-1-11112-1-1-2-2-22-122-1-1-2-211112i2i−2i−2i−i−iii-1111-1-1-1-111002i−2i00000000000000002i2i−2i−2i−ii−i−iii−i−i−i−iiiii2i−2i−i−iii20-20-1-1001100000000
χ5022-2-2-222-122-2-22-1-2-2-2-211222-1-11112-1-1-2-2-22-122-1-1-2-211112i2i−2i−2i−i−iii-1111-1-1-1-11100−2i2i00000000000000002i2i−2i−2i−iiii−i−i−i−i−i−iiiii−2i2iii−i−i-20201100-1-100000000
χ5122-2-2-222-122-2-22-1-2-2-2-211222-1-11112-1-1-2-2-22-122-1-1-2-21111−2i−2i2i2iii−i−i-1111-1-1-1-111002i−2i0000000000000000−2i−2i2i2ii−i−i−iiiiiii−i−i−i−i2i−2i−i−iii-20201100-1-100000000
χ5222-2-2-222-122-2-22-1-2-2-2-211222-1-11112-1-1-2-2-22-122-1-1-2-21111−2i−2i2i2iii−i−i-1111-1-1-1-11100−2i2i0000000000000000−2i−2i2i2ii−iii−i−iiiii−i−i−i−i−2i2iii−i−i20-20-1-1001100000000
χ5322-2-2-22-1222-2-2-12-2-211-2-222-12-1-2-2-2-12-1111-12-1-12211-2-21100000000-1111-1-1-1-1112i−2i2i−2i2i2i−2i−2i−i−i−i−i−i−iiiiiii0000002i2i−2i−2i00000000−ii−i−iii020-20000000000-1100
χ5422-2-2-22-1222-2-2-12-2-211-2-222-12-1-2-2-2-12-1111-12-1-12211-2-21100000000-1111-1-1-1-1112i−2i−2i2i2i2i−2i−2i−i−i−i−i−i−iiiiiii000000−2i−2i2i2i00000000i−iii−i−i0-20200000000001-100
χ5522-2-2-22-1222-2-2-12-2-211-2-222-12-1-2-2-2-12-1111-12-1-12211-2-21100000000-1111-1-1-1-111−2i2i2i−2i−2i−2i2i2iiiiiii−i−i−i−i−i−i0000002i2i−2i−2i00000000−ii−i−iii0-20200000000001-100
χ5622-2-2-22-1222-2-2-12-2-211-2-222-12-1-2-2-2-12-1111-12-1-12211-2-21100000000-1111-1-1-1-111−2i2i−2i2i−2i−2i2i2iiiiiii−i−i−i−i−i−i000000−2i−2i2i2i00000000i−iii−i−i020-20000000000-1100
χ5722-2-2-2-1222-1112211-2-2-2-2-1-1-1-12-211-1-12-21122-1-1-1-11111-2-22i2i−2i−2i2i2i−2i−2i-1-211-12-1-1112i−2i00−i−iii2i2i−i−i−i−i−2i−2iiiii−i−iii2i−2i0000−i−i−i−iiiii0000000000002-200-1-1110000
χ5822-2-2-2-1222-1112211-2-2-2-2-1-1-1-12-211-1-12-21122-1-1-1-11111-2-22i2i−2i−2i2i2i−2i−2i-1-211-12-1-111−2i2i00ii−i−i−2i−2iiiii2i2i−i−i−i−i−i−iii2i−2i0000−i−i−i−iiiii000000000000-220011-1-10000
χ5922-2-2-2-1222-1112211-2-2-2-2-1-1-1-12-211-1-12-21122-1-1-1-11111-2-2−2i−2i2i2i−2i−2i2i2i-1-211-12-1-1112i−2i00−i−iii2i2i−i−i−i−i−2i−2iiiiiii−i−i−2i2i0000iiii−i−i−i−i000000000000-220011-1-10000
χ6022-2-2-2-1222-1112211-2-2-2-2-1-1-1-12-211-1-12-21122-1-1-1-11111-2-2−2i−2i2i2i−2i−2i2i2i-1-211-12-1-111−2i2i00ii−i−i−2i−2iiiii2i2i−i−i−i−iii−i−i−2i2i0000iiii−i−i−i−i0000000000002-200-1-1110000
χ61444444-2-24444-2-244-2-2-2-244-2-21-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-21100000000111111111100440000000000000000000000-2-2-2-200000000-2-21111000000000000000000
χ62444444-2-24444-2-244-2-2-2-244-2-21-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-21100000000111111111100-4-4000000000000000000000022220000000022-1-1-1-1000000000000000000
χ6344444-24-24-2-2-24-2-2-244-2-2-2-2-21-2-211-21-24-2-24-2-2-211-2-211-2-24444-2-2-2-21-2111-2111100000000000000000000-2-2-2-2-2-2000011111111000000000000000000000000
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χ1258-8−8i8i0-4-4-404−4i34i3444i−4i4i−4i4i−4i−434322202i3−2i3-2-2-202i3−2i30023−2323−23−2i2i−2i2i−2i2i00000000-10−i3i310−33i−i00000000000000000000000000000000000000000000000000000000000000
χ1268-8−8i8i0-4-4-4044i3−4i3444i−4i4i−4i4i−4i43−432220−2i32i3-2-2-20−2i32i300−2323−2323−2i2i−2i2i−2i2i00000000-10i3−i3103−3i−i00000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.