Finite Group Databasebeta

← Group #13155433

Character table — Group #13155433

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order124423334666661212121212121212333666666666121212121212121212121212224466121236666121212121244666666688121212121212121212121212121212121212121212121224242424242424242424244488121212122424242461224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-11111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-111
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
χ911-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-1i−i1-1-111-1-1i−i11-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1ii−i−ii−iii−i−i1-1i−ii−iii−i−iii−i−i1-1-11
χ1011-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-1i−i1-1-111-1-1−ii11-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1−i−iii−ii−i−iii-11i−i−iiii−i−i−i−iii-111-1
χ1111-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-1−ii1-1-111-1-1i−i11-1−i−iii−i−i−i−i−i−iiiiiii11-1-1ii−i−ii−iii−i−i-11−iii−i−i−iiiii−i−i-111-1
χ1211-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-11-11-111-1-11-1-1-11111-1-1−ii1-1-111-1-1−ii11-1−i−iii−i−i−i−i−i−iiiiiii11-1-1−i−iii−ii−i−iii1-1−ii−ii−i−iii−i−iii1-1-11
χ1311-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-1i−i-111-1-111i−i-1-11ii−i−iiiiiii−i−i−i−i−i−i-1-111ii−i−ii−iii−i−i1-1−ii−ii−i−iii−i−iii1-11-1
χ1411-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-1i−i-111-1-111−ii-1-11ii−i−iiiiiii−i−i−i−i−i−i-1-111−i−iii−ii−i−iii-11−iii−i−i−iiiii−i−i-11-11
χ1511-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-1−ii-111-1-111i−i-1-11−i−iii−i−i−i−i−i−iiiiiii-1-111ii−i−ii−iii−i−i-11i−i−iiii−i−i−i−iii-11-11
χ1611-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-111111-1-111-1-1-1-1-11-11-1-1111-1-1-11111-1-1−ii-111-1-111−ii-1-11−i−iii−i−i−i−i−i−iiiiiii-1-111−i−iii−ii−i−iii1-1i−ii−iii−i−iii−i−i1-11-1
χ172222222-1222-1222222-1-122-1-12222-1-1-1-1-122-1-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-1220000000220002222-1-1-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-122000000000000-1-100
χ182222222-1222-1222222-1-122-1-12222-1-1-1-1-122-1-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-1220000000-2-20002222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2111111-2-20000000000001100
χ192222222-1222-1222222-1-122-1-12222-1-1-1-1-122-1-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2000000022000-2-2-2-211111111111100002222-1-1-1-1-1-1-2-20000000000001100
χ202222222-1222-1222222-1-122-1-12222-1-1-1-1-122-1-1-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-1-1-2-20000000-2-2000-2-2-2-21111111111110000-2-2-2-211111122000000000000-1-100
χ21222222-1222-1222222222-1-12-1-1-1-1-12-1222-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1-1222-120000000000000000-1-1-1-1-1-1-1-122-1-1-1-10000220000-1-1-1-10000
χ22222222-1222-1222222222-1-12-1-1-1-1-12-1222-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1-1-2-22-120000000000000000-1-1-1-11111-2-211110000-2-2000011110000
χ23222222-1222-1222222222-1-12-1-1-1-1-12-1222-1-122222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-100-2-21111122-21-200000000000000001111-1-1-1-122-1-1-1-10000-2-2000011110000
χ24222222-1222-1222222222-1-12-1-1-1-1-12-1222-1-122222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-100-2-211111-2-2-21-2000000000000000011111111-2-211110000220000-1-1-1-10000
χ2522222-1222-122-1-1-1-1-1-12222-12-12-1-1-122-1-1-122-1-1-1-1-1-1-1-12222222222-12-1-1-12-1-1-1-122-1-12-1-1-1-100-12-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-10000000000002200-1-1-1-100000000
χ2622222-1222-122-1-1-1-1-1-12222-12-12-1-1-122-1-1-122-1-1-1-1-1-1-1-12222222222-12-1-1-12-1-1-1-1-2-2-1-12-1-1-1-100-12-11111-2-21111-2-21111-1-1-1-1000000000000-2-200111100000000
χ2722222-1222-122-1-1-1-1-1-12222-12-12-1-1-122-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-12211-21111001-21-1-1-1-122-1-1-1-122-1-1-1-11111000000000000-2-200111100000000
χ2822222-1222-122-1-1-1-1-1-12222-12-12-1-1-122-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-1-2-211-21111001-211111-2-21111-2-2111111110000000000002200-1-1-1-100000000
χ292222-2222-2222-2-2-2-2222222222-2-2-222-2-2-22-2-2-2-222-2-222222-2-2222222-2-2-22-2-2-222002-2-222-2-200-2-220000000000000000-2-2220000000000000000000000000000
χ302222-2222-2222-2-2-2-2222222222-2-2-222-2-2-22-2-2-2-222-2-22222-222-2-2-2-2-22-2-2-22-2-2-22200-222-2-2220022-2000000000000000022-2-20000000000000000000000000000
χ312222-22-12-22-12-2-2-2-22222-1-12-1-11112-1-2-2-2-11-2-2-22211-1-1-1-12-2-22-1-1-1-1-1111-1111-1-1002-21-1-11100-212000000000000000011-1-1−i3i3−i3i300−i3i3−i3i30000000000−i3i3−i3i30000
χ322222-22-12-22-12-2-2-2-22222-1-12-1-11112-1-2-2-2-11-2-2-22211-1-1-1-12-2-22-1-1-1-1-1111-1111-1-1002-21-1-11100-212000000000000000011-1-1i3−i3i3−i300i3−i3i3−i30000000000i3−i3i3−i30000
χ332222-22-12-22-12-2-2-2-22222-1-12-1-11112-1-2-2-2-11-2-2-22211-1-1-1-1-222-21111-1111-1111-1-100-22-111-1-1002-1-20000000000000000-1-111−i3i3−i3i300−i3i3−i3i30000000000i3−i3i3−i30000
χ342222-22-12-22-12-2-2-2-22222-1-12-1-11112-1-2-2-2-11-2-2-22211-1-1-1-1-222-21111-1111-1111-1-100-22-111-1-1002-1-20000000000000000-1-111i3−i3i3−i300i3−i3i3−i30000000000−i3i3−i3i30000
χ352222-2-122-2-1221111-1-12222-12-1-211-12-211-1-2-211-1-111-1-1222-2-222222-1-211-1-211-1-100-11-2-1-111001-2-13−33−30033−3−30033−3−311-1-100000000000000003−33−300000000
χ362222-2-122-2-1221111-1-12222-12-1-211-12-211-1-2-211-1-111-1-1222-2-222222-1-211-1-211-1-100-11-2-1-111001-2-1−33−3300−3−33300−3−33311-1-10000000000000000−33−3300000000
χ372222-2-122-2-1221111-1-12222-12-1-211-12-211-1-2-211-1-111-1-122-222-2-2-2-2-2-1-211-1-211-1-1001-1211-1-100-1213−33−30033−3−30033−3−3-1-1110000000000000000−33−3300000000
χ382222-2-122-2-1221111-1-12222-12-1-211-12-211-1-2-211-1-111-1-122-222-2-2-2-2-2-1-211-1-211-1-1001-1211-1-100-121−33−3300−3−33300−3−333-1-11100000000000000003−33−300000000
χ3922-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222222-2-2-2-2-200222222200-2-2-20000000000000000-2-2-2-20000000000000000000000000000
χ4022-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222-2-2-2-2-200-2-2-2-2-2-2-200222000000000000000022220000000000000000000000000000
χ4122-2-222-12-22-1222-2-2-2-2-2-2112-1-1-1-1-12-1222-11-2-2-2-2-211111122-2-2-1-111-1-1-1-1-1111110022-1-1-1-1-100-21-2000000000000000011113−3−33003−3−3300000000003−3−330000
χ4222-2-222-12-22-1222-2-2-2-2-2-2112-1-1-1-1-12-1222-11-2-2-2-2-211111122-2-2-1-111-1-1-1-1-1111110022-1-1-1-1-100-21-200000000000000001111−333−300−333−30000000000−333−30000
χ4322-2-222-12-22-1222-2-2-2-2-2-2112-1-1-1-1-12-1222-11-2-2-2-2-2111111-2-22211-1-1-1-1-1-1-11111100-2-211111002-120000000000000000-1-1-1-13−3−33003−3−330000000000−333−30000
χ4422-2-222-12-22-1222-2-2-2-2-2-2112-1-1-1-1-12-1222-11-2-2-2-2-2111111-2-22211-1-1-1-1-1-1-11111100-2-211111002-120000000000000000-1-1-1-1−333−300−333−300000000003−3−330000
χ4522-2-22-122-2-122-1-11111-2-2-2-2-12-12-1-1-122-1-1-1-2-211111111-2-222-2-222-2-2-12-1-1-1-2111100-1-12-1-1-1-1001-21−i3i3i3−i300−i3−i3i3i300i3i3−i3−i311110000000000000000−i3i3i3−i300000000
χ4622-2-22-122-2-122-1-11111-2-2-2-2-12-12-1-1-122-1-1-1-2-211111111-2-222-2-222-2-2-12-1-1-1-2111100-1-12-1-1-1-1001-21i3−i3−i3i300i3i3−i3−i300−i3−i3i3i311110000000000000000i3−i3−i3i300000000
χ4722-2-22-122-2-122-1-11111-2-2-2-2-12-12-1-1-122-1-1-1-2-211111111-2-2-2-222-2-222-12-1-1-1-211110011-2111100-12-1−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-1-1-1-10000000000000000i3−i3−i3i300000000
χ4822-2-22-122-2-122-1-11111-2-2-2-2-12-12-1-1-122-1-1-1-2-211111111-2-2-2-222-2-222-12-1-1-1-211110011-2111100-12-1i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-1-1-1-10000000000000000−i3i3i3−i300000000
χ4922-2-2-222-1222-1-2-222-2-211-2-2-1-12-2-2-2-1-111122-1-1-11122-2-21100000000-1111-1-1-1-1112i−2i00000002i−2i0002i2i−2i−2i−i−i−i−i−i−iiiiiii00002i2i−2i−2i−ii−i−iii2-2000000000000-1100
χ5022-2-2-222-1222-1-2-222-2-211-2-2-1-12-2-2-2-1-111122-1-1-11122-2-21100000000-1111-1-1-1-1112i−2i0000000−2i2i0002i2i−2i−2i−i−i−i−i−i−iiiiiii0000−2i−2i2i2ii−iii−i−i-220000000000001-100
χ5122-2-2-222-1222-1-2-222-2-211-2-2-1-12-2-2-2-1-111122-1-1-11122-2-21100000000-1111-1-1-1-111−2i2i00000002i−2i000−2i−2i2i2iiiiiii−i−i−i−i−i−i00002i2i−2i−2i−ii−i−iii-220000000000001-100
χ5222-2-2-222-1222-1-2-222-2-211-2-2-1-12-2-2-2-1-111122-1-1-11122-2-21100000000-1111-1-1-1-111−2i2i0000000−2i2i000−2i−2i2i2iiiiiii−i−i−i−i−i−i0000−2i−2i2i2ii−iii−i−i2-2000000000000-1100
χ5322-2-2-22-1222-12-2-222-2-2-2-2112-1-11112-1-2-2-2-1-1222-2-2-1-111112-22-2-1-111-1111-1-1-1-111002-21-1-1112i−2i2-1-20000000000000000-1-111−i−iii2i−2i−i−iii00002i−2i0000−i−iii0000
χ5422-2-2-22-1222-12-2-222-2-2-2-2112-1-11112-1-2-2-2-1-1222-2-2-1-111112-22-2-1-111-1111-1-1-1-111002-21-1-111−2i2i2-1-20000000000000000-1-111ii−i−i−2i2iii−i−i0000−2i2i0000ii−i−i0000
χ5522-2-2-22-1222-12-2-222-2-2-2-2112-1-11112-1-2-2-2-1-1222-2-2-1-11111-22-2211-1-1-1111-1-1-1-11100-22-111-1-12i−2i-212000000000000000011-1-1−i−iii2i−2i−i−iii0000−2i2i0000ii−i−i0000
χ5622-2-2-22-1222-12-2-222-2-2-2-2112-1-11112-1-2-2-2-1-1222-2-2-1-11111-22-2211-1-1-1111-1-1-1-11100-22-111-1-1−2i2i-212000000000000000011-1-1ii−i−i−2i2iii−i−i00002i−2i0000−i−iii0000
χ5722-2-2-2-1222-12211-1-111-2-2-2-2-12-1-211-12-211-122-1-111-1-111-2-22-22-222-2-2-1-211-12-1-1112i−2i-11-2-1-11100-121−i−iii2i2i−i−i−i−i−2i−2iiiii-1-1110000000000002i−2i00−i−iii00000000
χ5822-2-2-2-1222-12211-1-111-2-2-2-2-12-1-211-12-211-122-1-111-1-111-2-22-22-222-2-2-1-211-12-1-111−2i2i-11-2-1-11100-121ii−i−i−2i−2iiiii2i2i−i−i−i−i-1-111000000000000−2i2i00ii−i−i00000000
χ5922-2-2-2-1222-12211-1-111-2-2-2-2-12-1-211-12-211-122-1-111-1-111-2-2-22-22-2-222-1-211-12-1-1112i−2i1-1211-1-1001-2-1−i−iii2i2i−i−i−i−i−2i−2iiiii11-1-1000000000000−2i2i00ii−i−i00000000
χ6022-2-2-2-1222-12211-1-111-2-2-2-2-12-1-211-12-211-122-1-111-1-111-2-2-22-22-2-222-1-211-12-1-111−2i2i1-1211-1-1001-2-1ii−i−i−2i−2iiiii2i2i−i−i−i−i11-1-10000000000002i−2i00−i−iii00000000
χ61444444-2-244-2-2444444-2-2-2-2-21-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2110000000011111111110000000004400000000000000000000000-2-2-2-2-2-21111000000000000000000
χ62444444-2-244-2-2444444-2-2-2-2-21-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-211000000001111111111000000000-4-400000000000000000000000222222-1-1-1-1000000000000000000
χ6344444-24-24-24-2-2-2-2-2-2-2-2-2441-2-24-2-21-2-211-24-21111-2-2-2-2-2-2000000001-2111-2111144000000000000-2-2-2-2-2-21111-2-2111100000000000000000000000000000000
χ6444444-24-24-24-2-2-2-2-2-2-2-2-2441-2-24-2-21-2-211-24-21111-2-2-2-2-2-2000000001-2111-21111-4-4000000000000222222-1-1-1-122-1-1-1-100000000000000000000000000000000
χ6544444-2-244-2-24-2-2-2-2-2-244-2-2-2-21-211-2-24-2-21-24-2-2-2-21111-2-24444-2-2-2-21-2111-2111100-2-2-2111100-2-2-2000000000000000011110000000000000000000000000000
χ6644444-2-244-2-24-2-2-2-2-2-244-2-2-2-21-211-2-24-2-21-24-2-2-2-21111-2-2-4-4-4-422221-2111-2111100222-1-1-1-1002220000000000000000-1-1-1-10000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.