Finite Group Databasebeta

← Group #13156729

Character table — Group #13156729

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order12222222333666666666666666666666333666666666666666666666444436666666444412121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222224444666612121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ9111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1i−ii−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−i11-1-1ii−i−iii−i−i11-1-1
χ10111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1i−i−ii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111i−i−ii-1-111ii−i−i−i−iii-1-111
χ11111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1−iii−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−iii−i-1-111−i−iiiii−i−i-1-111
χ12111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1−ii−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii11-1-1−i−iii−i−iii11-1-1
χ13111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1i−ii−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-1−ii−ii11-1-1−i−iii−i−iii-1-111
χ14111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1i−i−ii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111−iii−i-1-111−i−iiiii−i−i11-1-1
χ15111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1−iii−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111i−i−ii-1-111ii−i−i−i−iii11-1-1
χ16111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1−ii−ii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-1i−ii−i11-1-1ii−i−iii−i−i-1-111
χ172222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-10000-1-1-1-1-1-1-1-122220000000022-1-122-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1000000000000
χ182222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-10000-1-1-1-1-1-1-1-122-2-20000000022-1-122-1-1-2-211-2-21100000000-1-1-1-1-1-1-1-111111111-2-2-2-200001111000000000000
χ192222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-10000-1-1-1-1-1-1-1-1-2-22200000000-2-211-2-21122-1-122-1-10000000011111111-1-1-1-1-1-1-1-1-2-2-2-200001111000000000000
χ202222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-10000-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211-2-211-2-211-2-21100000000111111111111111122220000-1-1-1-1000000000000
χ21222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-12222-1-1-1-1-1-1-1-1002222-1-122-1-100000000-1-122-1-122-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000002200000000-1-1-1-10000
χ22222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-12222-1-1-1-1-1-1-1-100-2-222-1-122-1-10000000011-2-211-2-2-1-1-1-1-1-1-1-10000000011111111000000-2-20000000011110000
χ23222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-2-2-2-2-1-1-1-1-1-1-1-10022-2-211-2-21100000000-1-122-1-1221111111100000000-1-1-1-1-1-1-1-1000000-2-20000000011110000
χ24222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-2-2-2-2-1-1-1-1-1-1-1-100-2-2-2-211-2-2110000000011-2-211-2-21111111100000000111111110000002200000000-1-1-1-10000
χ2522222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-122222-1-1-1-1-1-1-1-12200-1-122-1-122-1-122-1-12200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022000000-1-1-1-100000000
χ2622222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-122222-1-1-1-1-1-1-1-1-2-200-1-122-1-12211-2-211-2-200000000-1-1-1-1-1-1-1-111111111000000000000-2-2000000111100000000
χ2722222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-12-2-2-2-2-1-1-1-1-1-1-1-1220011-2-211-2-2-1-122-1-1220000000011111111-1-1-1-1-1-1-1-1000000000000-2-2000000111100000000
χ2822222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-12-2-2-2-2-1-1-1-1-1-1-1-1-2-20011-2-211-2-211-2-211-2-200000000111111111111111100000000000022000000-1-1-1-100000000
χ29222-2-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-21111112110000-1-1-1-111112i−2i2i−2i000000002i2i−i−i−2i−2iii2i2i−i−i−2i−2iii00000000−i−i−i−iiiii−i−i−i−iiiii22-2-20000-1-111000000000000
χ30222-2-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-21111112110000-1-1-1-111112i−2i−2i2i000000002i2i−i−i−2i−2iii−2i−2iii2i2i−i−i00000000−i−i−i−iiiiiiiii−i−i−i−i-2-222000011-1-1000000000000
χ31222-2-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-21111112110000-1-1-1-11111−2i2i2i−2i00000000−2i−2iii2i2i−i−i2i2i−i−i−2i−2iii00000000iiii−i−i−i−i−i−i−i−iiiii-2-222000011-1-1000000000000
χ32222-2-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-21111112110000-1-1-1-11111−2i2i−2i2i00000000−2i−2iii2i2i−i−i−2i−2iii2i2i−i−i00000000iiii−i−i−i−iiiii−i−i−i−i22-2-20000-1-111000000000000
χ33222-2-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-2122-2-2-1-1-1-11111002i−2i22-1-1-2-21100000000−i−i2i2iii−2i−2i-1-1-1-1111100000000−i−i−i−iiiii0000002i−2i00000000−i−iii0000
χ34222-2-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-2122-2-2-1-1-1-1111100−2i2i22-1-1-2-21100000000ii−2i−2i−i−i2i2i-1-1-1-1111100000000iiii−i−i−i−i000000−2i2i00000000ii−i−i0000
χ35222-2-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-21-2-222-1-1-1-11111002i−2i-2-21122-1-100000000−i−i2i2iii−2i−2i1111-1-1-1-100000000−i−i−i−iiiii000000−2i2i00000000ii−i−i0000
χ36222-2-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-21-2-222-1-1-1-1111100−2i2i-2-21122-1-100000000ii−2i−2i−i−i2i2i1111-1-1-1-100000000iiii−i−i−i−i0000002i−2i00000000−i−iii0000
χ37222-2-2-2-22-122-1-12211-2-2222-2-2-121-2-2-21-2-1-12-1-1-1-1-12221111111-2-2-2-11-222-2-2-1-1-1-111112i−2i00-1-12211-2-2−i−i2i2iii−2i−2i00000000-1-1-1-11111−i−i−i−iiiii0000000000002i−2i000000−i−iii00000000
χ38222-2-2-2-22-122-1-12211-2-2222-2-2-121-2-2-21-2-1-12-1-1-1-1-12221111111-2-2-2-11-222-2-2-1-1-1-11111−2i2i00-1-12211-2-2ii−2i−2i−i−i2i2i00000000-1-1-1-11111iiii−i−i−i−i000000000000−2i2i000000ii−i−i00000000
χ39222-2-2-2-22-122-1-12211-2-2222-2-2-121-2-2-21-2-1-12-1-1-1-1-12221111111-2-2-2-11-2-2-222-1-1-1-111112i−2i0011-2-2-1-122−i−i2i2iii−2i−2i000000001111-1-1-1-1−i−i−i−iiiii000000000000−2i2i000000ii−i−i00000000
χ40222-2-2-2-22-122-1-12211-2-2222-2-2-121-2-2-21-2-1-12-1-1-1-1-12221111111-2-2-2-11-2-2-222-1-1-1-11111−2i2i0011-2-2-1-122ii−2i−2i−i−i2i2i000000001111-1-1-1-1iiii−i−i−i−i0000000000002i−2i000000−i−iii00000000
χ4122-22-22-2-22222-22-222-2-22-2-22-2-2-2-222-2-222222-22-2-22-2-222-2-222-22-2-2-2-22000022-2-222-2-20000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ4222-22-22-2-22222-22-222-2-22-2-22-2-2-2-222-2-222222-22-2-22-2-222-2-222-22-2-2-2-22000022-2-222-2-2000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4322-2-22-22-22222-22-2-2-2222-2-2-22-2-22-2-222-22222-22-2-22-2-2-2-222-2-22-222-22-2000022-2-2-2-2220000000000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ4422-2-22-22-22222-22-2-2-2222-2-2-22-2-22-2-222-22222-22-2-22-2-2-2-222-2-22-222-22-2000022-2-2-2-222000000000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ452-222-2-22-2222-22-222-22-2-22-2-22-2-2-222-22-2222-22-22-2-22-22-22-22-22-22-2-2-222i−2i2i−2i2-22-22-22-200002i−2i2i−2i2i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ462-222-2-22-2222-22-222-22-2-22-2-22-2-2-222-22-2222-22-22-2-22-22-22-22-22-22-2-2-22−2i2i−2i2i2-22-22-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ472-222-2-22-22-12-221-12-2-11-22-2-22-21-2-12-221-12-11-1-22-21-11-11-112-221-111-2-12i−2i2i−2i-11-11-11-1100002i−2i−ii2i−2i−ii00000000−i3i300−i3i300−i−iii−i−iii00000000−i3−i3i3i3−i3−i3i3i300000000000000003−33−30000
χ482-222-2-22-22-12-221-12-2-11-22-2-22-21-2-12-221-12-11-1-22-21-11-11-112-221-111-2-12i−2i2i−2i-11-11-11-1100002i−2i−ii2i−2i−ii00000000i3−i300i3−i300−i−iii−i−iii00000000i3i3−i3−i3i3i3−i3−i30000000000000000−33−330000
χ492-222-2-22-22-12-221-12-2-11-22-2-22-21-2-12-221-12-11-1-22-21-11-11-112-221-111-2-1−2i2i−2i2i-11-11-11-110000−2i2ii−i−2i2ii−i00000000−i3i300−i3i300ii−i−iii−i−i00000000−i3−i3i3i3−i3−i3i3i30000000000000000−33−330000
χ502-222-2-22-22-12-221-12-2-11-22-2-22-21-2-12-221-12-11-1-22-21-11-11-112-221-111-2-1−2i2i−2i2i-11-11-11-110000−2i2ii−i−2i2ii−i00000000i3−i300i3−i300ii−i−iii−i−i00000000i3i3−i3−i3i3i3−i3−i300000000000000003−33−30000
χ512-222-2-22-2-1221-1-22-112-2-22-2-221-2122-2-1-2-1-121-11-11-22-2-11-11-11-1-22-21122i−2i2i−2i-11-11-11-110000−ii2i−2i−ii2i−2i3−3003−30000000000−i−iii−i−iii33−3−333−3−300000000000000000000−i3i3−i3i300000000
χ522-222-2-22-2-1221-1-22-112-2-22-2-221-2122-2-1-2-1-121-11-11-22-2-11-11-11-1-22-21122i−2i2i−2i-11-11-11-110000−ii2i−2i−ii2i−2i−3300−330000000000−i−iii−i−iii−3−333−3−33300000000000000000000i3−i3i3−i300000000
χ532-222-2-22-2-1221-1-22-112-2-22-2-221-2122-2-1-2-1-121-11-11-22-2-11-11-11-1-22-2112−2i2i−2i2i-11-11-11-110000i−i−2i2ii−i−2i2i3−3003−30000000000ii−i−iii−i−i33−3−333−3−300000000000000000000i3−i3i3−i300000000
χ542-222-2-22-2-1221-1-22-112-2-22-2-221-2122-2-1-2-1-121-11-11-22-2-11-11-11-1-22-2112−2i2i−2i2i-11-11-11-110000i−i−2i2ii−i−2i2i−3300−330000000000ii−i−iii−i−i−3−333−3−33300000000000000000000−i3i3−i3i300000000
χ552-22-222-2-2222-22-22-22-22-22-22-2-2-22-2-22-22222-22-22-2-22-2-22-22-22-22-22-22-22i−2i−2i2i2-22-2-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ562-22-222-2-2222-22-22-22-22-22-22-2-2-22-2-22-22222-22-22-2-22-2-22-22-22-22-22-22-2−2i2i2i−2i2-22-2-22-220000−2i2i−2i2i2i−2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
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χ1364-4-4-4-4444-2-2422222-2-22-4-4444-2-222-4-4-2-21-2-2-1-122-222-2-111-12-2-2-2-2212200001-1-11-111-10000000000000000000000000000-333-33-3-330000000000000000000000000000000000000000
χ13788888888-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-42222222222222222222222220000-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ138888-8-8-8-88-4-4-4-4-4-4-44444-4-4-444-4-444444422222222222-2-2-2-2-2-2-2-2-2-22-2-20000-1-1-1-111110000000000000000000000000000000000000000000000000000000000000000000000000000
χ13988-88-88-8-8-4-4-4-44-44-4-444-444-44444-4-444-42222-22-2-22-2-222-2-222-22-2-2-2-220000-1-111-1-1110000000000000000000000000000000000000000000000000000000000000000000000000000
χ14088-8-88-88-8-4-4-4-44-4444-4-4-4444-444-444-4-442222-22-2-22-2-2-2-222-2-22-222-22-20000-1-11111-1-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ1418-888-8-88-8-4-4-44-44-4-44-444-444-4444-4-44-44222-22-22-2-22-22-22-22-22-22-2-2-220000-11-11-11-110000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-88-888-8-8-4-4-44-44-44-44-44-44-4444-444-44-4222-22-22-2-22-2-22-22-22-22-22-22-20000-11-111-11-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ1438-8-888-8-88-4-4-44444-444-444-444-4-4-4-4-4-444222-2-2-2-22-2-222-2-222-2-2-2-222220000-111-1-111-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ1448-8-8-8-8888-4-4-444444-4-4444-4-4-4-4-44444-4-4222-2-2-2-22-2-22-222-2-22222-22-2-20000-111-11-1-110000000000000000000000000000000000000000000000000000000000000000000000000000

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