Finite Group Databasebeta

← Group #13156806

Character table — Group #13156806

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order12222222333666666666666666666666333666666666666666666666444436666666224466666666666666661212121212121212121212121212121212121212121212121212121212121212444444441212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
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
χ911-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1ii−i−i1111-1-1-1-11-1i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i1-1i−iii−i−i11-1-1ii−i−i11-1-1
χ1011-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1ii−i−i1111-1-1-1-11-1−ii1111-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iii-11i−iii−i−i-1-111−i−iii-1-111
χ1111-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1ii−i−i1111-1-1-1-1-11i−i-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii1-1−ii−i−iii11-1-1−i−iii-1-111
χ1211-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1ii−i−i1111-1-1-1-1-11−ii-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i-11−ii−i−iii-1-111ii−i−i11-1-1
χ1311-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1−i−iii1111-1-1-1-11-1i−i1111-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11−ii−i−iii-1-111ii−i−i-1-111
χ1411-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1−i−iii1111-1-1-1-11-1−ii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii1-1−ii−i−iii11-1-1−i−iii11-1-1
χ1511-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1−i−iii1111-1-1-1-1-11i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii-11i−iii−i−i-1-111−i−iii11-1-1
χ1611-1-1-11-1111111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1−i−iii1111-1-1-1-1-11−ii-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−i1-1i−iii−i−i11-1-1ii−i−i-1-111
χ172222222222-12222222-1-1-122-1-1222-122-12-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-12-10000-1-1-1-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-10000000022-1-122-1-100000000-1-1-1-1-1-1-1-12222000000000000-1-1-1-10000
χ182222222222-12222222-1-1-122-1-1222-122-12-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-12-10000-1-1-1-1-1-1-1-122-2-222-1-122-1-1-1-1-1-1-1-1-1-100000000-2-211-2-2110000000011111111-2-2-2-200000000000011110000
χ192222222222-12222222-1-1-122-1-1222-122-12-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-12-10000-1-1-1-1-1-1-1-1-2-222-2-211-2-211111111110000000022-1-122-1-100000000-1-1-1-1-1-1-1-1-2-2-2-200000000000011110000
χ202222222222-12222222-1-1-122-1-1222-122-12-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-12-10000-1-1-1-1-1-1-1-1-2-2-2-2-2-211-2-2111111111100000000-2-211-2-21100000000111111112222000000000000-1-1-1-10000
χ21222222222-122222-1-1-1222-1-12222-122-12-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12200-1-122-1-122-1-1-1-1-1-1-1-122-1-122-1-100000000-1-1-1-1-1-1-1-10000000000000022-1-1-1-1000000000000
χ22222222222-122222-1-1-1222-1-12222-122-12-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-20011-2-211-2-21111111122-1-122-1-100000000-1-1-1-1-1-1-1-100000000000000-2-21111000000000000
χ23222222222-122222-1-1-1222-1-12222-122-12-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-12-2-2-2-2-1-1-1-1-1-1-1-12200-1-122-1-122-1-1-1-1-1-1-1-1-2-211-2-211000000001111111100000000000000-2-21111000000000000
χ24222222222-122222-1-1-1222-1-12222-122-12-12-1-1-1-1222-1-1-1222-1-1-1-1-1-1-1-12-2-2-2-2-1-1-1-1-1-1-1-1-2-20011-2-211-2-211111111-2-211-2-21100000000111111110000000000000022-1-1-1-1000000000000
χ2522222222-122-1-1-1-12222222222-1-122-122-1-12-1-1-1-1-1-1-1-1-1-1-1-12222222-1-12222-1-1-1-1-1-1-1-100220000000000000000-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022000000-1-1-1-100000000
χ2622222222-122-1-1-1-12222222222-1-122-122-1-12-1-1-1-1-1-1-1-1-1-1-1-12222222-1-12222-1-1-1-1-1-1-1-100-2-20000000000000000-1-122-1-12211-2-211-2-2-1-1-1-1-1-1-1-1111111110000-2-2000000111100000000
χ2722222222-122-1-1-1-12222222222-1-122-122-1-12-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-2-2-2-2-1-1-1-1-1-1-1-10022000000000000000011-2-211-2-2-1-122-1-12211111111-1-1-1-1-1-1-1-10000-2-2000000111100000000
χ2822222222-122-1-1-1-12222222222-1-122-122-1-12-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-2-2-2-2-1-1-1-1-1-1-1-100-2-2000000000000000011-2-211-2-211-2-211-2-21111111111111111000022000000-1-1-1-100000000
χ29222-2-2-22-22222-2222-2-22-2-22-22-2-2-2-2-2-2222222-2-22-2-222-222-22-2-222-2-2-2-2000022-2-222-2-20000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ30222-2-2-22-22222-2222-2-22-2-22-22-2-2-2-2-2-2222222-2-22-2-222-222-22-2-222-2-2-2-2000022-2-222-2-2000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ3122-222-2-2-22222-2-2-22-2-22-2-2-22-222222-2-2-22222-2-22-2-2-2-22-2-222-2-2-2-22222000022-2-2-2-2220000000000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ3222-222-2-2-22222-2-2-22-2-22-2-2-22-222222-2-2-22222-2-22-2-2-2-22-2-222-2-2-2-22222000022-2-2-2-222000000000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ3322-2-2-22-2222-122-2-2222-1-1-1-2-211-2-2-212-212-1-1222-1-1-1-2-2-2111-1-1-11111-210000-1-1-1-111112-22i−2i22-1-1-2-211-1-1-1-11111000000002i2i−i−i−2i−2iii00000000−i−i−i−iiiii2i2i−2i−2i000000000000−i−iii0000
χ3422-2-2-22-2222-122-2-2222-1-1-1-2-211-2-2-212-212-1-1222-1-1-1-2-2-2111-1-1-11111-210000-1-1-1-111112-2−2i2i22-1-1-2-211-1-1-1-1111100000000−2i−2iii2i2i−i−i00000000iiii−i−i−i−i−2i−2i2i2i000000000000ii−i−i0000
χ3522-2-2-22-2222-122-2-2222-1-1-1-2-211-2-2-212-212-1-1222-1-1-1-2-2-2111-1-1-11111-210000-1-1-1-11111-222i−2i-2-21122-1-11111-1-1-1-1000000002i2i−i−i−2i−2iii00000000−i−i−i−iiiii−2i−2i2i2i000000000000ii−i−i0000
χ3622-2-2-22-2222-122-2-2222-1-1-1-2-211-2-2-212-212-1-1222-1-1-1-2-2-2111-1-1-11111-210000-1-1-1-11111-22−2i2i-2-21122-1-11111-1-1-1-100000000−2i−2iii2i2i−i−i00000000iiii−i−i−i−i2i2i−2i−2i000000000000−i−iii0000
χ3722-2-2-22-222-1222-2-2-1-1-122211-2-2-2-21-221-2-12-1-1-1-1222111-2-2-2-1-1-111111-22i2i−2i−2i-1-1-1-111112-200-1-12211-2-2-1-1-1-111112i2i−i−i−2i−2iii00000000−i−i−i−iiiii000000000000002i−2i−i−iii000000000000
χ3822-2-2-22-222-1222-2-2-1-1-122211-2-2-2-21-221-2-12-1-1-1-1222111-2-2-2-1-1-111111-22i2i−2i−2i-1-1-1-11111-220011-2-2-1-1221111-1-1-1-12i2i−i−i−2i−2iii00000000−i−i−i−iiiii00000000000000−2i2iii−i−i000000000000
χ3922-2-2-22-222-1222-2-2-1-1-122211-2-2-2-21-221-2-12-1-1-1-1222111-2-2-2-1-1-111111-2−2i−2i2i2i-1-1-1-111112-200-1-12211-2-2-1-1-1-11111−2i−2iii2i2i−i−i00000000iiii−i−i−i−i00000000000000−2i2iii−i−i000000000000
χ4022-2-2-22-222-1222-2-2-1-1-122211-2-2-2-21-221-2-12-1-1-1-1222111-2-2-2-1-1-111111-2−2i−2i2i2i-1-1-1-11111-220011-2-2-1-1221111-1-1-1-1−2i−2iii2i2i−i−i00000000iiii−i−i−i−i000000000000002i−2i−i−iii000000000000
χ4122-2-2-22-22-122-1-111222222-2-2-2-211-2-2-1-2-2-1-12-1-1-1-1-1-1111111222-2-2-2-2112i2i−2i−2i-1-1-1-11111002i−2i0000000000000000−i−i2i2iii−2i−2i−i−i2i2iii−2i−2i−i−i−i−iiiii−i−i−i−iiiii00002-2000000-1-11100000000
χ4222-2-2-22-22-122-1-111222222-2-2-2-211-2-2-1-2-2-1-12-1-1-1-1-1-1111111222-2-2-2-2112i2i−2i−2i-1-1-1-1111100−2i2i0000000000000000−i−i2i2iii−2i−2iii−2i−2i−i−i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000-2200000011-1-100000000
χ4322-2-2-22-22-122-1-111222222-2-2-2-211-2-2-1-2-2-1-12-1-1-1-1-1-1111111222-2-2-2-211−2i−2i2i2i-1-1-1-11111002i−2i0000000000000000ii−2i−2i−i−i2i2i−i−i2i2iii−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000-2200000011-1-100000000
χ4422-2-2-22-22-122-1-111222222-2-2-2-211-2-2-1-2-2-1-12-1-1-1-1-1-1111111222-2-2-2-211−2i−2i2i2i-1-1-1-1111100−2i2i0000000000000000ii−2i−2i−i−i2i2iii−2i−2i−i−i2i2iiiii−i−i−i−iiiii−i−i−i−i00002-2000000-1-11100000000
χ452-222-22-2-2222-2-22-2-22-2-22-22-2222-22-22-2-2222-22-2-22-22-2-22-22-22-22-22-22-200002-22-22-22-200000000000000000000000000000000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i0000
χ462-222-22-2-2222-2-22-2-22-2-22-22-2222-22-22-2-2222-22-2-22-22-2-22-22-22-22-22-22-200002-22-22-22-20000000000000000000000000000000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i0000
χ472-222-22-2-222-1-2-22-2-22-21-112-2-1-12-2212-212-1-1-22-21-112-2-2-11-11-11-11-11210000-11-11-11-11000000−i3i300−i3i3−i3−i3i3i3−i3−i3i3i300000000003−3003−30000000033−3−333−3−32i−2i2i−2i000000000000−ii−ii0000
χ482-222-22-2-222-1-2-22-2-22-21-112-2-1-12-2212-212-1-1-22-21-112-2-2-11-11-11-11-11210000-11-11-11-11000000−i3i300−i3i3−i3−i3i3i3−i3−i3i3i30000000000−3300−3300000000−3−333−3−333−2i2i−2i2i000000000000i−ii−i0000
χ492-222-22-2-222-1-2-22-2-22-21-112-2-1-12-2212-212-1-1-22-21-112-2-2-11-11-11-11-11210000-11-11-11-11000000i3−i300i3−i3i3i3−i3−i3i3i3−i3−i300000000003−3003−30000000033−3−333−3−3−2i2i−2i2i000000000000i−ii−i0000
χ502-222-22-2-222-1-2-22-2-22-21-112-2-1-12-2212-212-1-1-22-21-112-2-2-11-11-11-11-11210000-11-11-11-11000000i3−i300i3−i3i3i3−i3−i3i3i3−i3−i30000000000−3300−3300000000−3−333−3−3332i−2i2i−2i000000000000−ii−ii0000
χ512-22-22-2-22222-222-2-2-22-2-22222-2-22-22-2-2-2222-2-22-2-222-222-2-2-2-222-2-22-222i−2i2i−2i2-2-222-2-22000000000000000000002i−2i2i−2i2i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ522-22-22-2-22222-222-2-2-22-2-22222-2-22-22-2-2-2222-2-22-2-222-222-2-2-2-222-2-22-22−2i2i−2i2i2-2-222-2-2200000000000000000000−2i2i−2i2i−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ532-22-22-2-222-12-222-211-1-2-22-1-12-2-2212-21-2-12-111-1-2-22-11-12-2-211-1-111-1122i−2i2i−2i-111-1-111-10000−i3i300−i3i300−i3i3−i3i3−i3i3−i3i32i−2i−ii2i−2i−ii00000000−i−iii−i−iii00000000000000003−33−3000000000000
χ542-22-22-2-222-12-222-211-1-2-22-1-12-2-2212-21-2-12-111-1-2-22-11-12-2-211-1-111-1122i−2i2i−2i-111-1-111-10000i3−i300i3−i300i3−i3i3−i3i3−i3i3−i32i−2i−ii2i−2i−ii00000000−i−iii−i−iii0000000000000000−33−33000000000000
χ552-22-22-2-222-12-222-211-1-2-22-1-12-2-2212-21-2-12-111-1-2-22-11-12-2-211-1-111-112−2i2i−2i2i-111-1-111-10000−i3i300−i3i300−i3i3−i3i3−i3i3−i3i3−2i2ii−i−2i2ii−i00000000ii−i−iii−i−i0000000000000000−33−33000000000000
χ562-22-22-2-222-12-222-211-1-2-22-1-12-2-2212-21-2-12-111-1-2-22-11-12-2-211-1-111-112−2i2i−2i2i-111-1-111-10000i3−i300i3−i300i3−i3i3−i3i3−i3i3−i3−2i2ii−i−2i2ii−i00000000ii−i−iii−i−i00000000000000003−33−3000000000000
χ572-22-22-2-22-1221-1-11-2-22-2-22222-21-1-221-2-2-1-1211-111-1-11-1-111-2-222-2-221-12i−2i2i−2i-111-1-111-100000000000000000000−ii2i−2i−ii2i−2i−i3i300−i3i300−i−iii−i−iii−i3i3−i3i3−i3i3−i3i30000000000003−33−300000000
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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
χ138888-8-8-88-8-4-4-4-44-4-4-444-444-44-4444444-4-42222-2-22-2-222-222-22-2-222-2-2-2-20000-1-111-1-1110000000000000000000000000000000000000000000000000000000000000000000000000000
χ13988-888-8-8-8-4-4-4-4444-444-4444-44-4-4-4-4-44442222-2-22-2-2-2-22-2-222-2-2-2-222220000-1-11111-1-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ14088-8-8-88-88-4-4-4-4-444-4-4-4-4-4-444444444-444222222222-2-2-2-2-2-2222-2-2-2-2-2-20000-1-1-1-111110000000000000000000000000000000000000000000000000000000000000000000000000000
χ1418-888-88-8-8-4-4-444-444-444-44-44-4-4-44-44-444222-22-2-22-22-2-22-22-22-22-22-22-20000-11-11-11-110000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-88-88-8-88-4-4-44-4-4444-444-4-4-4-444-44-4444222-2-22-2-222-222-2-2-2-222-2-22-220000-111-1-111-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ1438-8-88-8-888-4-4-44-44-444-444-4444-4-44-444-4-4222-2-22-2-22-22-2-222-2-22-222-22-20000-111-11-1-110000000000000000000000000000000000000000000000000000000000000000000000000000
χ1448-8-8-8888-8-4-4-4444-44-444-444-4444-44-4-4-4-4222-22-2-22-2-222-22-2-22-2-22-22-220000-11-111-11-10000000000000000000000000000000000000000000000000000000000000000000000000000

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