Finite Group Databasebeta

← Group #13156822

Character table — Group #13156822

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order122222223336666666666666666666663336666666666666666666664444444412121212121212121212121212121212366666664412121212121212121212121212121212121212121212121212121212121212121212121212121212444412121212121212124444121212121212121222
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1
χ911-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−ii−i1-1ii−i−i11-1-11-1
χ1011-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1−ii11-1-1−i−iiiii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i−ii-11−i−iii-1-111-11
χ1111-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1i−i11-1-1ii−i−i−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−i−i−iiiiii−i-11ii−i−i-1-111-11
χ1211-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−ii1-1−i−iii11-1-11-1
χ1311-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1i−i-1-111ii−i−iii−i−iii−i−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii−ii1-1−i−iii11-1-1-11
χ1411-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−ii-1-111−i−iiiii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iii−i−i−i−iiiiii−i-11ii−i−i-1-1111-1
χ1511-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1i−i-1-111ii−i−i−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−iiiii−i−i−i−i−ii-11−i−iii-1-1111-1
χ1611-11-11-1-1111111111-1-1-1-1-1-1-111-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1−ii-1-111−i−iii−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iiiii−i−i−i−ii−i1-1ii−i−i11-1-1-11
χ172222222222-12222-1-122222-1-12-12-1222-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-12-1222200002222222200000000-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000000000002200-1-1-1-1000000
χ182222222222-12222-1-122222-1-12-12-1222-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-12-1222200002222222200000000-1-1-1-1-1-1-1-1-2-2-1-1-1-111110000-2-2-2-2-1-1-1-1-1-1-1-10000000011111111000000000000-2-2001111000000
χ192222222222-12222-1-122222-1-12-12-1222-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-12-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1221111-1-1-1-1000022221111111100000000-1-1-1-1-1-1-1-1000000000000-2-2001111000000
χ202222222222-12222-1-122222-1-12-12-1222-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-12-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-2-2111111110000-2-2-2-21111111100000000111111110000000000002200-1-1-1-1000000
χ21222222222-1222-1-122222-1-122-12-1222-12-12-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002222000022220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000000000
χ22222222222-1222-1-122222-1-122-12-1222-12-12-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10022220000-2-2-2-20000-1-1-1-1-1-1-1-11111111100000000-2-2-2-21111111100000000000000
χ23222222222-1222-1-122222-1-122-12-1222-12-12-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-12-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-200002222000011111111-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000000000
χ24222222222-1222-1-122222-1-122-12-1222-12-12-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-12-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-100-2-2-2-20000-2-2-2-200001111111111111111000000002222-1-1-1-1-1-1-1-100000000000000
χ2522222222-122-1-12222-1-1-122222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-122222-1-1000022220000000022222222-1-1-1-1-1-1-1-12200002222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-100
χ2622222222-122-1-12222-1-1-122222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-122222-1-1000022220000000022222222-1-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-1-1-1111100000000-1-1-1-1-1-1-1-11111111100000000000000-2-20000111100
χ2722222222-122-1-12222-1-1-122222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-122222-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122000022221111-1-1-1-10000000011111111-1-1-1-1-1-1-1-100000000000000-2-20000111100
χ2822222222-122-1-12222-1-1-122222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-122222-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-20000-2-2-2-21111111100000000111111111111111100000000000000220000-1-1-1-100
χ29222-22-2-2-22222-22-22-22-2-22-22-2-2-2222-2-2-22222-2-22-2-22-22-2-22-2-222-2-2-2222i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000000022-2-222-2-2002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000
χ30222-22-2-2-22222-22-22-22-2-22-22-2-2-2222-2-2-22222-2-22-2-22-22-2-22-2-222-2-2-222−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000022-2-222-2-200−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000
χ31222-22-2-2-222-12-22-2-112-2-22-2-11-212-12-2-212-1-12-2-2-111-112-2-2-111-1-11112-12i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000-1-111-1-11100−ii−ii−i3i3−i3i300000000−i−iii−i−iii00000000−i3−i3i3i3−i3−i3i3i300000000000000003−33−3000000
χ32222-22-2-2-222-12-22-2-112-2-22-2-11-212-12-2-212-1-12-2-2-111-112-2-2-111-1-11112-12i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000-1-111-1-11100−ii−iii3−i3i3−i300000000−i−iii−i−iii00000000i3i3−i3−i3i3i3−i3−i30000000000000000−33−33000000
χ33222-22-2-2-222-12-22-2-112-2-22-2-11-212-12-2-212-1-12-2-2-111-112-2-2-111-1-11112-1−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000-1-111-1-11100i−ii−i−i3i3−i3i300000000ii−i−iii−i−i00000000−i3−i3i3i3−i3−i3i3i30000000000000000−33−33000000
χ34222-22-2-2-222-12-22-2-112-2-22-2-11-212-12-2-212-1-12-2-2-111-112-2-2-111-1-11112-1−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000-1-111-1-11100i−ii−ii3−i3i3−i300000000ii−i−iii−i−i00000000i3i3−i3−i3i3i3−i3−i300000000000000003−33−3000000
χ35222-22-2-2-22-122-2-112-22-2-2-112-21-2-122-21-2-12-1-1112-2-2-11-1112-2-2-1-1111-122i−2i2i−2i0000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i3-1-111-1-111002i−2i2i−2i000000000000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i300000000000033−3−333−3−300000000000000
χ36222-22-2-2-22-122-2-112-22-2-2-112-21-2-122-21-2-12-1-1112-2-2-11-1112-2-2-1-1111-122i−2i2i−2i0000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3-1-111-1-111002i−2i2i−2i000000000000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3000000000000−3−333−3−33300000000000000
χ37222-22-2-2-22-122-2-112-22-2-2-112-21-2-122-21-2-12-1-1112-2-2-11-1112-2-2-1-1111-12−2i2i−2i2i0000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−2i2i−2i2i000000000000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3000000000000−3−333−3−33300000000000000
χ38222-22-2-2-22-122-2-112-22-2-2-112-21-2-122-21-2-12-1-1112-2-2-11-1112-2-2-1-1111-12−2i2i−2i2i0000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i3-1-111-1-11100−2i2i−2i2i000000000000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i300000000000033−3−333−3−300000000000000
χ3922-22-22-2-222-12222-1-1-2-2-2-2-2112-1-21-22-212-1-1222-1-1-1-1-1-2-2-21111111-1-2122-2-200002222-2-2-2-200000000-1-1-1-111112i−2i-1-111−i−iii00002i2i−2i−2i-1-1-1-1111100000000−i−i−i−iiiii0000000000002i−2i00−i−iii000000
χ4022-22-22-2-222-12222-1-1-2-2-2-2-2112-1-21-22-212-1-1222-1-1-1-1-1-2-2-21111111-1-2122-2-200002222-2-2-2-200000000-1-1-1-11111−2i2i-1-111ii−i−i0000−2i−2i2i2i-1-1-1-1111100000000iiii−i−i−i−i000000000000−2i2i00ii−i−i000000
χ4122-22-22-2-222-12222-1-1-2-2-2-2-2112-1-21-22-212-1-1222-1-1-1-1-1-2-2-21111111-1-21-2-2220000-2-2-2-2222200000000-1-1-1-111112i−2i11-1-1−i−iii00002i2i−2i−2i1111-1-1-1-100000000−i−i−i−iiiii000000000000−2i2i00ii−i−i000000
χ4222-22-22-2-222-12222-1-1-2-2-2-2-2112-1-21-22-212-1-1222-1-1-1-1-1-2-2-21111111-1-21-2-2220000-2-2-2-2222200000000-1-1-1-11111−2i2i11-1-1ii−i−i0000−2i−2i2i2i1111-1-1-1-100000000iiii−i−i−i−i0000000000002i−2i00−i−iii000000
χ4322-22-22-2-22-1222-1-122-2-2-211-2-2-121-2-221-2-12-1-1-1-1222-1-1111-2-2-21111-11-222-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii-1-1-1-111110022-2-200002i2i−2i−2i0000-1-1-1-11111−i−i−i−iiiii000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ4422-22-22-2-22-1222-1-122-2-2-211-2-2-121-2-221-2-12-1-1-1-1222-1-1111-2-2-21111-11-222-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i-1-1-1-111110022-2-20000−2i−2i2i2i0000-1-1-1-11111iiii−i−i−i−i00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ4522-22-22-2-22-1222-1-122-2-2-211-2-2-121-2-221-2-12-1-1-1-1222-1-1111-2-2-21111-11-2-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii-1-1-1-1111100-2-22200002i2i−2i−2i00001111-1-1-1-1−i−i−i−iiiii00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ4622-22-22-2-22-1222-1-122-2-2-211-2-2-121-2-221-2-12-1-1-1-1222-1-1111-2-2-21111-11-2-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i-1-1-1-1111100-2-2220000−2i−2i2i2i00001111-1-1-1-1iiii−i−i−i−i000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ4722-22-22-2-2-122-1-12222111-2-2-2-222-2-21-1-2-2-1-12-1-1-1-1-1-122111111-2-2-2-221100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-111112i−2i00002i2i−2i−2i−i−iii−i−iii00000000−i−i−i−iiiii−i−i−i−iiiii000000000000002-20000-1-11100
χ4822-22-22-2-2-122-1-12222111-2-2-2-222-2-21-1-2-2-1-12-1-1-1-1-1-122111111-2-2-2-221100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-11111−2i2i0000−2i−2i2i2i−i−iiiii−i−i00000000−i−i−i−iiiiiiiii−i−i−i−i00000000000000-22000011-1-100
χ4922-22-22-2-2-122-1-12222111-2-2-2-222-2-21-1-2-2-1-12-1-1-1-1-1-122111111-2-2-2-22110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-111112i−2i00002i2i−2i−2iii−i−i−i−iii00000000iiii−i−i−i−i−i−i−i−iiiii00000000000000-22000011-1-100
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χ1254-444-4-44-4-2-242-222-4-4-2-22-2-24-4-242-422241-2-2-11-12-222211-1-2-22-22-22-2-12000000000000000023−2323−2323−2323−231-11-11-11-100000000000000000000000000−33−33−33−330000000000000000000000000000000000
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χ1284-44-4-44-444-2-2-4-42-22-24-44-22-2-22222-44-22-2-2122-222-2-11-22-2-22-21-1-11-1220000000023−23−232323−23−2323000000001-1-111-1-11000000000000000000−333−3−333−3000000000000000000000000000000000000000000
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χ1484-4-4-4444-4-2-24222-2-442-222-2-4-42-4-24-2-2241-2-2-1-1122-22-2-11-12-222-2-2221-20000-444-4000000002-2-22-222-21-1-11-111-100000000002-2-22000000000000-111-11-1-110000000000000000000000000000000000
χ14988888888-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222222222222222000000000000000000000000-1-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000000000000000
χ150888-88-8-8-8-4-4-4-44-44-44-444-44-4444-4-4-44442222-2-22-2-22-22-2-22-2-222-2-2-222000000000000000000000000-1-111-1-11100000000000000000000000000000000000000000000000000000000000000000000
χ15188-88-88-8-8-4-4-4-4-4-4-4-4-44444444-4-4444-44422222222222-2-2-2-2-2-2-2-2-2-22-2-2000000000000000000000000-1-1-1-1111100000000000000000000000000000000000000000000000000000000000000000000
χ15288-8-8-8-888-4-4-4-44-44-444-4-44-44-4444444-4-42222-2-22-2-22-2-222-222-2-222-2-2-2000000000000000000000000-1-11111-1-100000000000000000000000000000000000000000000000000000000000000000000
χ1538-888-8-88-8-4-4-44-44444-4-44-4-4-44-4-444444-4222-22-2-22-2-2-222-222-22-22-22-2-2000000000000000000000000-11-11-11-1100000000000000000000000000000000000000000000000000000000000000000000
χ1548-88-8-88-88-4-4-4444-44-4-44-4-44-4-444444-4-44222-2-22-2-22-222-222-222-2-22-2-2-2000000000000000000000000-111-1-111-100000000000000000000000000000000000000000000000000000000000000000000
χ1558-8-888-8-88-4-4-44-4444444-4444-4-4-4-4-4-44-44222-22-2-22-2-2-2-2-22-2-22-22-22222000000000000000000000000-11-111-11-100000000000000000000000000000000000000000000000000000000000000000000
χ1568-8-8-8888-8-4-4-4444-44-44-444-44444-4-4-4-44-4222-2-22-2-22-22-22-2-22-2-222-2-222000000000000000000000000-111-11-1-1100000000000000000000000000000000000000000000000000000000000000000000

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