Finite Group Databasebeta

← Group #13144419

Character table — Group #13144419

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137
size11111111111122222222222244444444444444466666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212363636363636363636363636727272727272
order122233666666444412121212121212122244466661212121212123333666666666666121212121212121212121212121212126666666666666666121212121212121212121212121212121212121212121212121212121212121288882424242424242424226666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111-1-1111-1-1-1-11111-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ61111111111111-1-1111-1-1-1-11111-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ71111111111111-1-1111-1-1-1-111-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-1-11-1-111
χ81111111111111-1-1111-1-1-1-111-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111111-111-1-1
χ92222222222222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
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χ12222222222222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000
χ13222222222222222222222222-2-22-2-2-2-2-2-222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111000000000000000000
χ14222222222222222222222222-2-22-2-2-2-2-2-222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-211111111-1-122-1-1-1-1-1-122-1-1-1-11111-2-2-2-211111111000000000000000000
χ15222222222222222222222222-2-22-2-2-2-2-2-222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-111111111-2-2-2-21111-1-1-1-122-1-1-1-1-1-122-1-111111111-2-2-2-21111000000000000000000
χ16222222222222222222222222-2-22-2-2-2-2-2-222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222111111111111-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-122111111111111-2-2-2-2000000000000000000
χ172222222222222-2-2222-2-2-2-22222-2-2-22222-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2-2-2111111111111000000000000000000
χ182222222222222-2-2222-2-2-2-22222-2-2-22222-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-111-2-211111111-2-2-2-211111111000000000000000000
χ192222222222222-2-2222-2-2-2-22222-2-2-22222-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-111111111-2-2-2-21111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-11111-2-21111111111-2-2-2-21111000000000000000000
χ202222222222222-2-2222-2-2-2-22222-2-2-22222-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12111111111111-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-122111111-2-2111111111111-2-2-2-2000000000000000000
χ212222222222222-2-2222-2-2-2-222-2-2-222-2-2-2-2-2-222222-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-2111111111111-2-2-2-211111111111122-1-1-1-1-1-1-2-21111112222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ222222222222222-2-2222-2-2-2-222-2-2-222-2-2-2-2-2-22222-12-1-1-1-122-1-1-1-1-12-1-11111-2-2-2-2111111111111-2-2-2-211111111-1-122-1-1-1-111-2-21111-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ232222222222222-2-2222-2-2-2-222-2-2-222-2-2-2-2-2-22222-1-12-1-1-1-1-122-1-1-1-12-111111111-2-2-2-2111111111111-2-2-2-21111-1-1-1-122-1-11111-2-211-1-1-1-1-1-1-1-12222-1-1-1-1000000000000000000
χ242222222222222-2-2222-2-2-2-222-2-2-222-2-2-2-2-2-22222-1-1-12-1-1-1-1-1-122-1-1-12111111111111-2-2-2-2111111111111-2-2-2-2-1-1-1-1-1-122111111-2-2-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000
χ25222222222222-222-2-2-22222-2-200-2000000-2-20000222222222222222222222222222222220000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ26222222222222-222-2-2-22222-2-200-2000000-2-200002-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-2-2111111-2-21111110000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000
χ27222222222222-222-2-2-22222-2-200-2000000-2-200002-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-2-2111111-2-21111110000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000
χ28222222222222-222-2-2-22222-2-200-2000000-2-20000-12-1-1-1-122-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i311-2-2111111-2-21111−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3000000000000000000
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χ30222222222222-222-2-2-22222-2-200-2000000-2-20000-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i31111-2-2111111-2-211−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i3000000000000000000
χ31222222222222-222-2-2-22222-2-200-2000000-2-20000-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i31111-2-2111111-2-211i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i3000000000000000000
χ32222222222222-222-2-2-22222-2-200-2000000-2-20000-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000111111-2-2111111-2-2−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000000000
χ33222222222222-222-2-2-22222-2-200-2000000-2-20000-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000111111-2-2111111-2-2i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000000000
χ34222222222222-2-2-2-2-2-2-2-2-2-2-2-20020000002200002222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-20020000002200002-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-21111111111110000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-2-211111122-1-1-1-1-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000
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χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2002000000220000-12-1-1-1-122-1-1-1-1-12-1-11111-2-2-2-211111111i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i311-2-21111-1-122-1-1-1-1−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3000000000000000000
χ39222222222222-2-2-2-2-2-2-2-2-2-2-2-2002000000220000-1-12-1-1-1-1-122-1-1-1-12-111111111-2-2-2-21111−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i31111-2-211-1-1-1-122-1-1i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i3000000000000000000
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χ5022-2-22222-2-2-2-2200-2220000-2-20002i−2i0000002i2i−2i−2i-1-1-12-11-11-112-2111-233−3−333−3−3−3−3330000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000-11-11-112-23−33−3−3300−ii−ii−ii−ii−ii−ii2i−2i2i−2i000000000000000000
χ5122-2-22222-2-2-2-2200-2220000-2-20002i−2i0000002i2i−2i−2i-1-1-12-11-11-112-2111-2−3−333−3−33333−3−30000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000-11-11-112-2−33−333−300−ii−ii−ii−ii−ii−ii2i−2i2i−2i000000000000000000
χ5222-2-22222-2-2-2-2200-2220000-2-2000−2i2i000000−2i−2i2i2i22222-22-22-22-2-2-2-2-2000000000000000000000000000000002-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000
χ5322-2-22222-2-2-2-2200-2220000-2-2000−2i2i000000−2i−2i2i2i2-1-1-12-2-11-11-11-2111000033−3−333−3−333−3−30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i32-2-11-11-11003−33−33−3−2i2i−2i2ii−ii−ii−ii−ii−ii−i000000000000000000
χ5422-2-22222-2-2-2-2200-2220000-2-2000−2i2i000000−2i−2i2i2i2-1-1-12-2-11-11-11-21110000−3−333−3−333−3−3330000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i32-2-11-11-1100−33−33−33−2i2i−2i2ii−ii−ii−ii−ii−ii−i000000000000000000
χ5522-2-22222-2-2-2-2200-2220000-2-2000−2i2i000000−2i−2i2i2i-12-1-1-112-2-11-111-21133−3−3000033−3−3−3−333i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3-112-2-11-113−3003−3−33i−ii−i−2i2i−2i2ii−ii−ii−ii−i000000000000000000
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χ12366-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3-60063+3i33−3i30000−3−3i3−3+3i3-660003+3i33−3i3−3−3i3−3+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12466-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3600-6−3+3i3−3−3i300003−3i33+3i30006i−6i0000006ζ146ζ22−6ζ14−6ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12566-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3600-6−3+3i3−3−3i300003−3i33+3i3000−6i6i000000−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12666-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3-60063−3i33+3i30000−3+3i3−3−3i36-6000−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12766-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3-60063−3i33+3i30000−3+3i3−3−3i3-660003−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1286-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i306-6000−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002−22−2−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000000
χ1296-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i306-6000−3−3i3−3+3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−22−22ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23000000
χ1306-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30-660003+3i33−3i3−3−3i3−3+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002−2−22−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23000000
χ1316-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30-660003+3i33−3i3−3−3i3−3+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−222−2ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000000
χ1326-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i306-6000−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002−22−2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000
χ1336-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i306-6000−3+3i3−3−3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−22−22−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000
χ1346-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30-660003−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002−2−22ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000
χ1356-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30-660003−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−222−2−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000
χ13612-1212-12−6−6i3−6+6i36+6i36−6i3−6−6i3−6+6i36+6i36−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13712-1212-12−6+6i3−6−6i36−6i36+6i3−6+6i3−6−6i36−6i36+6i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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