Finite Group Databasebeta

← Group #13144436

Character table — Group #13144436

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137
size11111111111122222222222244444444444444466666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212363636363636363636363636727272727272
order122233666666444412121212121212124444412121212121212121212333366666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212888824242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111-1-1111-1-1-1-111-111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ61111111111111-1-1111-1-1-1-111-111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ71111111111111-1-1111-1-1-1-111-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-1-11-1-111
χ81111111111111-1-1111-1-1-1-111-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111111-111-1-1
χ92222222222222222222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
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χ132222222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-2111111111111000000000000000000
χ142222222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-11111-2-2-2-2111111111111-2-2-2-211111111000000000000000000
χ152222222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-111111111-2-2-2-2111111111111-2-2-2-21111000000000000000000
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χ172222222222222-2-2222-2-2-2-222-222-2-2-2-22222-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-211111111111122-1-1-1-1-1-1-2-21111112222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000000000
χ182222222222222-2-2222-2-2-2-222-222-2-2-2-22222-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-11111-2-2-2-211111111-1-122-1-1-1-111-2-21111-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000000000000
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χ212222222222222-2-2222-2-2-2-222-2-2-222-2-2-2-2-2-222222-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-211111111111122-1-1-1-1-1-1-2-2111111-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
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χ25222222222222-222-2-2-22222-2-2-20000-2-20000000022222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000
χ26222222222222-222-2-2-22222-2-2-20000-2-2000000002-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111-2-21111110000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000
χ27222222222222-222-2-2-22222-2-2-20000-2-2000000002-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111-2-21111110000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000
χ28222222222222-222-2-2-22222-2-2-20000-2-200000000-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111-2-2111111-2-21111−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3000000000000000000
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χ33222222222222-222-2-2-22222-2-2-20000-2-200000000-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222111111-2-2111111-2-2i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000000000
χ34222222222222-2-2-2-2-2-2-2-2-2-2-2-22000022000000002222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-22000022000000002-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111-2-211111122-1-1-1-1-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000
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χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2200002200000000-12-1-1-12-1-1-1-122-1-1-1-11111-2-2-2-21111111111-2-21111-1-122-1-1-1-1i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3000000000000000000
χ39222222222222-2-2-2-2-2-2-2-2-2-2-2-2200002200000000-1-12-1-1-12-1-1-1-1-122-1-111111111-2-2-2-211111111-2-211-1-1-1-122-1-1−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i3000000000000000000
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χ42222222222222-2-2-2-2-2-2-2-2-2-2-2-2200002200000000-1-1-12-1-1-12-1-1-1-1-1-122111111111111-2-2-2-2111111-2-2-1-1-1-1-1-122i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000000000
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χ4522-2-22222-2-2-2-2200-2220000-2-20002-200000022-2-22-1-1-1-21112-2-11-11-110000−3−333−3−333−3−3332-2-11-11-1100−33−33−330000−33−33−33−33−33−332-22-2-11-11-11-11-11-11000000000000000000
χ4622-2-22222-2-2-2-2200-2220000-2-20002-200000022-2-2-12-1-11-211-112-2-11-1133−3−3000033−3−3−3−333-112-2-11-113−3003−3−333−33−300003−33−3−33−33-11-112-22-2-11-11-11-11000000000000000000
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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+3i30−6i6i0000−6ζ22−6ζ146ζ226ζ14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12466-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3600-6−3+3i3−3−3i300003−3i33+3i30006-6000000−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12566-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3600-6−3+3i3−3−3i300003−3i33+3i3000-660000003−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12666-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3-60063−3i33+3i30000−3+3i3−3−3i306i−6i00006ζ146ζ22−6ζ14−6ζ22000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12766-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3-60063−3i33+3i30000−3+3i3−3−3i30−6i6i0000−6ζ14−6ζ226ζ146ζ22000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1286-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i306-6000−3−3i3−3+3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−i2i2−i2i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000
χ1296-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i306-6000−3−3i3−3+3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000i2−i2i2−i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000
χ1306-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30-660003+3i33−3i3−3−3i3−3+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−i2i2i2−i2ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000
χ1316-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30-660003+3i33−3i3−3−3i3−3+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000i2−i2−i2i2−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000
χ1326-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i306-6000−3+3i3−3−3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−i2i2−i2i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000000
χ1336-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i306-6000−3+3i3−3−3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000i2−i2i2−i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000
χ1346-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30-660003−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000−i2i2i2−i2ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000
χ1356-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30-660003−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000i2−i2−i2i2−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−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.