Finite Group Databasebeta

← Group #13159924

Character table — Group #13159924

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size111122222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441212121224242424242424242424242424242424363636365454545472727272108108
order12442333334666661212121212121212121233336666666666666666688121212121212121212121212121212121212121212242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424248888242424242424242424242424242424242244888866121244
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χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-11-111111-11-1-1-1
χ611111111111111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1111
χ711111111111111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-11-11-111
χ811111111111111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-111111-11-11-1-1
χ911-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1i−i
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χ1311-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111i−i−iiiiii−i−i−i−i−i−i−i−iiiii1-1-11ii−i−i1-1-11−ii
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χ1494-4−4i4i0-2-24-2-2022-4222i−2i2i−2i2i−2i−4i4i2i−2i11-2100000-333-300-33-1-12-100−ii−ii2i−2i−ii000003i−3i−3i3i003i−3i6−6−66006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6i6−i600−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
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χ1524-4−4i4i0-2-2-2440222-4-4−4i4i2i−2i2i−2i2i−2i−4i4i-2-2-240000000000000222-4002i−2i2i−2i2i−2i−4i4i0000000000000−66−666−60000−666−6−666−66−6−660000i6−i6i6−i6−i6i60000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000000000
χ1534-4−4i4i0-2-2-24-20222-422i−2i2i−2i2i−2i2i−2i−4i4i111-2000003-33-3-3300-1-1-1200−ii−ii−ii2i−2i00000−3i3i−3i3i3i−3i006−66−6−6600−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−i6i6−i6i6−i6i6−i6i6i6−i6006−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−66−60000000000000000000000000000000000
χ1544-4−4i4i0-2-2-24-20222-422i−2i2i−2i2i−2i2i−2i−4i4i111-2000003-33-3-3300-1-1-1200−ii−ii−ii2i−2i00000−3i3i−3i3i3i−3i00−66−666−600i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i6i6−i6i6−i6i6−i6−i6i600−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−660000000000000000000000000000000000
χ1554-4−4i4i0-2-2-24-20222-422i−2i2i−2i2i−2i2i−2i−4i4i111-200000-33-333-300-1-1-1200−ii−ii−ii2i−2i000003i−3i3i−3i−3i3i006−66−6−6600i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6i6−i6−i6i6−i6i6i6−i600−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−660000000000000000000000000000000000
χ1564-4−4i4i0-2-2-24-20222-422i−2i2i−2i2i−2i2i−2i−4i4i111-200000-33-333-300-1-1-1200−ii−ii−ii2i−2i000003i−3i3i−3i−3i3i00−66−666−600−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i6−i6i6i6−i6i6−i6−i6i6006−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−66−60000000000000000000000000000000000

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