Finite Group Databasebeta

← Group #13159926

Character table — Group #13159926

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
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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
χ511111111111111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111
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χ811111111111111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-11111-1-1111111-1-111-1-1
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χ1311-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-111111-1-1-1-1-1-1-1-11111i−i−iiii−i−ii−i−ii−ii
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χ1454-4−4i4i0-2-24-2-2022-4222i−2i−4i4i2i−2i2i−2i2i−2i1-211000003-3003-3-33-12-1-100−ii2i−2i−ii−ii00000−3i3i00−3i3i3i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13006−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300i6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
χ1464-4−4i4i0-2-24-2-2022-4222i−2i−4i4i2i−2i2i−2i2i−2i1-211000003-3003-3-33-12-1-100−ii2i−2i−ii−ii00000−3i3i00−3i3i3i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ1474-4−4i4i0-2-24-2-2022-4222i−2i−4i4i2i−2i2i−2i2i−2i1-21100000-3300-333-3-12-1-100−ii2i−2i−ii−ii000003i−3i003i−3i−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23006−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300i6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ1484-4−4i4i0-2-24-2-2022-4222i−2i−4i4i2i−2i2i−2i2i−2i1-21100000-3300-333-3-12-1-100−ii2i−2i−ii−ii000003i−3i003i−3i−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ1494-4−4i4i0-2-2-24-20222-422i−2i2i−2i−4i4i2i−2i2i−2i11-21000003-3-33003-3-1-12-100−ii−ii2i−2i−ii00000−3i3i3i−3i00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23006−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300i6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ1504-4−4i4i0-2-2-24-20222-422i−2i2i−2i−4i4i2i−2i2i−2i11-21000003-3-33003-3-1-12-100−ii−ii2i−2i−ii00000−3i3i3i−3i00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ1514-4−4i4i0-2-2-24-20222-422i−2i2i−2i−4i4i2i−2i2i−2i11-2100000-333-300-33-1-12-100−ii−ii2i−2i−ii000003i−3i−3i3i003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13006−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300i6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
χ1524-4−4i4i0-2-2-24-20222-422i−2i2i−2i−4i4i2i−2i2i−2i11-2100000-333-300-33-1-12-100−ii−ii2i−2i−ii000003i−3i−3i3i003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ1534-4−4i4i0-2-2-2-2402222-42i−2i2i−2i2i−2i−4i4i2i−2i111-2000003-33-3-3300-1-1-1200−ii−ii−ii2i−2i00000−3i3i−3i3i3i−3i006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23006−6−66−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300i6−i6−i6i60000000000000000000000000000000000
χ1544-4−4i4i0-2-2-2-2402222-42i−2i2i−2i2i−2i−4i4i2i−2i111-2000003-33-3-3300-1-1-1200−ii−ii−ii2i−2i00000−3i3i−3i3i3i−3i00−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300−666−6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300−i6i6i6−i60000000000000000000000000000000000
χ1554-4−4i4i0-2-2-2-2402222-42i−2i2i−2i2i−2i−4i4i2i−2i111-200000-33-333-300-1-1-1200−ii−ii−ii2i−2i000003i−3i3i−3i−3i3i006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13006−6−66−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300i6−i6−i6i60000000000000000000000000000000000
χ1564-4−4i4i0-2-2-2-2402222-42i−2i2i−2i2i−2i−4i4i2i−2i111-200000-33-333-300-1-1-1200−ii−ii−ii2i−2i000003i−3i3i−3i−3i3i00−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300−666−6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300−i6i6i6−i60000000000000000000000000000000000

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