Finite Group Databasebeta

← Group #13155510

Character table — Group #13155510

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order124423334666121212121212333666666661212121212121212121212366666121212121212888888242424242424242424242424242424242424242424242424242424242424242488888824242424224424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
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χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-111-1-1-1-111111-1-1i−ii−i-11-1-1-1-1-1-1-1-111111111i−ii−ii−ii−iii−i−iii−i−i−ii−ii1-111-1-1-11-11−ii−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-111-1-1-1-111111-1-1i−i−ii1-111111111-1-1-1-1-1-1-1-1i−i−iii−i−iiii−i−i−i−iiii−i−ii-11-1-111-11-11i−i−ii
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-111-1-1-1-111111-1-1i−i−ii-11-1-1-1-1-1-1-1-111111111i−i−iii−i−iiii−i−i−i−iii−iii−i-11-1-1111-11-1−iii−i
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-111-1-1-1-111111-1-1−iii−i1-111111111-1-1-1-1-1-1-1-1−iii−i−iii−i−i−iiiii−i−i−iii−i-11-1-111-11-11−iii−i
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χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-111-1-1-1-111111-1-1−ii−ii-11-1-1-1-1-1-1-1-111111111−ii−ii−ii−ii−i−iii−i−iiii−ii−i1-111-1-1-11-11i−ii−i
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χ2722222-1222-122-1-12222-1-12-12222-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22200000000000000000011-1-1-2-2221111-1-1-1-10000-2-2111100000000
χ2822222-1222-122-1-12222-1-12-12222-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000001111-2-2-2-211111111000022-1-1-1-100000000
χ292222-2222-2222222222222-2-2-2-2-222222-2-2-2-22222-22-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000000000002-2-220000
χ302222-2222-2222222222222-2-2-2-2-222222-2-2-2-22222-22-2-2-2-22-2-2-2-222000000000000000000000000000000000000000000000000-222-20000
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χ3522-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-1112-1-1-1-2-2112-1-2111-12-1-1-11100−2i2i2-222-1-1-1-1-1-1-2-211111100−2i2i00i−i0000ii−i−i00−2i2i000000000000i−i
χ3622-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-1112-1-1-1-2-2112-1-2111-12-1-1-11100−2i2i-22-2-211111122-1-1-1-1-1-100−2i2i00i−i0000ii−i−i002i−2i000000000000−ii
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χ3822-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-111-12-1-111-2-22-11-211-1-12-1-1112i−2i00-2211-2-21111-1-122-1-1-1-12i−2i00−ii00−i−iii0000−2i2i000000000000i−i00
χ3922-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-111-12-1-111-2-22-11-211-1-12-1-111−2i2i002-2-1-122-1-1-1-111-2-21111−2i2i00i−i00ii−i−i0000−2i2i000000000000i−i00
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χ45444444-2-244-2-244-2-2-2-2-2-214-2-211-2-2111-2-211-2-2-2-241-2-2111-2-21111000044-2-2-2-21111-2-2-2-211110000000000000000000000000000000000
χ46444444-2-244-2-244-2-2-2-2-2-214-2-211-2-2111-2-211-2-2-2-241-2-2111-2-211110000-4-42222-1-1-1-12222-1-1-1-10000000000000000000000000000000000
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χ844-44i−4i0-24402-4-4−2i2i4i−4i4i−4i-2-240000022-44i−4i0000−2i2i−2i2i0-2000020000−2i2i00000000000000000000000000000000000000000000i6−i66−600000000
χ854-44i−4i0-24402-4-4−2i2i4i−4i4i−4i-2-240000022-44i−4i0000−2i2i−2i2i0-2000020000−2i2i00000000000000000000000000000000000000000000−i6i6−6600000000
χ864-4−4i4i04440-4-4-4−4i4i−4i4i−4i4i44400000-4-4-4−4i4i0000−4i4i−4i4i040000-40000−4i4i00000000000000000000000000000000000000000000000000000000
χ874-4−4i4i044-20-4-42−4i4i−4i4i2i−2i4-2-200000-4222i−2i0000−4i4i2i−2i0-20000200002i−2i000000006−66−66−600−i6i6−i6i6−i6i60000000000000000000000000000000000
χ884-4−4i4i044-20-4-42−4i4i−4i4i2i−2i4-2-200000-4222i−2i0000−4i4i2i−2i0-20000200002i−2i00000000−66−66−6600i6−i6i6−i6i6−i60000000000000000000000000000000000
χ894-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-24-2000002-422i−2i00002i−2i−4i4i0-20000200002i−2i000000i6−i600i6−i6−i6i6−66006−6−660000000000000000000000000000000000
χ904-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-24-2000002-422i−2i00002i−2i−4i4i0-20000200002i−2i000000−i6i600−i6i6i6−i66−600−666−60000000000000000000000000000000000
χ914-4−4i4i04-2-20-422−4i4i2i−2i2i−2i-2-210003-322-1−ii00−3i3i2i−2i2i−2i01003-3-100−3i3i−ii000000i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ924-4−4i4i04-2-20-422−4i4i2i−2i2i−2i-2-210003-322-1−ii00−3i3i2i−2i2i−2i01003-3-100−3i3i−ii000000−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ934-4−4i4i04-2-20-422−4i4i2i−2i2i−2i-2-21000-3322-1−ii003i−3i2i−2i2i−2i0100-33-1003i−3i−ii000000i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
χ944-4−4i4i04-2-20-422−4i4i2i−2i2i−2i-2-21000-3322-1−ii003i−3i2i−2i2i−2i0100-33-1003i−3i−ii000000−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ954-4−4i4i0-24402-4-42i−2i−4i4i−4i4i-2-240000022-4−4i4i00002i−2i2i−2i0-20000200002i−2i00000000000000000000000000000000000000000000i6−i6−6600000000
χ964-4−4i4i0-24402-4-42i−2i−4i4i−4i4i-2-240000022-4−4i4i00002i−2i2i−2i0-20000200002i−2i00000000000000000000000000000000000000000000−i6i66−600000000
χ9788888-4-4-48-4-4-4-4-4-4-4-4-4222-4-4-42222222-4-4222222-4-122-1-1-122-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-8-4-4-4-8-4-4-4-4-4-4-4-4-4222444-2-22222244-2-222224-1-2-211-1-2-211-1-100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-4-8-4-4-4444444222-4-4-422222-2-244-2-2-2-2-2-24-122-1-1-1-2-2111100000000000000000000000000000000000000000000000000000000
χ10088-8-8-8-4-4-48-4-4-4444444222444-2-2222-2-2-4-422-2-2-2-2-4-1-2-211-122-1-11100000000000000000000000000000000000000000000000000000000
χ1018-88i−8i0-48-404-84−4i4i8i−8i−4i4i-42-4000004-24−4i4i0000−4i4i2i−2i020000-200002i−2i00000000000000000000000000000000000000000000000000000000
χ1028-88i−8i0-4-48044-8−4i4i−4i4i8i−8i2-4-400000-244−4i4i00002i−2i−4i4i020000-200002i−2i00000000000000000000000000000000000000000000000000000000
χ1038-88i−8i0-4-4-40444−4i4i−4i4i−4i4i2220006-6-2-2-22i−2i006i−6i2i−2i2i−2i0-100-33100−3i3i−ii00000000000000000000000000000000000000000000000000000000
χ1048-88i−8i0-4-4-40444−4i4i−4i4i−4i4i222000-66-2-2-22i−2i00−6i6i2i−2i2i−2i0-1003-31003i−3i−ii00000000000000000000000000000000000000000000000000000000
χ1058-8−8i8i0-48-404-844i−4i−8i8i4i−4i-42-4000004-244i−4i00004i−4i−2i2i020000-20000−2i2i00000000000000000000000000000000000000000000000000000000
χ1068-8−8i8i0-4-48044-84i−4i4i−4i−8i8i2-4-400000-2444i−4i0000−2i2i4i−4i020000-20000−2i2i00000000000000000000000000000000000000000000000000000000
χ1078-8−8i8i0-4-4-404444i−4i4i−4i4i−4i2220006-6-2-2-2−2i2i00−6i6i−2i2i−2i2i0-100-331003i−3ii−i00000000000000000000000000000000000000000000000000000000
χ1088-8−8i8i0-4-4-404444i−4i4i−4i4i−4i222000-66-2-2-2−2i2i006i−6i−2i2i−2i2i0-1003-3100−3i3ii−i00000000000000000000000000000000000000000000000000000000

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