Finite Group Databasebeta

← Group #13170668

Character table — Group #13170668

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order12442333466612121212121233366666666121212121212121212121236666612121212121222448824242424242424242424242424242424666666661212121212121212224488242424242244661212
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
χ311111111111111111111111111111111111111111111111111111-11-11111111111111111111-11-111-1-11-11-111-1-11-11-1-1-1-1-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-1-11-11-1-1-1-1-1-11111-11-11
χ51111111111111111111111111111111111111111111111111111-11-11111111111111111111-11-11-1-111-11-11-1-111-11-11-1-1-1-1-1-1-1-1-1-1-11-11
χ61111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-1111-11-1-1-1-1-1-1-111111-11-1
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
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111111-1-111-1-11-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-111-1-11-11-11-1-11
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χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-111-111111111-1-1-1-1-1-1-1-11-11-111-1-1-11-11-1-11111-1-1-11-1-111-11-1111-1-1
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-11-11-1-1-1-1-1-1-1-1111111111-11-111-1-1-11-11-1-111-1-111-11-1-1111-11-1-1-111
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χ874-4−4i4i044-20-4-42−4i4i−4i4i2i−2i-24-2000002-422i−2i−4i4i2i−2i00000-20000200002i−2i000000006−66−66−600−i6i6−i6i6−i6i60000000000000000000000000000000000
χ884-4−4i4i044-20-4-42−4i4i−4i4i2i−2i-24-2000002-422i−2i−4i4i2i−2i00000-20000200002i−2i00000000−66−66−6600i6−i6i6−i6i6−i60000000000000000000000000000000000
χ894-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-2-240000022-42i−2i2i−2i−4i4i00000-20000200002i−2i000000i6−i600i6−i6−i6i6−66006−6−660000000000000000000000000000000000
χ904-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-2-240000022-42i−2i2i−2i−4i4i00000-20000200002i−2i000000−i6i600−i6i6i6−i66−600−666−60000000000000000000000000000000000
χ914-4−4i4i04-2-20-422−4i4i2i−2i2i−2i1-2-20003-3-122−ii2i−2i2i−2i00−3i3i01003-3-100−3i3i−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−2i1-2-20003-3-122−ii2i−2i2i−2i00−3i3i01003-3-100−3i3i−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−2i1-2-2000-33-122−ii2i−2i2i−2i003i−3i0100-33-1003i−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−2i1-2-2000-33-122−ii2i−2i2i−2i003i−3i0100-33-1003i−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−4i4i4-2-200000-422−4i4i2i−2i2i−2i00000-20000200002i−2i00000000000000000000000000000000000000000000i6−i6−6600000000
χ964-4−4i4i0-24402-4-42i−2i−4i4i−4i4i4-2-200000-422−4i4i2i−2i2i−2i00000-20000200002i−2i00000000000000000000000000000000000000000000−i6i66−600000000
χ9788888-4-4-48-4-4-4-4-4-4-4-4-4222-4-4-422222222222-4-422-4-122-1-1-122-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-8-4-4-4-8-4-4-4-4-4-4-4-4-4222444-2-222222222244-2-24-1-2-211-1-2-211-1-100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-4-8-4-4-4444444222-4-4-422222-2-2-2-2-2-244-2-24-122-1-1-1-2-2111100000000000000000000000000000000000000000000000000000000
χ10088-8-8-8-4-4-48-4-4-4444444222444-2-2222-2-2-2-2-2-2-4-422-4-1-2-211-122-1-11100000000000000000000000000000000000000000000000000000000
χ1018-88i−8i0-48-404-84−4i4i8i−8i−4i4i-4-420000044-2−4i4i−4i4i2i−2i0000020000-200002i−2i00000000000000000000000000000000000000000000000000000000
χ1028-88i−8i0-4-48044-8−4i4i−4i4i8i−8i-42-4000004-24−4i4i2i−2i−4i4i0000020000-200002i−2i00000000000000000000000000000000000000000000000000000000
χ1038-88i−8i0-4-4-40444−4i4i−4i4i−4i4i2220006-6-2-2-22i−2i2i−2i2i−2i006i−6i0-100-33100−3i3i−ii00000000000000000000000000000000000000000000000000000000
χ1048-88i−8i0-4-4-40444−4i4i−4i4i−4i4i222000-66-2-2-22i−2i2i−2i2i−2i00−6i6i0-1003-31003i−3i−ii00000000000000000000000000000000000000000000000000000000
χ1058-8−8i8i0-48-404-844i−4i−8i8i4i−4i-4-420000044-24i−4i4i−4i−2i2i0000020000-20000−2i2i00000000000000000000000000000000000000000000000000000000
χ1068-8−8i8i0-4-48044-84i−4i4i−4i−8i8i-42-4000004-244i−4i−2i2i4i−4i0000020000-20000−2i2i00000000000000000000000000000000000000000000000000000000
χ1078-8−8i8i0-4-4-404444i−4i4i−4i4i−4i2220006-6-2-2-2−2i2i−2i2i−2i2i00−6i6i0-100-331003i−3ii−i00000000000000000000000000000000000000000000000000000000
χ1088-8−8i8i0-4-4-404444i−4i4i−4i4i−4i222000-66-2-2-2−2i2i−2i2i−2i2i006i−6i0-1003-3100−3i3ii−i00000000000000000000000000000000000000000000000000000000

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