Finite Group Databasebeta

← Group #13155713

Character table — Group #13155713

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order122233344666666666333666666666121212121212121212123666121212121212121222228824242424242424242424242424242424666666666666666644448824242424444412121212
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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χ1111-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-11-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-111-1-1111-1-1-1-111i−i−ii-11-1-111−i−iiii−i−ii
χ1211-1-1111-11-1-1-1-1111-1-1111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1-111-1-11-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii1-1-111-1-1111-1-1-1-111−iii−i-11-1-111ii−i−i−iii−i
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χ914-4-44-2440024-442-4-4-2-4-2-242-22-2-4422-40000000000-22-2200000000000000i6−i600i6−i6−i6i6−i6i600−i6i6i6−i60000000000000000000000000000000000
χ924-4-44-2440024-442-4-4-2-4-2-242-22-2-4422-40000000000-22-2200000000000000−i6i600−i6i6i6−i6i6−i600i6−i6−i6i60000000000000000000000000000000000
χ934-4-44-2-24002-2-4422-4-221-2-2-112-22-2-1220003i−3i00−3i3i01-11-100003i−3i−3i3i000000i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ944-4-44-2-24002-2-4422-4-221-2-2-112-22-2-1220003i−3i00−3i3i01-11-100003i−3i−3i3i000000−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
χ954-4-44-2-24002-2-4422-4-221-2-2-112-22-2-122000−3i3i003i−3i01-11-10000−3i3i3i−3i000000i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ964-4-44-2-24002-2-4422-4-221-2-2-112-22-2-122000−3i3i003i−3i01-11-10000−3i3i3i−3i000000−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-48-84444-4-4-444222-2-2-2-2-2-222244-4-2-2-4-4224-111-1-2-22211-1-100000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-884444-4-4-444222-2-2-2-2-2-2222-4-442244-2-2-4-111-122-2-2-1-11100000000000000000000000000000000000000000000000000000000
χ1018-88-88-4-40084-44-844-8-4-4-42-44-442-244-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-400-4-8-444-8448-42-4-442-2-444-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-44-444444-42222-22-22-2-2-2-20006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-400-44-444444-42222-22-22-2-2-2-2000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-400-8-44-4-84484-4-424-44-4-2244-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-400484-44-84-4-8-42-44-4-224-44-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4004-44-4444-44222-22-22-22-2-2-20006i−6i00−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4004-44-4444-44222-22-22-22-2-2-2000−6i6i006i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

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