Finite Group Databasebeta

← Group #13155996

Character table — Group #13155996

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order122233344666666666333666666666121212121212121212123666121212121212121244882424242424242424242424242424242426666666612121212121212124488242424244426612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1111
χ51111111111111111111111111111111111111111111111111111-1-1111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000002200000-2
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χ11222222-122222-12-12-12-1-12-1-1-122-1-12-12-12-1-1-12-1-12-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000000022-1-1-1-1-1-100000000002-1-1000
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χ13222222-122222-12-12-12-1-12-1-1-122-1-12-12-12-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1000000000-2-21111110000000000-211000
χ14222222-122222-12-12-12-1-12-1-1-122-1-12-12-12-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111000000000-2-211111100000000002-1-1000
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χ202222-12222-1-1222222-1-12-1-1-12-1-1-12-1222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-10022-1-1-1-12222-1-1-1-1-1-1-1-1-211-2-2111100000000-2-200000000000110
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χ874-4-444-2400-442-42-4-24-44-2-2-4422-2-422-20000000000-22-220000000000000000000000000000000000000000000000000−i6i6i6−i600000000
χ884-4-44-244002-2-4-4-4-4442-24-22-2-42-22-4240000000000-22-220000000000006−6−6600006−6−666−6−66000000000000000000000000000000000
χ894-4-44-244002-2-4-4-4-4442-24-22-2-42-22-4240000000000-22-22000000000000−666−60000−666−6−666−6000000000000000000000000000000000
χ904-4-44-24-2002-2-42-424-221-2-2-1122-2-122-20003i−3i00−3i3i01-11-100003i−3i−3i3i00006−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ914-4-44-24-2002-2-42-424-221-2-2-1122-2-122-20003i−3i00−3i3i01-11-100003i−3i−3i3i0000−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ924-4-44-24-2002-2-42-424-221-2-2-1122-2-122-2000−3i3i003i−3i01-11-10000−3i3i3i−3i00006−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ934-4-44-24-2002-2-42-424-221-2-2-1122-2-122-2000−3i3i003i−3i01-11-10000−3i3i3i−3i0000−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ948888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ958888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-48-84444-4-444-4222-2-2-2-2-2222-2-4-4-42244-2-24-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-4-884444-4-444-4222-2-2-2-2-2222-2444-2-2-4-422-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000
χ988-88-88-4-4008-8-4-44444-8-42-4-442-444-24-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4800-44-484-84-84-4-42-44-42-244-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-400-44-4-4444442222-222-2-2-2-2-20006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-400-44-4-4444442222-222-2-2-2-2-2000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1028-8-888-4-400-884444-4-4-8-42-44-4-24-44-24200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-48004-44-84-8-484-4-424-44-2244-2-400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4004-44444-4-44222-22-2-22-2-2-220006i−6i00−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4004-44444-4-44222-22-2-22-2-2-22000−6i6i006i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000

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