Finite Group Databasebeta

← Group #13156494

Character table — Group #13156494

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818242424242424242424242424363636727272727272108108
order12223334466666666633366666666612121212121212121212366612121212121212124444881212121212121212242424242424242424242424242424244412121212121212121212121212121212266441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-11111
χ51111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11-111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
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χ11222222-1222222-1-1-1222-1-122-1-12-1-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-12-1-100000000
χ12222222-1222222-1-1-1222-1-122-1-12-1-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111110000000000000000-2-2111122-2-2-1-1-1-11111-21100000000
χ13222222-1222222-1-1-1222-1-122-1-12-1-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-1-1-10000000000000000-2-21111-2-2221111-1-1-1-1-21100000000
χ14222222-1222222-1-1-1222-1-122-1-12-1-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20011111111000000000000000022-1-1-1-1-2-2-2-2111111112-1-100000000
χ15222222-1-2-22222-1-1-1222-1-122-1-12-1-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000−i3−i3i3i3−i3−i3i3i3000000000000000022-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-21100000000
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χ17222222-1-2-22222-1-1-1222-1-122-1-12-1-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3i3−i3−i3−i3−i3i3i30000000000000000-2-211110000i3i3−i3−i3−i3−i3i3i32-1-100000000
χ18222222-1-2-22222-1-1-1222-1-122-1-12-1-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3i3−i3−i3i3i3−i3−i3000000000000000022-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-21100000000
χ1922222-12222-12-1222-12-12-1-1-12-1-12-12-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1220022222200002222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-100-1-1-1-1000000020-1-10000
χ2022222-12222-12-1222-12-12-1-1-12-1-12-12-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12200-2-222220000-2-2-2-2111111111111000000-1-100-1-1-1-10000000-20110000
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χ2222222-12222-12-1222-12-12-1-1-12-1-12-12-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-2-2-2-20000-2-2-2-211111111111100000011001111000000020-1-10000
χ232222-12222-12-122222-1-1-12-1-1-12-1-12-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-100222200002222-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-10000-1-1-1-10000200-1-100
χ242222-12222-12-122222-1-1-12-1-1-12-1-12-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-10022-2-2000022221111-2-2-2-21111111100000000-1-10000-1-1-1-10000-2001100
χ252222-12222-12-122222-1-1-12-1-1-12-1-12-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-100-2-2220000-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10000000011000011110000-2001100
χ262222-12222-12-122222-1-1-12-1-1-12-1-12-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-20000-2-2-2-21111-2-2-2-2111111110000000011000011110000200-1-100
χ272-22-222200-2-22-22-2-22-22222-2-22-2-2-22-2000000000022-2-2000000000000−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i2i2i−2i−2i0000000000000000000002−2
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χ412-2-2222-1-22-22-2-211-1-222-1-1-2-2112-1-11121-1222-2-2-2-2-111-11-11-111-1-100−2i2i003−3−33i−ii−i000000000000000000i3−i3i3−i300−2i2i3−3−33i−ii−i0−i3i300000000
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χ844-44-4-2-240022-224-4-4-221-2-21-12-2-122-220000−3i3i003i−3i11-1-100003i−3i−3i3i0000−2i22i200000000i2i2−i2−i2i2i2−i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000000000000000
χ854-44-4-2-240022-224-4-4-221-2-21-12-2-122-220000−3i3i003i−3i11-1-100003i−3i−3i3i00002i2−2i200000000−i2−i2i2i2−i2−i2i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ2300000000000000000000000000000
χ864-4-444-24-44-4-2-42-4-4424-24-222-42-24-2-42-2-444-2-22-422-222-2-442-222-2-200000000000000000000000000000000000000000000000000000000000
χ874-4-444-2-24-4-4-2-4222-224-2-21222-1-2-212-12-22-422-24-2-21-1-11-221-111-1-14i−4i0000−2i2i−2i2i00000000000000000000000000−2i2i00i−ii−i000000000000000
χ884-4-444-2-24-4-4-2-4222-224-2-21222-1-2-212-12-22-422-24-2-21-1-11-221-111-1-1−4i4i00002i−2i2i−2i000000000000000000000000002i−2i00−ii−ii000000000000000
χ894-4-444-2-2-44-4-2-4222-224-2-21222-1-2-212-1-22-24-2-22-4221-1-112-2-11-1-11100000023−23−2323000000000000000000000000000000−333−3000000000000000
χ904-4-444-2-2-44-4-2-4222-224-2-21222-1-2-212-1-22-24-2-22-4221-1-112-2-11-1-111000000−232323−230000000000000000000000000000003−3−33000000000000000
χ914-4-44-2444-4242-4-4-44-4-2-2-24222-4-2-242-4-44-42224-2-2-2-222-2-224-4-2-22200000000000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-4242-422-2-4-2-21-222-12-21-2-12-4-222224-2-2-21-1-111-1-2211-1-1000000000023−23−2323000000000000000000000000000000−333−300000000000
χ934-4-44-24-24-4242-422-2-4-2-21-222-12-21-2-12-4-222224-2-2-21-1-111-1-2211-1-10000000000−232323−230000000000000000000000000000003−3−3300000000000
χ944-4-44-24-2-44242-422-2-4-2-21-222-12-21-2-1242-2-2-2-2-42221-1-11-112-2-1-111004i−4i000000−2i2i−2i2i000000000000000000000000−2i2i0000i−ii−i00000000000
χ954-4-44-24-2-44242-422-2-4-2-21-222-12-21-2-1242-2-2-2-2-42221-1-11-112-2-1-11100−4i4i0000002i−2i2i−2i0000000000000000000000002i−2i0000−ii−ii00000000000
χ964-4-44-2-244-42-222-4-442-21-2-2-1-1221-2-22224-42-1-1-2-2111-1-11-22-2211-1-1000000000000000000−2i32i3−2i32i3i3i3−i3−i3i3i3−i3−i300000000000000000000000000000
χ974-4-44-2-244-42-222-4-442-21-2-2-1-1221-2-22224-42-1-1-2-2111-1-11-22-2211-1-10000000000000000002i3−2i32i3−2i3−i3−i3i3i3−i3−i3i3i300000000000000000000000000000
χ984-4-44-2-24-442-222-4-442-21-2-2-1-1221-2-222-2-44-21122-1-11-1-112-22-2-1-1110000000000000023−2323−230000−33−33−33−3300000000000000000000000000000
χ994-4-44-2-24-442-222-4-442-21-2-2-1-1221-2-222-2-44-21122-1-11-1-112-22-2-1-11100000000000000−2323−232300003−33−33−33−300000000000000000000000000000
χ1008888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-422-4-422-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1018888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-2-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10288-8-88-4-40084-8-44-444-8-4-424-4-4-244-24200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-400-4-8484-44-84-42-44-4244-24-2-400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-444-44-4444222-222-2-2-2-2-2200006i−6i006i−6i-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-444-44-4444222-222-2-2-2-2-220000−6i6i00−6i6i-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1068-88-88-4-400-8484-444-4-8-4-42-444244-2-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-48-4004-8-4-8-44484-42-4-44-2-44-2424000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-40044-44-444-442222-2-22-2-2-22-200006i−6i00−6i6i-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-40044-44-444-442222-2-22-2-2-22-20000−6i6i006i−6i-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-84-44444-44-4222-2-2-2-2222-2-24-444-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-884-44444-44-4222-2-2-2-2222-2-2-44-4-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000

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