Finite Group Databasebeta

← Group #13156377

Character table — Group #13156377

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818242424242424242424242424363636727272727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212444488121212121212121224242424242424242424242424242424441212121212121212121212121212121241212441212121288
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
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-11-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-11111
χ51111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-111-1-111
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
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000222222000000000000-2-2-200000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-2-2-2-2-200000000000022200000000
χ11222222-1222222-1-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-12-1-100000000
χ12222222-1222222-1-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111110000000000000000-2-2111122-2-21111-1-1-1-1-21100000000
χ13222222-1222222-1-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-1-1-10000000000000000-2-21111-2-222-1-1-1-11111-21100000000
χ14222222-1222222-1-1-1222-1-122-1-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20011111111000000000000000022-1-1-1-1-2-2-2-2111111112-1-100000000
χ15222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000−i3−i3i3i3−i3−i3i3i3000000000000000022-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-21100000000
χ16222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000−i3−i3i3i3i3i3−i3−i30000000000000000-2-211110000i3i3−i3−i3−i3−i3i3i32-1-100000000
χ17222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000i3i3−i3−i3−i3−i3i3i30000000000000000-2-211110000−i3−i3i3i3i3i3−i3−i32-1-100000000
χ18222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000i3i3−i3−i3i3i3−i3−i3000000000000000022-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-21100000000
χ1922222-12222-12-1222-12-12-1-1-12-1-1-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1220022222200002222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1000000-1-1-1-100020-1-10000
χ2022222-12222-12-1222-12-12-1-1-12-1-1-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-12200-2-222220000-2-2-2-2111111111111000000-1-1000000-1-1-1-1000-20110000
χ2122222-12222-12-1222-12-12-1-1-12-1-1-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20022-2-2-2-200002222-1-1-1-1-1-1-1-1-1-1-1-1000000110000001111000-20110000
χ2222222-12222-12-1222-12-12-1-1-12-1-1-122-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-2-2-2-20000-2-2-2-211111111111100000011000000111100020-1-10000
χ232222-12222-12-122222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100222200002222-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-100000000200-1-100
χ242222-12222-12-122222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-10022-2-2000022221111-2-2-2-21111111100000000-1-1-1-1-1-100000000-2001100
χ252222-12222-12-122222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2220000-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10000000011111100000000-2001100
χ262222-12222-12-122222-1-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-20000-2-2-2-21111-2-2-2-2111111110000000011111100000000200-1-100
χ2722-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-222-22222-222-2-2-2-22-2-222-22-222-2-22-200002-22-2000000000000000000000000002-20000002-22-200000000000
χ2822-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-222-22222-222-2-2-2-22-2-222-22-222-2-2-220000-22-2200000000000000000000000000-22000000-22-2200000000000
χ2922-2-2222-22-2-2222-2-2-2-2222-2-2-2-2-222-22-2-2-22-2-222222-2-22-22-22-2-222002i−2i0000002i−2i2i−2i0000000000000000000000002i−2i2i−2i2i−2i000000000000000
χ3022-2-2222-22-2-2222-2-2-2-2222-2-2-2-2-222-22-2-2-22-2-222222-2-22-22-22-2-22200−2i2i000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i−2i2i000000000000000
χ3122-2-222-12-2-2-222-111-2-22-1-1-2-21112-11-122-1122-2-2-2-2-111-1-11-11-1-1112-20000-11-113−3−3300000000000000000033−3−32-2003−3−33-11-1103−300000000
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χ3422-2-222-12-2-2-222-111-2-22-1-1-2-21112-11-122-1122-2-2-2-2-111-1-11-11-1-111-2200001-11-1−333−300000000000000000033−3−3-2200−333−31-11-103−300000000
χ3522-2-222-1-22-2-222-111-2-22-1-1-2-21112-11-1-2-21-1-2-22222-111-11-11-111-1-1002i−2i00−i3i3i3−i3−ii−ii00000000000000000033−3−3002i−2i−ii−ii−i3i3i3−i30−3300000000
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χ3922-2-22-122-2-212-12-2-21-2-12-111-211-12-2-12-12-2-1-1-2111-111-12-2-11-1-1112-200002-22-20000000033−3−33333−3−3−3−3000000-11000000-11-11000003−30000
χ4022-2-22-122-2-212-12-2-21-2-12-111-211-12-2-12-12-2-1-1-2111-111-12-2-11-1-1112-200002-22-200000000−3−333−3−3−3−33333000000-11000000-11-1100000−330000
χ4122-2-22-122-2-212-12-2-21-2-12-111-211-12-2-12-12-2-1-1-2111-111-12-2-11-1-111-220000-22-220000000033−3−33333−3−3−3−30000001-10000001-11-100000−330000
χ4222-2-22-122-2-212-12-2-21-2-12-111-211-12-2-12-12-2-1-1-2111-111-12-2-11-1-111-220000-22-2200000000−3−333−3−3−3−333330000001-10000001-11-1000003−30000
χ4322-2-2-122-221-2-122-2-2-21-1-12111-2-2-1-1121-2-2211-12-1-1-111-11-1-2211-1-1002i−2i0000002i−2i2i−2i−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i300000000−ii−ii−ii000000000003−300
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χ472-2-2222200-22-2-2-2-22-222222-2-22-2-2-22-2000000000022-2-20000000000002−2000000002−22−22−22−22−22−22−22−22i−2i2i−2i2i−2i000000000000000000000−i2i2
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χ5244444-2-2444-24-2-2-2-2-24-2-21-2-2-211-2-2-214-2-2-2-2-24-2-2-21111-2-2111111440000-2-2-2-200000000000000000000000000-2-2000000111100000000000
χ5344444-2-2444-24-2-2-2-2-24-2-21-2-2-211-2-2-214-2-2-2-2-24-2-2-21111-2-2111111-4-4000022220000000000000000000000000022000000-1-1-1-100000000000
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χ884-44-4-2-2400-2222-44-4-221-2-2-11-22-2-12220000−3i3i00−3i3i1-11-10000−3i3i−3i3i00000000000000i6−i6−i6i6−666−6−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000000000000
χ894-44-4-2-2400-2222-44-4-221-2-2-11-22-2-12220000−3i3i00−3i3i1-11-10000−3i3i−3i3i00000000000000−i6i6i6−i66−6−66ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000000000000
χ904-4-4444-200-44-4-422-2-444-2-24-42-22-42-220000000000-2-222000000000000000000000000000000000000004i−4i−2i2i−2i2i00000000000000000000000
χ914-4-4444-200-44-4-422-2-444-2-24-42-22-42-220000000000-2-22200000000000000000000000000000000000000−4i4i2i−2i2i−2i00000000000000000000000
χ924-4-444-2400-4-2-42-4-4424-24-2-22-4-222-4420000000000-2-22200000000000022−220000000022−2222−22−22−22−22−22−22−2200000000000000000000000000000
χ934-4-444-2400-4-2-42-4-4424-24-2-22-4-222-4420000000000-2-222000000000000−222200000000−2222−22222−22−22−22−22−22−200000000000000000000000000000
χ944-4-44-24400242-4-4-44-4-2-2-24-2224-422-2-40000000000-2-22200000000000022−2200000000−22−2222−2222−22−22−22−22−2200000000000000000000000000000
χ954-4-44-24400242-4-4-44-4-2-2-24-2224-422-2-40000000000-2-222000000000000−2222000000002−22−2−2222−22222−22−22−22−200000000000000000000000000000
χ964-4-44-2-24002-222-4-442-21-2-21-12-22-12-2200003i−3i00−3i3i11-1-100003i−3i−3i3i000022−2200000000−22−22−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000000000000
χ974-4-44-2-24002-222-4-442-21-2-21-12-22-12-2200003i−3i00−3i3i11-1-100003i−3i−3i3i0000−2222000000002−22−22−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ2300000000000000000000000000000
χ984-4-44-2-24002-222-4-442-21-2-21-12-22-12-220000−3i3i003i−3i11-1-10000−3i3i3i−3i000022−2200000000−22−22−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000000000000
χ994-4-44-2-24002-222-4-442-21-2-21-12-22-12-220000−3i3i003i−3i11-1-10000−3i3i3i−3i0000−2222000000002−22−22−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ2300000000000000000000000000000
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
χ10288-8-8-4-4-48-844-4-4-44444222-2-2-2-2-222-22-4-4-442244-2-2-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-8844-4-4-44444222-2-2-2-2-222-22444-4-2-2-4-422-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-40084-844-44-4-8-4-424-4-4-22444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-400-4-84-84-4484-42-44-424-44-2-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-400-44444-44-44222-222-22-2-2-2-200006i−6i006i−6i-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-400-44444-44-44222-222-22-2-2-2-20000−6i6i00−6i6i-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-400-8-4-8444-448-4-42-4442-244-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-400484-844-4-8-4-42-4-44-2-444-224000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4004-44444-44-42222-2-22-2-2-22-200006i−6i00−6i6i-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4004-44444-44-42222-2-22-2-2-22-20000−6i6i006i−6i-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000

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