Finite Group Databasebeta

← Group #13156024

Character table — Group #13156024

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
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-11111
χ51111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11-111-1-111
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
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
χ11222222-1222222-1-1-1222-1-122-1-1-12-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-12-1-100000000
χ12222222-1222222-1-1-1222-1-122-1-1-12-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2001111-1-1-1-10000000000000000-2-2111122-2-2-1-1-1-11111-21100000000
χ13222222-1222222-1-1-1222-1-122-1-1-12-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22200-1-1-1-111110000000000000000-2-21111-2-2221111-1-1-1-1-21100000000
χ14222222-1222222-1-1-1222-1-122-1-1-12-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20011111111000000000000000022-1-1-1-1-2-2-2-2111111112-1-100000000
χ15222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-111-2-2-2-2-2-2-2-2-1-1-1-111111111000000−i3−i3i3i3−i3−i3i3i3000000000000000022-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-21100000000
χ16222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-111-2-2-2-2-2-2-2-2-1-1-1-111111111000000−i3−i3i3i3i3i3−i3−i30000000000000000-2-211110000i3i3−i3−i3−i3−i3i3i32-1-100000000
χ17222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-111-2-2-2-2-2-2-2-2-1-1-1-111111111000000i3i3−i3−i3−i3−i3i3i30000000000000000-2-211110000−i3−i3i3i3i3i3−i3−i32-1-100000000
χ18222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-111-2-2-2-2-2-2-2-2-1-1-1-111111111000000i3i3−i3−i3i3i3−i3−i3000000000000000022-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-21100000000
χ1922222-122222-1-1222-12-12-1-1-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1220022000022222222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-100-1-1-1-1000000020-1-10000
χ2022222-122222-1-1222-12-12-1-1-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-12200-2-200002222-2-2-2-2111111111111000000-1-100-1-1-1-10000000-20110000
χ2122222-122222-1-1222-12-12-1-1-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200220000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000110011110000000-20110000
χ2222222-122222-1-1222-12-12-1-1-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-20000-2-2-2-2-2-2-2-211111111111100000011001111000000020-1-10000
χ232222-12222-1-1222222-1-1-12-1-1-1-12-122-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-100222222220000-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-10000-1-1-1-10000200-1-100
χ242222-12222-1-1222222-1-1-12-1-1-1-12-122-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-10022-2-2222200001111-2-2-2-21111111100000000-1-10000-1-1-1-10000-2001100
χ252222-12222-1-1222222-1-1-12-1-1-1-12-122-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-100-2-222-2-2-2-20000-1-1-1-12222-1-1-1-1-1-1-1-10000000011000011110000-2001100
χ262222-12222-1-1222222-1-1-12-1-1-1-12-122-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2-2-200001111-2-2-2-2111111110000000011000011110000200-1-100
χ2722-2-2222002-22-2-22-2-2-22222-22-22-2-2-2-2000000000022-2-20000000000002−20000000022−2−222−2−22222−2−2−2−22-222-2-20000000000000000000002−2
χ2822-2-2222002-22-2-22-2-2-22222-22-22-2-2-2-2000000000022-2-20000000000002−20000000022−2−222−2−22222−2−2−2−2-22-2-222000000000000000000000−22
χ2922-2-2222002-22-2-22-2-2-22222-22-22-2-2-2-2000000000022-2-2000000000000−2200000000−2−222−2−222−2−2−2−222222-222-2-2000000000000000000000−22
χ3022-2-2222002-22-2-22-2-2-22222-22-22-2-2-2-2000000000022-2-2000000000000−2200000000−2−222−2−222−2−2−2−22222-22-2-2220000000000000000000002−2
χ312-2-222222-2-2-2-2-22-2-222222-2-2-2-2-222-222-22222-2-2-2-22-2-222-22-222-2-22i−2i000000002i−2i2i−2i00000000000000000000002i−2i002i−2i2i−2i000000000000000
χ322-2-222222-2-2-2-2-22-2-222222-2-2-2-2-222-222-22222-2-2-2-22-2-222-22-222-2-2−2i2i00000000−2i2i−2i2i0000000000000000000000−2i2i00−2i2i−2i2i000000000000000
χ332-2-22222-22-2-2-2-22-2-222222-2-2-2-2-222-22-22-2-2-2-222222-2-22-22-22-2-222002-2002-22-200000000000000000000000000002-200002-22-200000000000
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χ382-2-2222-12-2-2-2-2-2-111222-1-1-2-21112-11-1-112222-2-2-2-2-111-1-11-11-1-111−2i2i0000i3−i3−i3i3i−ii−i0000000000000000003−33−3−2i2i00i−ii−ii3−i3−i3i303−300000000
χ392-2-2222-1-22-2-2-2-2-111222-1-1-2-21112-11-11-1-2-2-2-22222-111-11-11-111-1-1002-200-11-113−3−330000000000000000003−33−3002-23−3−33-11-110−3300000000
χ402-2-2222-1-22-2-2-2-2-111222-1-1-2-21112-11-11-1-2-2-2-22222-111-11-11-111-1-1002-200-11-11−333−3000000000000000000−33−33002-2−333−3-11-1103−300000000
χ412-2-2222-1-22-2-2-2-2-111222-1-1-2-21112-11-11-1-2-2-2-22222-111-11-11-111-1-100-22001-11-13−3−33000000000000000000−33−3300-223−3−331-11-103−300000000
χ422-2-2222-1-22-2-2-2-2-111222-1-1-2-21112-11-11-1-2-2-2-22222-111-11-11-111-1-100-22001-11-1−333−30000000000000000003−33−300-22−333−31-11-10−3300000000
χ432-2-222-122-2-2-2112-2-2-12-12-111-2-21-1-1122-2-12-1-11-211-111-1-112-2-1-1112i−2i000000002i−2i2i−2i00003−33−333−3−333−3−3000000−ii00−ii−ii000000000−i3i30000
χ442-2-222-122-2-2-2112-2-2-12-12-111-2-21-1-1122-2-12-1-11-211-111-1-112-2-1-1112i−2i000000002i−2i2i−2i0000−33−33−3−333−3−333000000−ii00−ii−ii000000000i3−i30000
χ452-2-222-122-2-2-2112-2-2-12-12-111-2-21-1-1122-2-12-1-11-211-111-1-112-2-1-111−2i2i00000000−2i2i−2i2i00003−33−333−3−333−3−3000000i−i00i−ii−i000000000i3−i30000
χ462-2-222-122-2-2-2112-2-2-12-12-111-2-21-1-1122-2-12-1-11-211-111-1-112-2-1-111−2i2i00000000−2i2i−2i2i0000−33−33−3−333−3−333000000i−i00i−ii−i000000000−i3i30000
χ472-2-22-122-2211-2-22-2-22-1-1-121111-2-12-2-1-22-21112-1-1-1-111-1-221-111-1-1002-2002-22-20000−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300000000-110000-11-110000000−i3i300
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χ5144444-24-4-444-2-2444-24-24-2-2-244-2-2-2-24-4-42-4222-422-2-2-2-222-4-4222200000000000000000000000000000000000000000000000000000000000
χ5244444-2-24444-2-2-2-2-2-24-2-21-2-2-2-21-211-2-2-2-24-2-2-24-2-2111111-2-211114400000000-2-2-2-20000000000000000000000-2-2001111000000000000000
χ5344444-2-24444-2-2-2-2-2-24-2-21-2-2-2-21-211-2-2-2-24-2-2-24-2-2111111-2-21111-4-400000000222200000000000000000000002200-1-1-1-1000000000000000
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χ614444-2-2444-2-2-2-2444-2-21-2-211-2-2-21-2-2-244-2-211-2-2111111-2-2-2-2111100004400000000-2-2-2-2-2-2-2-21111111100000000000000000000000000000
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χ844-44-4-2-24002-22-2-4-44221-2-2-112-22-12-220000−3i3i003i−3i1-11-10000−3i3i3i−3i00000000000000i6−i6−i6i6−666−6−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ2300000000000000000000000000000
χ854-44-4-2-24002-22-2-4-44221-2-2-112-22-12-220000−3i3i003i−3i1-11-10000−3i3i3i−3i00000000000000−i6i6i6−i66−6−66ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ2300000000000000000000000000000
χ864-4-444-24-44-4-4224-4-4-24-24-222-4-42-2-224-442-422-24-2-2-222-22-2-4422-2-200000000000000000000000000000000000000000000000000000000000
χ874-4-444-2-24-4-4-422-222-24-2-212222-1-21-1-2-22-24-2-22-4221-1-111-1-2211-1-14i−4i00000000−2i2i−2i2i0000000000000000000000−2i2i00i−ii−i000000000000000
χ884-4-444-2-24-4-4-422-222-24-2-212222-1-21-1-2-22-24-2-22-4221-1-111-1-2211-1-1−4i4i000000002i−2i2i−2i00000000000000000000002i−2i00−ii−ii000000000000000
χ894-4-444-2-2-44-4-422-222-24-2-212222-1-21-1-22-22-422-24-2-21-1-11-112-2-1-111000000000023−23−232300000000000000000000000000−333−3000000000000000
χ904-4-444-2-2-44-4-422-222-24-2-212222-1-21-1-22-22-422-24-2-21-1-11-112-2-1-1110000000000−232323−23000000000000000000000000003−3−33000000000000000
χ914-4-44-2444-422-4-44-4-44-2-2-242222-4-24-4-24-44-2-2-2-4222-222-24-4-22-2-22200000000000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-422-4-4-2224-2-21-222-1-12-2-221-224-2-2-2-42221-1-11-221-111-1-1000000−2i32i32i3−2i30000000000000000000000000000000000i3−i3−i3i300000000000
χ934-4-44-24-24-422-4-4-2224-2-21-222-1-12-2-221-224-2-2-2-42221-1-11-221-111-1-10000002i3−2i3−2i32i30000000000000000000000000000000000−i3i3i3−i300000000000
χ944-4-44-24-2-4422-4-4-2224-2-21-222-1-12-2-2212-2-42224-2-2-21-1-112-2-11-1-111004-400-22-220000000000000000000000000000-2200001-11-100000000000
χ954-4-44-24-2-4422-4-4-2224-2-21-222-1-12-2-2212-2-42224-2-2-21-1-112-2-11-1-11100-44002-22-200000000000000000000000000002-20000-11-1100000000000
χ964-4-44-2-244-422224-4-4-2-21-2-2-1-12221-22-24-4-2-21122-1-11-1-11-22-2211-1-100000000000000000023−2323−23−3−333−3−33300000000000000000000000000000
χ974-4-44-2-244-422224-4-4-2-21-2-2-1-12221-22-24-4-2-21122-1-11-1-11-22-2211-1-1000000000000000000−2323−232333−3−333−3−300000000000000000000000000000
χ984-4-44-2-24-4422224-4-4-2-21-2-2-1-12221-22-2-4422-1-1-2-2111-1-112-22-2-1-11100000000000000−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i300000000000000000000000000000
χ994-4-44-2-24-4422224-4-4-2-21-2-2-1-12221-22-2-4422-1-1-2-2111-1-112-22-2-1-111000000000000002i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i300000000000000000000000000000
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
χ10288-8-88-4-4008-8-444-444-8-4-42-44-4424-2-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-400-448-84-44-84-42-4-442-2-4444-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-44-444-44442222-22-22-2-2-2-200006i−6i006i−6i-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-44-444-44442222-22-22-2-2-2-20000−6i6i00−6i6i-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1068-88-88-4-400-884-444-44-8-4-424-44-4-24-22400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-48-4004-4-8844-4-84-42-44-4-22444-4-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4004-44-444-444222-22-22-2-2-22-200006i−6i00−6i6i-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4004-44-444-444222-22-22-2-2-22-20000−6i6i006i−6i-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-84444-444-4-4222-2-2-2-2-222-22-44-4-42244-2-2-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-884444-444-4-4222-2-2-2-2-222-224-444-2-2-4-422-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000

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