Finite Group Databasebeta

← Group #13156396

Character table — Group #13156396

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818242424242424242424242424363636727272727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212444488121212121212121224242424242424242424242424242424226666121212121212121212121212412122466121288
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
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
χ11222222-12222-12-1-12222-1-12-1-1-12-1-12-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1220022222200002222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-100-1-1-1-1000000020-1-10000
χ12222222-12222-12-1-12222-1-12-1-1-12-1-12-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-12200-2-222220000-2-2-2-2111111111111000000-1-100-1-1-1-10000000-20110000
χ13222222-12222-12-1-12222-1-12-1-1-12-1-12-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20022-2-2-2-200002222-1-1-1-1-1-1-1-1-1-1-1-1000000110011110000000-20110000
χ14222222-12222-12-1-12222-1-12-1-1-12-1-12-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-2-2-2-20000-2-2-2-211111111111100000011001111000000020-1-10000
χ1522222-12222-12222-1-12-12-1-122-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-12-1-100000000
χ1622222-12222-12222-1-12-12-1-122-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111110000000000000000-2-2111122-2-2-1-1-1-11111-21100000000
χ1722222-12222-12222-1-12-12-1-122-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-1-1-10000000000000000-2-21111-2-2221111-1-1-1-1-21100000000
χ1822222-12222-12222-1-12-12-1-122-1-12-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20011111111000000000000000022-1-1-1-1-2-2-2-2111111112-1-100000000
χ1922222-12-2-22-12222-1-12-12-1-122-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000−i3−i3i3i3−i3−i3i3i3000000000000000022-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-21100000000
χ2022222-12-2-22-12222-1-12-12-1-122-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000−i3−i3i3i3i3i3−i3−i30000000000000000-2-211110000−i3−i3i3i3i3i3−i3−i32-1-100000000
χ2122222-12-2-22-12222-1-12-12-1-122-1-12-1-1-1-2-211-2-2-2-2-2-2-1-1-1-111111111000000i3i3−i3−i3−i3−i3i3i30000000000000000-2-211110000i3i3−i3−i3−i3−i3i3i32-1-100000000
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χ232222-12222-122-12222-1-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100222200002222-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-10000-1-1-1-10000200-1-100
χ242222-12222-122-12222-1-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-10022-2-2000022221111-2-2-2-21111111100000000-1-10000-1-1-1-10000-2001100
χ252222-12222-122-12222-1-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2220000-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10000000011000011110000-2001100
χ262222-12222-122-12222-1-1-12-1-1-12-1-12-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-20000-2-2-2-21111-2-2-2-2111111110000000011000011110000200-1-100
χ272-22-22222-2-2-2-222-22-2-2222-2-2-2-2222-2-2-2-22-2-2-222222-2-222-22-222-2-2002i−2i0000002i−2i2i−2i0000000000000000000000002i−2i00002i−2i2i−2i00000000000
χ282-22-22222-2-2-2-222-22-2-2222-2-2-2-2222-2-2-2-22-2-2-222222-2-222-22-222-2-200−2i2i000000−2i2i−2i2i000000000000000000000000−2i2i0000−2i2i−2i2i00000000000
χ292-22-2222-22-2-2-222-22-2-2222-2-2-2-2222-2-222-2222-2-2-2-22-2-22-22-22-2-2222i−2i00002i−2i2i−2i000000000000000000000000002i−2i002i−2i2i−2i000000000000000
χ302-22-2222-22-2-2-222-22-2-2222-2-2-2-2222-2-222-2222-2-2-2-22-2-22-22-22-2-222−2i2i0000−2i2i−2i2i00000000000000000000000000−2i2i00−2i2i−2i2i000000000000000
χ312-22-222-1-22-2-212-112-2-22-1-1-21112-1-1-212-1-22-1-1-2111-111-1-221-111-1-12i−2i00002i−2i2i−2i0000000033−3−33333−3−3−3−3000000−ii00−ii−ii000000000−i3i30000
χ322-22-222-1-22-2-212-112-2-22-1-1-21112-1-1-212-1-22-1-1-2111-111-1-221-111-1-12i−2i00002i−2i2i−2i00000000−3−333−3−3−3−33333000000−ii00−ii−ii000000000i3−i30000
χ332-22-222-1-22-2-212-112-2-22-1-1-21112-1-1-212-1-22-1-1-2111-111-1-221-111-1-1−2i2i0000−2i2i−2i2i0000000033−3−33333−3−3−3−3000000i−i00i−ii−i000000000i3−i30000
χ342-22-222-1-22-2-212-112-2-22-1-1-21112-1-1-212-1-22-1-1-2111-111-1-221-111-1-1−2i2i0000−2i2i−2i2i00000000−3−333−3−3−3−33333000000i−i00i−ii−i000000000−i3i30000
χ352-22-22-122-2-21-222-2-11-2-12-11-2-21-12-111-2-2-11-2-22222-111-1-11-11-1-111002i−2i003−3−33−ii−ii000000000000000000−i3−i3i3i3002i−2i3−3−33−ii−ii0−i3i300000000
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χ382-22-22-122-2-21-222-2-11-2-12-11-2-21-12-111-2-2-11-2-22222-111-1-11-11-1-11100−2i2i00−333−3i−ii−i000000000000000000−i3−i3i3i300−2i2i−333−3i−ii−i0−i3i300000000
χ392-22-22-12-22-21-222-2-11-2-12-11-2-21-12-111221-122-2-2-2-2-111-11-11-111-1-12i−2i0000−ii−ii3−3−33000000000000000000−i3−i3i3i32i−2i00−ii−ii3−3−330i3−i300000000
χ402-22-22-12-22-21-222-2-11-2-12-11-2-21-12-111221-122-2-2-2-2-111-11-11-111-1-12i−2i0000−ii−ii−333−3000000000000000000i3i3−i3−i32i−2i00−ii−ii−333−30−i3i300000000
χ412-22-22-12-22-21-222-2-11-2-12-11-2-21-12-111221-122-2-2-2-2-111-11-11-111-1-1−2i2i0000i−ii−i3−3−33000000000000000000i3i3−i3−i3−2i2i00i−ii−i3−3−330−i3i300000000
χ422-22-22-12-22-21-222-2-11-2-12-11-2-21-12-111221-122-2-2-2-2-111-11-11-111-1-1−2i2i0000i−ii−i−333−3000000000000000000−i3−i3i3i3−2i2i00i−ii−i−333−30i3−i300000000
χ432-22-2-1222-21-2-2-12-22-21-1-12111-2-1-121-21-22-211-12-1-1-111-1-112-2-1-111002i−2i0000002i−2i2i−2i−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i300000000−ii0000−ii−ii00000003−300
χ442-22-2-1222-21-2-2-12-22-21-1-12111-2-1-121-21-22-211-12-1-1-111-1-112-2-1-111002i−2i0000002i−2i2i−2ii3i3−i3−i30000i3i3−i3−i3i3i3−i3−i300000000−ii0000−ii−ii0000000−3300
χ452-22-2-1222-21-2-2-12-22-21-1-12111-2-1-121-21-22-211-12-1-1-111-1-112-2-1-11100−2i2i000000−2i2i−2i2i−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i300000000i−i0000i−ii−i0000000−3300
χ462-22-2-1222-21-2-2-12-22-21-1-12111-2-1-121-21-22-211-12-1-1-111-1-112-2-1-11100−2i2i000000−2i2i−2i2ii3i3−i3−i30000i3i3−i3−i3i3i3−i3−i300000000i−i0000i−ii−i00000003−300
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χ854-44-4-24-2-442-42-2-224-42-21-22-1-12-21-222-2-2-441122-1-11-1-112-22-2-1-111000000000000000000−23−2323233333−3−3−3−300000000000000000000000000000
χ864-44-4-2-244-422-4-24-4-2221-2-2-12221-2-2-122-4-2222-24-2-21-1-111-1-2211-1-1004i−4i000000−2i2i−2i2i000000000000000000000000−2i2i0000i−ii−i00000000000
χ874-44-4-2-244-422-4-24-4-2221-2-2-12221-2-2-122-4-2222-24-2-21-1-111-1-2211-1-100−4i4i0000002i−2i2i−2i0000000000000000000000002i−2i0000−ii−ii00000000000
χ884-44-4-2-24-4422-4-24-4-2221-2-2-12221-2-2-12-242-2-2-22-4221-1-11-112-2-1-111000000000023−23−2323000000000000000000000000000000−333−300000000000
χ894-44-4-2-24-4422-4-24-4-2221-2-2-12221-2-2-12-242-2-2-22-4221-1-11-112-2-1-1110000000000−232323−230000000000000000000000000000003−3−3300000000000
χ904-4-4444-200-4-42-42-2-4444-2-2-4-222-4224-20000000000-2-22200000000000022−220000000022−2222−22−22−22−22−22−22−2200000000000000000000000000000
χ914-4-4444-200-4-42-42-2-4444-2-2-4-222-4224-20000000000-2-222000000000000−222200000000−2222−22222−22−22−22−22−22−200000000000000000000000000000
χ924-4-444-2400-42-4-4-442-24-24-224-422-42-2-20000000000-2-222000000000000000000000000000000000000004-4-22-2200000000000000000000000
χ934-4-444-2400-42-4-4-442-24-24-224-422-42-2-20000000000-2-22200000000000000000000000000000000000000-442-22-200000000000000000000000
χ944-4-44-244002-4-42-44-44-2-2-242-22-422-4-240000000000-2-22200000000000022−2200000000−22−2222−2222−22−22−22−22−2200000000000000000000000000000
χ954-4-44-244002-4-42-44-44-2-2-242-22-422-4-240000000000-2-222000000000000−2222000000002−22−2−2222−22222−22−22−22−200000000000000000000000000000
χ964-4-44-24-2002-4222-2-44-2-21-221-122-12-2-200003i−3i00−3i3i11-1-10000−3i3i3i−3i000022−2200000000−22−22−22−22−2ζ5−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
χ974-4-44-24-2002-4222-2-44-2-21-221-122-12-2-200003i−3i00−3i3i11-1-10000−3i3i3i−3i0000−2222000000002−22−22−22−22ζ5+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
χ984-4-44-24-2002-4222-2-44-2-21-221-122-12-2-20000−3i3i003i−3i11-1-100003i−3i−3i3i000022−2200000000−22−22−22−22ζ5+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
χ994-4-44-24-2002-4222-2-44-2-21-221-122-12-2-20000−3i3i003i−3i11-1-100003i−3i−3i3i0000−2222000000002−22−22−22−2−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
χ10288-8-88-4-4008-4-4-84444-8-4-42-44-4244-24-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4800-4-484-8-84442-4-424-4-4-244-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-4-4-44444442222-222-2-2-2-2-200006i−6i006i−6i-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-4-4-44444442222-222-2-2-2-2-20000−6i6i00−6i6i-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-48-8444-4-44-444222-2-2-2-2222-2-244-44-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-88444-4-44-444222-2-2-2-2222-2-2-4-44-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-400-844-84-44-48-4-424-44-244-2-42000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-480044-84-884-4-42-4-4-2-444-2442-4000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-40044444-44-4-4222-22-2-2-2-2-22200006i−6i00−6i6i-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-40044444-44-4-4222-22-2-2-2-2-2220000−6i6i006i−6i-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000

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