Finite Group Databasebeta

← Group #13168608

Character table — Group #13168608

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121222446666121212121212121212121212224444441212121266666612121212121212121212446612121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1-1-111111111-1-111111111-1-1-1-11111-1111-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-111111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1111111-1-111111-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-111111111111111111111-111111-1-111-1-111-1-111-1-1-1-1-1-111-1-1-1-11111111-1-1-11111-1-1-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-1111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-1111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-11-1-1-111-1-1-1-111-1-1111-111-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-111111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1111111-1-1-1-11111111111-1111-1-11-1-1-1-1-11111-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-111-1-111111111111-1-1-111-111111-1-1-1-1-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1111-1-1-1-1-1-1-111111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1111-1-11111-1-111-1-11-111-1-1111-11-1
χ17222222-122-1-122-122-12-12-12-12-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1202000-1-1-1-1-1-12200-1-12222220000-1-1-1-102-1-10002-1-1-1-100-1-100-1-100000000
χ18222222-122-1-122-122-12-12-12-12-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-20200011-1-1112200-1-1-2-2-2-2-2-2000011110-2110002-1-11100-1-1001100000000
χ19222222-122-1-122-122-12-12-12-12-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-120-2000-1-111-1-1-2-2001122-2-2-2-20000111102-1-1000-211-1-10011001100000000
χ20222222-122-1-122-122-12-12-12-12-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-20-2000111111-2-20011-2-222220000-1-1-1-10-211000-21111001100-1-100000000
χ21222222-122-1-122-122-12-1-2-12-12-1-12-1-1112222-1-1-1-1-2-2-2-211111111-20-20001111-1-12200-1-12222-2-2000011110-211000-211-1-100-1-100-1-100000000
χ22222222-122-1-122-122-12-1-2-12-12-1-12-1-11122-2-2-1-1-1-1-2-2-2-21111111120-2000-1-111112200-1-1-2-2-2-2220000-1-1-1-102-1-1000-2111100-1-1001100000000
χ23222222-122-1-122-122-12-1-2-12-12-1-12-1-111-2-222-1-1-1-1-2-2-2-211111111-20200011-1-1-1-1-2-2001122-2-2220000-1-1-1-10-2110002-1-1-1-10011001100000000
χ24222222-122-1-122-122-12-1-2-12-12-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-211111111202000-1-1-1-111-2-20011-2-222-2-20000111102-1-10002-1-111001100-1-100000000
χ2522222-12-1-1222222-12-1-122-1-1-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-12202-1-1220022002200-1-10000002200002-1-1-1-1-1-1000-1-1-1-100020000-1-10-100
χ2622222-12-1-1222222-12-1-122-1-1-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-12-20-21122002200-2-200-1-1000000-2-20000-2-1-1-1111000-1-111000-20000110100
χ2722222-12-1-1222222-12-1-122-1-1-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2202-1-1-2-200-2-200220011000000-2-200002111-1-1-100011-1-1000-20000110100
χ2822222-12-1-1222222-12-1-122-1-1-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-211-2-200-2-200-2-20011000000220000-2111111000111100020000-1-10-100
χ2922222-12-1-1222222-12-1-1-22-1-1-1-12-1-12-2-20022-1-1-1-11-21111-2-21111-220-2-1-1-2-2002200-2-200-1-10000002200002111-1-11000-1-111000-20000-1-10100
χ3022222-12-1-1222222-12-1-1-22-1-1-1-12-1-12-2-20022-1-1-1-11-21111-2-21111-2-20211-2-20022002200-1-1000000-2-20000-211111-1000-1-1-1-100020000110-100
χ3122222-12-1-1222222-12-1-1-22-1-1-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-21111220-2-1-12200-2-200-2-20011000000-2-200002-1-1-1-1-11000111100020000110-100
χ3222222-12-1-1222222-12-1-1-22-1-1-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-211112-202112200-2-200220011000000220000-2-1-1-111-100011-1-1000-20000-1-10100
χ332222-1222222-1-12-12-1-122-1-12-12-1-12-1222200-1-1-1-12-1-1-122-1-1-1-1-1-1022222002200-1-1-1-12200000022000000-1000-1-12-1-1-100-1-1-1-12000-1-100-1000
χ342222-1222222-1-12-12-1-122-1-12-12-1-12-1222200-1-1-1-12-1-1-122-1-1-1-1-1-10-22-2-2-2002200-1-11122000000-2-2000000100011-2-1-1-10011-1-1-200011001000
χ352222-1222222-1-12-12-1-122-1-12-12-1-12-122-2-200-1-1-1-12-1-1-122-1-1-1-1-1-102-222200-2-20011-1-1-2-2000000-2-2000000-1000-1-1211100-1-111-200011001000
χ362222-1222222-1-12-12-1-122-1-12-12-1-12-122-2-200-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2-2-2-200-2-2001111-2-200000022000000100011-21110011112000-1-100-1000
χ372222-1222222-1-12-12-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-1-2111-2-211111102-2-22200-2-200-1-11122000000-2-2000000-1000-1-1-21110011-1-120001100-1000
χ382222-1222222-1-12-12-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-1-2111-2-21111110-2-22-2-200-2-200-1-1-1-12200000022000000100011211100-1-1-1-1-2000-1-1001000
χ392222-1222222-1-12-12-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-1-2111-2-2111111022-2220022001111-2-200000022000000-1000-1-1-2-1-1-1001111-2000-1-1001000
χ402222-1222222-1-12-12-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-1-2111-2-21111110-222-2-200220011-1-1-2-2000000-2-20000001000112-1-1-100-1-11120001100-1000
χ4122-2-22222-2-2-22-22-2-22220-2-2-222-2-2-220000002-2-2200000000000000000000000000000000002-22i−2i2i−2i22-2-2000000000000000000002i−2i2i−2i0000
χ4222-2-22222-2-2-22-22-2-22220-2-2-222-2-2-220000002-2-2200000000000000000000000000000000002-2−2i2i−2i2i22-2-200000000000000000000−2i2i−2i2i0000
χ4322-2-22222-2-2-22-22-2-22220-2-2-222-2-2-220000002-2-220000000000000000000000000000000000-222i−2i−2i2i-2-222000000000000000000002i−2i−2i2i0000
χ4422-2-22222-2-2-22-22-2-22220-2-2-222-2-2-220000002-2-220000000000000000000000000000000000-22−2i2i2i−2i-2-22200000000000000000000−2i2i2i−2i0000
χ452-22-2222-222-2-22-2-2-22220-2-22-2-222-2-2002i−2i2i−2i22-2-200000000000000000000002i−2i2i−2i002i−2i2i−2i2-2000000000000000000002i−2i002i−2i002-200000000
χ462-22-2222-222-2-22-2-2-22220-2-22-2-222-2-2002i−2i−2i2i22-2-20000000000000000000000−2i2i2i−2i002i−2i−2i2i-2200000000000000000000−2i2i002i−2i00-2200000000
χ472-22-2222-222-2-22-2-2-22220-2-22-2-222-2-200−2i2i2i−2i22-2-200000000000000000000002i−2i−2i2i00−2i2i2i−2i-22000000000000000000002i−2i00−2i2i00-2200000000
χ482-22-2222-222-2-22-2-2-22220-2-22-2-222-2-200−2i2i−2i2i22-2-20000000000000000000000−2i2i−2i2i00−2i2i−2i2i2-200000000000000000000−2i2i00−2i2i002-200000000
χ492-22-222-1-22-11-221-2-2-12-101-2-1-21-12113−32i−2i2i−2i-1-11100003−33−333−3−3000000−i3i3−i3i3−ii2i−2i00−ii2i−2i2-20000003−33−300−i3i30000−i3i3−ii00−ii00-1100000000
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χ512-22-222-1-22-11-221-2-2-12-101-2-1-21-12113−3−2i2i2i−2i-1-11100003−33−333−3−3000000−i3i3i3−i3−ii−2i2i00i−i2i−2i-22000000−33−3300−i3i30000i3−i3−ii00i−i001-100000000
χ522-22-222-1-22-11-221-2-2-12-101-2-1-21-12113−3−2i2i−2i2i-1-11100003−33−333−3−3000000i3−i3i3−i3i−i−2i2i00i−i−2i2i2-20000003−33−300i3−i30000i3−i3i−i00i−i00-1100000000
χ532-22-222-1-22-11-221-2-2-12-101-2-1-21-1211−332i−2i2i−2i-1-1110000−33−33−3−333000000i3−i3i3−i3−ii2i−2i00−ii2i−2i2-2000000−33−3300i3−i30000i3−i3−ii00−ii00-1100000000
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χ552-22-222-1-22-11-221-2-2-12-101-2-1-21-1211−33−2i2i2i−2i-1-1110000−33−33−3−333000000i3−i3−i3i3−ii−2i2i00i−i2i−2i-220000003−33−300i3−i30000−i3i3−ii00i−i001-100000000
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χ5744444-2-2-2-2-2-244-24-2-2-214-2-21-21-2-21-2-2-200441111-24-2-211-2-21111400000-2-200-2-2000000-2-20000000000000-211000000110000000000000000
χ5844444-2-2-2-2-2-244-24-2-2-214-2-21-21-2-21-2-2-200-4-41111-24-2-211-2-21111-4000002200220000002200000000000002-1-1000000-1-10000000000000000
χ5944444-2-2-2-2-2-244-24-2-2-21-4-2-21-21-2-21-222004411112-422-1-122-1-1-1-1-4000002200-2-2000000-2-200000000000002-1-1000000110000000000000000
χ6044444-2-2-2-2-2-244-24-2-2-21-4-2-21-21-2-21-22200-4-411112-422-1-122-1-1-1-1400000-2-20022000000220000000000000-211000000-1-10000000000000000
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χ624444-24-244-2-2-2-2-2-241-2-241-2-2-2-21-2-21-2-2-4-40011114-2-2-2-2-211111100-40000022002200220000000000000000000002-1-10000-1-1000000000000
χ634444-24-244-2-2-2-2-2-241-2-2-41-2-2-2-21-2-212244001111-422222-1-1-1-1-1-100-4000002200-2-200-2-20000000000000000000002-1-1000011000000000000
χ644444-24-244-2-2-2-2-2-241-2-2-41-2-2-2-21-2-2122-4-4001111-422222-1-1-1-1-1-100400000-2-200220022000000000000000000000-2110000-1-1000000000000
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χ804-44-44-2-22-2-22-442-42-2-2102212-1-2-2-12−232300−4i4i11-1-100003−3−232333−3−3000000−2i32i3002i−2i0000002i−2i00000000000000i3−i3000000−ii0000000000000000
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χ874-4-44444-4-4-44-4-4-444444044-4-4-4-4-44-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-2-4-42-2-4-4244-24-20-242-422-4-22000000-22-22000000000000000000000000000000000000000023−23−23230000000000000000000000000000
χ894-4-4444-2-4-42-2-4-4244-24-20-242-422-4-22000000-22-220000000000000000000000000000000000000000−232323−230000000000000000000000000000
χ904-4-444-2422-44-4-4-44-24-2-204-2222-42-2-4000000-22-220000000000000000−2i32i3000000000000000000000000000000−2i32i30000000000000000000000
χ914-4-444-2422-44-4-4-44-24-2-204-2222-42-2-4000000-22-2200000000000000002i3−2i30000000000000000000000000000002i3−2i30000000000000000000000
χ924-4-44-244-4-4-4422-4-24-2-240-2-2-42-42242000000-22-220000000000000000000000000023−23000000000000000000000000000023−2300000000000000
χ934-4-44-244-4-4-4422-4-24-2-240-2-2-42-42242000000-22-2200000000000000000000000000−23230000000000000000000000000000−232300000000000000
χ944-4-44-2-2422-4422-4-2-2-21-20-212-122-1-220000001-11-1003i−3i00003i−3i3i−3i0000−2i32i30000000023−2300000000000000000000i3−i3000000−3300000000000000
χ954-4-44-2-2422-4422-4-2-2-21-20-212-122-1-220000001-11-1003i−3i00003i−3i3i−3i00002i3−2i300000000−232300000000000000000000−i3i30000003−300000000000000
χ964-4-44-2-2422-4422-4-2-2-21-20-212-122-1-220000001-11-100−3i3i0000−3i3i−3i3i0000−2i32i300000000−232300000000000000000000i3−i30000003−300000000000000
χ974-4-44-2-2422-4422-4-2-2-21-20-212-122-1-220000001-11-100−3i3i0000−3i3i−3i3i00002i3−2i30000000023−2300000000000000000000−i3i3000000−3300000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-44448-8-4-84-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-48-844-44-44-82-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48-44-8-8-44844-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4444-44-4442220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-4444-44-4442220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-484-48-84-4-844-42-404-2-4-24-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44-4-444-44442220-2-22-2-222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-4-444-44442220-2-22-2-222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-4444-4-8-848-4-4-420-4-4-24-244240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-8-84-4444-482-4-402-4444-24-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-4444-4-4222022-2-2-2-2-22-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-4444-4-4222022-2-2-2-2-22-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).