Finite Group Databasebeta

← Group #13169357

Character table — Group #13169357

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121244441212121212121212121212121212121244444444121212121212121212121212121212121212121244121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1-1-1111111-1-111111111-1-1-1-11111111-11-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1111111111-1-1-1-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111111-1-1-1-11111-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111111-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-1111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111-1-11-1-1-111111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-111-1-111-1-111-1-1-1-1-1-1-11-1-11111-1-111-1-1-1111-1-111-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-111-111-1-111-1-1-1-11111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111111-1-11-1-111-1-11111-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1111-111-1-1-1-111-1-111-1111-1-111-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-1111-1-1-111111-11-1
χ17222222-12222-1-1-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12202220000-1-1-1-1222200002200000000-1-102-1-1-1-1-1-1-1-1000020-1-10000-1000
χ18222222-12222-1-1-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12-20-2-2-20000-1-11122220000-2-200000000-110-21111-1-1-1-10000-201100001000
χ19222222-12222-1-1-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-220222000011-1-1-2-2-2-20000-2-2000000001-102-1-1-1-111110000-201100001000
χ20222222-12222-1-1-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2-2-200001111-2-2-2-200002200000000110-211111111000020-1-10000-1000
χ21222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-220-2220000-1-11122-2-20000-2-2000000001-10-2-1-111-1-111000020110000-1000
χ22222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-2-202-2-20000-1-1-1-122-2-200002200000000110211-1-1-1-1110000-20-1-100001000
χ23222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-21111220-22200001111-2-22200002200000000-1-10-2-1-11111-1-10000-20-1-100001000
χ24222222-12222-1-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-211112-202-2-2000011-1-1-2-2220000-2-200000000-110211-1-111-1-1000020110000-1000
χ2522222-122-12-1222-12-12-12-1-12-1-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1202000-1-1-1-12200-1-1-1-12222000022-1-1-1-120200000-1-1-1-1-1-1-1-1000000-1-10000
χ2622222-122-12-1222-12-12-12-1-12-1-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-120-200011112200-1-1-1-1-2-2-2-20000-2-2111120-200000-1-1-1-11111000000110000
χ2722222-122-12-1222-12-12-12-1-12-1-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-202000-1-1-1-1-2-200111122-2-20000-2-21111-202000001111-1-1-1-1000000110000
χ2822222-122-12-1222-12-12-12-1-12-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-20001111-2-2001111-2-222000022-1-1-1-1-20-20000011111111000000-1-10000
χ2922222-122-12-1222-12-12-1-2-1-12-1-122-1-1112222-1-1-1-1-2-211-2-2111111-20-2000-1-1112200-1-11122-2-20000221111-20-200000-1-111-1-111000000-1-10000
χ3022222-122-12-1222-12-12-1-2-1-12-1-122-1-11122-2-2-1-1-1-1-2-211-2-2111111-20200011-1-12200-1-111-2-2220000-2-2-1-1-1-1-20200000-1-11111-1-1000000110000
χ3122222-122-12-1222-12-12-1-2-1-12-1-122-1-111-2-222-1-1-1-1-2-211-2-211111120-2000-1-111-2-20011-1-122220000-2-2-1-1-1-120-20000011-1-1-1-111000000110000
χ3222222-122-12-1222-12-12-1-2-1-12-1-122-1-111-2-2-2-2-1-1-1-1-2-211-2-211111120200011-1-1-2-20011-1-1-2-2-2-200002211112020000011-1-111-1-1000000-1-10000
χ332222-122-12-122222-1-1-122-1-1-122-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-10222-1-1222200220000-1-100002200000002-1-1-1-1-1-10000-1-1-1-10200-1-1000-100
χ342222-122-12-122222-1-1-122-1-1-122-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-10-22-211222200-2-20000-1-10000-2-20000000-2-1111110000-1-1-1-10-20011000100
χ352222-122-12-122222-1-1-122-1-1-122-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-102-22-1-1-2-2-2-200220000110000-2-2000000021-1-1-1-1-1000011110-20011000100
χ362222-122-12-122222-1-1-122-1-1-122-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-211-2-2-2-200-2-20000110000220000000-2111111000011110200-1-1000-100
χ372222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-20022-1-1-1-1-21-2-21111111102-2-2-1-122-2-200-2-20000-1-10000220000000211-1-1110000-1-1110-200-1-1000100
χ382222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-20022-1-1-1-1-21-2-2111111110-2-221122-2-200220000-1-10000-2-20000000-21-111-1-10000-1-111020011000-100
χ392222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111022-2-1-1-2-22200-2-20000110000-2-200000002-11-1-111000011-1-1020011000-100
χ402222-122-12-122222-1-1-12-2-1-1-122-1-12-1-2-200-2-2-1-1-1-1-21-2-2111111110-22211-2-22200220000110000220000000-2-1-111-1-1000011-1-10-200-1-1000100
χ4122-2-2222-2-2222-2-2-2-222202-222-2-2-2-2-200000022-2-2000000000000000000000000000000002-22-22-20022-2-20000000000000000002-22-2000000
χ4222-2-2222-2-2222-2-2-2-222202-222-2-2-2-2-200000022-2-2000000000000000000000000000000002-2-22-220022-2-2000000000000000000-22-22000000
χ4322-2-2222-2-2222-2-2-2-222202-222-2-2-2-2-200000022-2-200000000000000000000000000000000-222-2-2200-2-2220000000000000000002-2-22000000
χ4422-2-2222-2-2222-2-2-2-222202-222-2-2-2-2-200000022-2-200000000000000000000000000000000-22-222-200-2-222000000000000000000-222-2000000
χ452-2-22222-22-2-2-2-22-222220-2-2-2-22-22-22002i−2i2-22-2-220000000000000000002-2002i−2i002i−2i002-20000002i−2i0000000000002i−2i002-2000000002i−2i0000
χ462-2-22222-22-2-2-2-22-222220-2-2-2-22-22-22002i−2i-222-2-22000000000000000000-22002i−2i002i−2i00-22000000−2i2i0000000000002i−2i00-2200000000−2i2i0000
χ472-2-22222-22-2-2-2-22-222220-2-2-2-22-22-2200−2i2i2-22-2-220000000000000000002-200−2i2i00−2i2i002-2000000−2i2i000000000000−2i2i002-200000000−2i2i0000
χ482-2-22222-22-2-2-2-22-222220-2-2-2-22-22-2200−2i2i-222-2-22000000000000000000-2200−2i2i00−2i2i00-220000002i−2i000000000000−2i2i00-22000000002i−2i0000
χ492-2-222-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i32i−2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32i−2i00−ii3−32-20000002i−2i3−33−300000000−ii3−3-11−i3i3000000−ii0000
χ502-2-222-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i32i−2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i32i−2i00−ii3−3-22000000−2i2i−33−3300000000−ii3−31-1i3−i3000000i−i0000
χ512-2-222-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i3−2i2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i3−2i2i00i−i−332-2000000−2i2i−33−3300000000i−i−33-11−i3i3000000i−i0000
χ522-2-222-12-2-1-21-2-2212-12-1011-21-1-221-1−i3i3−2i2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3−2i2i00i−i−33-220000002i−2i3−33−300000000i−i−331-1i3−i3000000−ii0000
χ532-2-222-12-2-1-21-2-2212-12-1011-21-1-221-1i3−i32i−2i2-2-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32i−2i00−ii−332-20000002i−2i−33−3300000000−ii−33-11i3−i3000000−ii0000
χ542-2-222-12-2-1-21-2-2212-12-1011-21-1-221-1i3−i32i−2i-22-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i32i−2i00−ii−33-22000000−2i2i3−33−300000000−ii−331-1−i3i3000000i−i0000
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χ5744444-2-24-24-2-2-2-2-24-2-214-2-2-211-2-21-2-2-244001111-2411-2-2-2-211114000000000-2-200-2-2-2-200000000000000-2000000011110000000000000000
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χ894-4-444-2-2-4-2-4222-224-2-210222-112-2-1-2−2i32i3−4i4i001-1-1100i3−i300−2i32i3i3i3−i3−i300000000002i−2i002i−2i−23230000000000000000000000−ii3−30000000000000000
χ904-4-444-2-2-4-2-4222-224-2-210222-112-2-1-22i3−2i34i−4i001-1-1100−i3i3002i3−2i3−i3−i3i3i30000000000−2i2i00−2i2i−23230000000000000000000000i−i3−30000000000000000
χ914-4-444-2-2-4-2-4222-224-2-210222-112-2-1-22i3−2i3−4i4i001-1-1100−i3i3002i3−2i3−i3−i3i3i300000000002i−2i002i−2i23−230000000000000000000000−ii−330000000000000000
χ924-4-44-244242-4-4-44-4-2-2-240222-442-2-4-200004-4-222-20000000000000000004-40000000000-22000000000000000000000000-2200000000000000
χ934-4-44-244242-4-4-44-4-2-2-240222-442-2-4-20000-44-222-2000000000000000000-4400000000002-20000000000000000000000002-200000000000000
χ944-4-44-2-242-222-4-442-21-2-20-1-122-22-221−2i32i3004-41-1-1100−2i32i300i3−i3i3i3−i3−i3000000-22−2i32i300000000-220000000000000000000000001-1i3−i3000000000000
χ954-4-44-2-242-222-4-442-21-2-20-1-122-22-221−2i32i300-441-1-1100−2i32i300i3−i3i3i3−i3−i30000002-22i3−2i3000000002-2000000000000000000000000-11−i3i3000000000000
χ964-4-44-2-242-222-4-442-21-2-20-1-122-22-2212i3−2i3004-41-1-11002i3−2i300−i3i3−i3−i3i3i3000000-222i3−2i300000000-220000000000000000000000001-1−i3i3000000000000
χ974-4-44-2-242-222-4-442-21-2-20-1-122-22-2212i3−2i300-441-1-11002i3−2i300−i3i3−i3−i3i3i30000002-2−2i32i3000000002-2000000000000000000000000-11i3−i3000000000000
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
χ10088-8-88-4-4-848-4-4444-8-4-420-44-42-244-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-44-8-48-444-84-42-40-442-44-2-24400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4844-4-48-8-8442-4-402-2-4-44444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-444-4-4-4444422202-222-2-2-2-2-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-444-4-4-4444422202-222-2-2-2-2-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-484-844-44-4-8-4-4204-44-2-2-44240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-48-4444-88-8-442-4-40-22444-44-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-44444-44-442220-22-2-2-22-22-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-44444-44-442220-22-2-2-22-22-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4484-844-4-8-4-42-4044-24-4-224-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44-44444-44-42220-2-2-2-22-22-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44-44444-44-42220-2-2-2-22-22-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000

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