Finite Group Databasebeta

← Group #13168615

Character table — Group #13168615

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121244441212121212121212121212121212121222444444121212121212121212121212121212121212121224661212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-11111-1-111-1-11111111-1-111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111-111-1-11111-1-1111-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1111-1-11111-1-11111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-111-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-111111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11-1-1-111111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111-1-11111-1-111111111-1-111-1-111-1-111-1-111-1-111-1-111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-11-11-1-1111111-1-1-1-111-1-1-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-11-111-1-1-1-1-1-1111111-1-1-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-111-1-111-1-11111111111-1-111-1-111-1-111-1-1-1-111-1-111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11-1111111-1-1-1-1-1-1111-1-1-111111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11111111-1-1-1-1-1-1-111111-1-1-11-11
χ17222222-12-1-122-12222-1-122-1-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-120222222-1-10000-1-12200220000000000-1-120-1-100-1-1-1-100-1-120-1-10000-1000
χ18222222-12-1-122-12222-1-122-1-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-120-2-2-2-222-1-10000112200-2-20000000000-11-20-1-10011-1-10011-201100001000
χ19222222-12-1-122-12222-1-122-1-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-202222-2-2110000-1-1-2-200-2-200000000001-1201100-1-11100-1-1-201100001000
χ20222222-12-1-122-12222-1-122-1-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-2-2-2-2-211000011-2-20022000000000011-2011001111001120-1-10000-1000
χ21222222-12-1-122-12222-1-1-22-1-12-1-12-1-1-2-22200-1-1-1-1-21-2-211111111-202-2-2-222-1-10000-1-1-2-2002200000000001120110011-1-100-1-1-20-1-100001000
χ22222222-12-1-122-12222-1-1-22-1-12-1-12-1-1-2-22200-1-1-1-1-21-2-211111111-20-222222-1-1000011-2-200-2-200000000001-1-201100-1-1-1-1001120110000-1000
χ23222222-12-1-122-12222-1-1-22-1-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-211111111202-2-2-2-2-2110000-1-12200-2-20000000000-1120-1-100111100-1-120110000-1000
χ24222222-12-1-122-12222-1-1-22-1-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-21111111120-2222-2-2110000112200220000000000-1-1-20-1-100-1-1110011-20-1-100001000
χ2522222-122222-12-1-12-12-12-12-1-12-1-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1220000-1-12222-1-100-1-1-1-100220022-1-1-1-12002-1-1-1-100-1-1-1-1000000-1-1000000
χ2622222-122222-12-1-12-12-12-12-1-12-1-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-12-20000-1-122-2-21100-1-11100-2-200-2-21111200-2-1-11100-1-11100000011000000
χ2722222-122222-12-1-12-12-12-12-1-12-1-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-22000011-2-222-1-10011-1-100-2-200-2-21111-200211-1-10011-1-100000011000000
χ2822222-122222-12-1-12-12-12-12-1-12-1-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-2-2000011-2-2-2-21100111100220022-1-1-1-1-200-21111001111000000-1-1000000
χ2922222-122222-12-1-12-12-1-2-12-1-12-1-12-1112222-1-1-1-1-2-211-2-2111111-2-20000-1-12222-1-1001111002200-2-21111-200-2111100-1-1-1-1000000-1-1000000
χ3022222-122222-12-1-12-12-1-2-12-1-12-1-12-11122-2-2-1-1-1-1-2-211-2-2111111-220000-1-122-2-2110011-1-100-2-20022-1-1-1-1-200211-1-100-1-11100000011000000
χ3122222-122222-12-1-12-12-1-2-12-1-12-1-12-111-2-222-1-1-1-1-2-211-2-21111112-2000011-2-222-1-100-1-11100-2-20022-1-1-1-1200-2-1-1110011-1-100000011000000
χ3222222-122222-12-1-12-12-1-2-12-1-12-1-12-111-2-2-2-2-1-1-1-1-2-211-2-211111122000011-2-2-2-21100-1-1-1-1002200-2-211112002-1-1-1-1001111000000-1-1000000
χ332222-122-122-12222-1-1-122-1-12-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-10222-1-10000-1-12222002200002200000002-1-100-1-1-1-100-1-1-1-1020000-1-10-100
χ342222-122-122-12222-1-1-122-1-12-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-102-2-2110000-1-122-2-200220000-2-20000000-21-100-1-11100-1-1110-20000110100
χ352222-122-122-12222-1-1-122-1-12-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10-222-1-1000011-2-22200-2-20000-2-200000002-110011-1-10011-1-10-20000110100
χ362222-122-122-12222-1-1-122-1-12-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10-2-2-211000011-2-2-2-200-2-20000220000000-211001111001111020000-1-10-100
χ372222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-20022-1-1-1-11-21111-2-211110-22-2110000-1-1222200-2-20000-2-20000000-2-1100111100-1-1-1-1020000110-100
χ382222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-20022-1-1-1-11-21111-2-211110-2-22-1-10000-1-122-2-200-2-200002200000002110011-1-100-1-1110-20000-1-10100
χ392222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-21111022-211000011-2-22200220000220000000-2-1-100-1-1110011-1-10-20000-1-10100
χ402222-122-122-12222-1-1-12-2-1-12-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-2111102-22-1-1000011-2-2-2-200220000-2-2000000021-100-1-1-1-1001111020000110-100
χ4122-2-2222-22-2-2-2-2-2222220-22-22-22-2-2-2002i−2i2i−2i22-2-20000000000000000002i−2i2i−2i2i−2i2i−2i000000002-20000000000000000002i−2i2i−2i0000002-2000000
χ4222-2-2222-22-2-2-2-2-2222220-22-22-22-2-2-2002i−2i−2i2i22-2-20000000000000000002i−2i2i−2i−2i2i−2i2i00000000-220000000000000000002i−2i−2i2i000000-22000000
χ4322-2-2222-22-2-2-2-2-2222220-22-22-22-2-2-200−2i2i2i−2i22-2-2000000000000000000−2i2i−2i2i2i−2i2i−2i00000000-22000000000000000000−2i2i2i−2i000000-22000000
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χ4922-2-22-12-22-2-21-21-12-12-10121-1-2-11-21−332i−2i2i−2i-1-11100−3300−33−3−333000000−ii2i−2i2i−2i−ii00i3−i3i3−i3002-20000−3−3330000i3−i3i3−i300−ii−ii000000-11000000
χ5022-2-22-12-22-2-21-21-12-12-10121-1-2-11-21−332i−2i−2i2i-1-11100−3300−33−3−333000000−ii2i−2i−2i2ii−i00i3−i3−i3i300-22000033−3−30000i3−i3−i3i300−iii−i0000001-1000000
χ5122-2-22-12-22-2-21-21-12-12-10121-1-2-11-21−33−2i2i2i−2i-1-11100−3300−33−3−333000000i−i−2i2i2i−2i−ii00−i3i3i3−i300-22000033−3−30000−i3i3i3−i300i−i−ii0000001-1000000
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χ874-4-444444-44-4-4-44-4-444404-44-44-4-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-242-2-4-424-4-44-2-2042-2-4-22-422000000-22-220000000000000000000000000023−2300000000000000000000000000000023−23000000000000
χ894-4-4444-242-2-4-424-4-44-2-2042-2-4-22-422000000-22-2200000000000000000000000000−2323000000000000000000000000000000−2323000000000000
χ904-4-444-244-44-42-4-22-4-24-20-2-4-22422-42000000-22-220000000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ914-4-444-244-44-42-4-22-4-24-20-2-4-22422-42000000-22-2200000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ924-4-44-244-2-442-4-44-42-2-240-2242-2-422-4000000-22-220000000000000000−2i32i30000000000000000000000000000000000−2i32i3000000000000000000
χ934-4-44-244-2-442-4-44-42-2-240-2242-2-422-4000000-22-2200000000000000002i3−2i300000000000000000000000000000000002i3−2i3000000000000000000
χ944-4-44-24-2-22-22-424-42-21-20-2-1-22122-120000001-11-100003i−3i003i−3i3i−3i0000−2i32i30000000023−23000000000000000000000000i3−i30000−33000000000000
χ954-4-44-24-2-22-22-424-42-21-20-2-1-22122-120000001-11-100003i−3i003i−3i3i−3i00002i3−2i300000000−2323000000000000000000000000−i3i300003−3000000000000
χ964-4-44-24-2-22-22-424-42-21-20-2-1-22122-120000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i300000000−2323000000000000000000000000i3−i300003−3000000000000
χ974-4-44-24-2-22-22-424-42-21-20-2-1-22122-120000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i30000000023−23000000000000000000000000−i3i30000−33000000000000
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
χ10088-8-8-48-44-444-84-88-4-42-40424-4-2-44-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-444444-4-42220-22-22-22-2-2-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-444444-4-42220-22-22-22-2-2-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-8448-4-444-8-4-42044-244-2-4-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-4444-48-4-8-84-42-404-244-24-42-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-484-8-8-4-484442-4-40-244-2442-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4444-4-4-44442220-2-2-2-2-2-2222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4444-4-4-44442220-2-2-2-2-2-2222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-484-4-844-44-8-4-420-4424-4-244-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-4-8844-8-4442-4-4024-4-2-44-2440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-44-4444-44422202-22-22-2-2-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-44-4444-44422202-22-22-2-2-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

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