Finite Group Databasebeta

← Group #13168382

Character table — Group #13168382

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212244466121212121212121212121212121244444444121212126661212121212121212121212121244121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-1111111-1-111111111-1-1-1-1111111-1-1-11-11-1-111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111-1111111-1-1-1-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-11111-1-1-1-11111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111-11-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1111-1-1-1-1-111-1-111-1-11-1-1-111111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-111111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-11111-1-1-1-1-1-1111111-1-1-111-111-1-11111-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-111-111111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1-111111-11-1
χ17222222-12-122-12-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1220222-1-10000-1-1222200002200000000-1-1-1-120-1-1-1-1-1-1000020-1-10000-1000
χ18222222-12-122-12-1222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1-220-2-2-2-1-100001122220000-2-200000000111-1-2011-1-1-1-10000-201100001000
χ19222222-12-122-12-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-12-20222110000-1-1-2-2-2-20000-2-200000000-1-1-1120-1-111110000-201100001000
χ20222222-12-122-12-1222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2-2-211000011-2-2-2-2000022000000001111-20111111000020-1-10000-1000
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χ22222222-12-122-12-1222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-2-202-2-2-1-10000-1-122-2-200002200000000111120-1-1-1-1110000-20-1-100001000
χ23222222-12-122-12-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-21111220-22211000011-2-22200002200000000-1-1-1-1-201111-1-10000-20-1-100001000
χ24222222-12-122-12-1222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-21111-2202-2-2110000-1-1-2-2220000-2-200000000111-120-1-111-1-1000020110000-1000
χ2522222-12-12222-122-1-12-12-1-12-12-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12022-1-1002222220000-1-10000220000002-1-10-1-1-1-10000-1-1-1-1020000-1-10-100
χ2622222-12-12222-122-1-12-12-1-12-12-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1-202-211002222-2-20000-1-10000-2-2000000-21101-1110000-1-1-1-10-20000110100
χ2722222-12-12222-122-1-12-12-1-12-12-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-120-22-1-100-2-2-2-2220000110000-2-20000002-1-10-11-1-1000011110-20000110100
χ2822222-12-12222-122-1-12-12-1-12-12-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-21100-2-2-2-2-2-2000011000022000000-2110111100001111020000-1-10-100
χ2922222-12-12222-122-1-12-1-2-1-12-12-1-12-1-2-20022-1-1-1-1-21-2-21111111120-2-2-1-10022-2-2-2-20000-1-10000220000002-1-1011110000-1-1110-20000-1-10100
χ3022222-12-12222-122-1-12-1-2-1-12-12-1-12-1-2-20022-1-1-1-1-21-2-211111111-20-22110022-2-2220000-1-10000-2-2000000-2110-11-1-10000-1-111020000110-100
χ3122222-12-12222-122-1-12-1-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111202-2-1-100-2-222-2-20000110000-2-20000002-1-101-111000011-1-1020000110-100
χ3222222-12-12222-122-1-12-1-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111-20221100-2-22222000011000022000000-2110-1-1-1-1000011-1-10-20000-1-10100
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χ352222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-10-22000-2-2-1-1-1-100111122-2-20000-2-21111000-202001111-1-1-1-1000011000000
χ362222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-10-2-2000-2-21111001111-2-222000022-1-1-1-1000-20-200111111110000-1-1000000
χ372222-12222-1-1222-12-1-12-2-1-1-12-122-1-1112222-1-1-1-1-2-211-2-21111110-2-200022-1-11100-1-11122220000-2-21111000-20-200-1-111-1-1110000-1-1000000
χ382222-12222-1-1222-12-1-12-2-1-1-12-122-1-11122-2-2-1-1-1-1-2-211-2-21111110-220002211-1-100-1-111-2-2-2-2000022-1-1-1-1000-20200-1-11111-1-1000011000000
χ392222-12222-1-1222-12-1-12-2-1-1-12-122-1-111-2-222-1-1-1-1-2-211-2-211111102-2000-2-2-1-1110011-1-122-2-2000022-1-1-1-100020-20011-1-1-1-111000011000000
χ402222-12222-1-1222-12-1-12-2-1-1-12-122-1-111-2-2-2-2-1-1-1-1-2-211-2-2111111022000-2-211-1-10011-1-1-2-2220000-2-211110002020011-1-111-1-10000-1-1000000
χ412-22-2222-2-22-22-2-2-222220-2-2-2-222-2-22002i−2i2-22-2-220000000000000000002i−2i2-200002i−2i002-22i−2i0000000000000000002i−2i002-20000002i−2i000000
χ422-22-2222-2-22-22-2-2-222220-2-2-2-222-2-22002i−2i-222-2-220000000000000000002i−2i-2200002i−2i00-22−2i2i0000000000000000002i−2i00-22000000−2i2i000000
χ432-22-2222-2-22-22-2-2-222220-2-2-2-222-2-2200−2i2i2-22-2-22000000000000000000−2i2i2-20000−2i2i002-2−2i2i000000000000000000−2i2i002-2000000−2i2i000000
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χ864-44-4-24-2-42-22-2-4224-21-2022-121-22-1-22i3−2i34i−4i001-1-1100−i3i3002i3−2i3−i3−i3i3i3000000−2i2i000000−2i2i−23230000000000000000000000i−i3−30000000000000000
χ874-44-4-24-2-42-22-2-4224-21-2022-121-22-1-22i3−2i3−4i4i001-1-1100−i3i3002i3−2i3−i3−i3i3i30000002i−2i0000002i−2i23−230000000000000000000000−ii−330000000000000000
χ884-44-4-2-242-4-2242-42-21-2-20-1-122-2-2221−2i32i3004-41-1-1100−2i32i300i3−i3i3i3−i3−i300000000-22−2i32i3000000-220000000000000000000000001-1i3−i3000000000000
χ894-44-4-2-242-4-2242-42-21-2-20-1-122-2-2221−2i32i300-441-1-1100−2i32i300i3−i3i3i3−i3−i3000000002-22i3−2i30000002-2000000000000000000000000-11−i3i3000000000000
χ904-44-4-2-242-4-2242-42-21-2-20-1-122-2-22212i3−2i3004-41-1-11002i3−2i300−i3i3−i3−i3i3i300000000-222i3−2i3000000-220000000000000000000000001-1−i3i3000000000000
χ914-44-4-2-242-4-2242-42-21-2-20-1-122-2-22212i3−2i300-441-1-11002i3−2i300−i3i3−i3−i3i3i3000000002-2−2i32i30000002-2000000000000000000000000-11i3−i3000000000000
χ924-4-4444-2-42-4424-2-4-44-2-204-4-2222-22-4000000-2-22200000000000000000000000000000000004i−4i00000000000000000000000000−2i2i00000000
χ934-4-4444-2-42-4424-2-4-44-2-204-4-2222-22-4000000-2-2220000000000000000000000000000000000−4i4i000000000000000000000000002i−2i00000000
χ944-4-444-242-4-44-4-24-42-24-20-2242-42-2-42000000-2-2220000000000000000000000000000000000004i−4i0000000000000000000000000000−2i2i0000
χ954-4-444-242-4-44-4-24-42-24-20-2242-42-2-42000000-2-222000000000000000000000000000000000000−4i4i00000000000000000000000000002i−2i0000
χ964-4-44-244-4-42-2-4442-4-2-240-22-2-42-4422000000-2-222000000000000000000000000000000000000004-4-22-220000000000000000000000000000
χ974-4-44-244-4-42-2-4442-4-2-240-22-2-42-4422000000-2-22200000000000000000000000000000000000000-442-22-20000000000000000000000000000
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
χ10088-8-8-48-48-4444-84-4-8-42-404-4-2-4-244240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-48-4844-84-8-442-4-40-224-4444-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-444444-442220-22-22-2-2-22-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4-444444-442220-22-22-2-2-22-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4448-8-444-8-4-4-420444-2-42-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444-44-4444-42220-2-2-2-222-2-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-44-4444-42220-2-2-2-222-2-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-444-884-4-4-84-4-420-44-4-24-224400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-844-448-44-8-42-40-4424-24-4-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-484-84-4-8-48442-4-402-2-4444-44-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-44-4-44422202-22-2-2-22-2-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-44-4-44422202-22-2-2-22-2-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000

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