Finite Group Databasebeta

← Group #13168417

Character table — Group #13168417

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212224466666666121212121212121222444444666666666666121212121212121244121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111-1-11111111111-1-111-1-111-1-111111-11111-1-11-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-1111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1111111-1-1111-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111111-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-11111-11-1-11111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-1-111-1-11-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-11-1-1-1-111-11-1-1-1-111-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-111-1-11-111-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-11111-111111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1-1-1111111-1-11111111-11111-1-1-11-1-1-1-111-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1111111-1-11111-1-1111111-11-1-1-1-1111-11111-1-1-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111-111-1-1-1-1-111111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-111-1-11111-1-1111-111-1-1111-11-1
χ17222222-1-12222-1-1222-1-122-1-12-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-120022200-1-1-1-1-1-1-1-1220022002200-1-1-1-120-1-1-1-10020-1-1-1-10000-1-100000000
χ18222222-1-12222-1-1222-1-122-1-12-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-20022200-1-111-1-111-2-200-2-200-2-2001111-20-1-1110020-1-11100001100000000
χ19222222-1-12222-1-1222-1-122-1-12-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1200-2-2-20011-1-111-1-12200-2-200-2-20011112011-1-100-2011-1-100001100000000
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χ23222222-1-12222-1-1222-1-1-22-1-12-1-12-1-111-2-222-1-1-1-1-2-2-2-211111111-2002-2-2001111-1-1-1-122002200-2-200-1-1-1-1-2011110020-1-1-1-100001100000000
χ24222222-1-12222-1-1222-1-1-22-1-12-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-2111111112002-2-20011-1-1-1-111-2-200-2-200220011112011-1-10020-1-1110000-1-100000000
χ2522222-1222-12-1222-1-12-12-12-1-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-1222000-1-100220022-1-122000000220000-1200-1-1-1-10-100-1-1-1-1020000-1-10-100
χ2622222-1222-12-1222-1-12-12-12-1-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-12-2-20001100220022-1-1-2-2000000-2-20000-1-200-1-1110100-1-1110-20000110100
χ2722222-1222-12-1222-1-12-12-12-1-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-222000-1-100-2-200-2-21122000000-2-20000120011-1-10-10011-1-10-20000110100
χ2822222-1222-12-1222-1-12-12-12-1-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-20001100-2-200-2-211-2-20000002200001-200111101001111020000-1-10-100
χ2922222-1222-12-1222-1-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-1-2111-2-2111111-22-2000-1-100-2-20022-1-1-2-2000000220000120011-1-10100-1-1110-20000-1-10100
χ3022222-1222-12-1222-1-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-1-2111-2-2111111-2-220001100-2-20022-1-122000000-2-200001-20011110-100-1-1-1-1020000110-100
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χ342222-1222-12-1222-12-1-122-1-12-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-10-2-22-1-1-2-222002200001100-2-20000000001-1-10011-1-2-1-10011-200011001000
χ352222-1222-12-1222-12-1-122-1-12-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1022-21122-2-200-2-20000-1-100-2-2000000000-11100-1-1121100-1-1-200011001000
χ362222-1222-12-1222-12-1-122-1-12-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-10-2-2-211-2-2-2-200-2-2000011002200000000011100111-21100112000-1-100-1000
χ372222-1222-12-1222-12-1-12-2-1-12-1-12-1-12-2-22200-1-1-1-11-21111-2-2111102-2-2-1-1222200-2-200001100-2-2000000000-1-1-100-1-11-211001120001100-1000
χ382222-1222-12-1222-12-1-12-2-1-12-1-12-1-12-2-22200-1-1-1-11-21111-2-211110-22-2-1-1-2-22200-2-20000-1-100220000000001-1-10011121100-1-1-2000-1-1001000
χ392222-1222-12-1222-12-1-12-2-1-12-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-2111102-221122-2-200220000110022000000000-11100-1-1-1-2-1-10011-2000-1-1001000
χ402222-1222-12-1222-12-1-12-2-1-12-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-211110-22211-2-2-2-200220000-1-100-2-20000000001110011-12-1-100-1-120001100-1000
χ4122-2-22222-2-2-22-2-22-22220-222-2-2-22-2-2002-22i−2i22-2-200000000000000002-2002-200002i−2i2i−2i0000002i−2i000000002-2000000002i−2i00002i−2i00000000
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χ884-4-4444-22-4-44-4-22-444-2-20422-422-4-2-2000000-22-220000000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ894-4-4444-22-4-44-4-22-444-2-20422-422-4-2-2000000-22-2200000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ904-4-444-24-4-42424-4-4-2-24-20-2-422-4224-2000000-22-22000000000000000000−2i32i3000000000000000000000000000000−2i32i300000000000000000000
χ914-4-444-24-4-42424-4-4-2-24-20-2-422-4224-2000000-22-220000000000000000002i3−2i30000000000000000000000000000002i3−2i300000000000000000000
χ924-4-44-244-42-4-2-44-424-2-240-22-422-42-24000000-22-2200000000000000000000000000000023−230000000000000000000000000023−23000000000000
χ934-4-44-244-42-4-2-44-424-2-240-22-422-42-24000000-22-22000000000000000000000000000000−232300000000000000000000000000−2323000000000000
χ944-4-44-2-24-422-224-42-21-2-20122-122-1-2-20000001-11-1003i−3i00003i−3i3i−3i000000−2i32i3000000000023−23000000000000000000i3−i3000000−33000000000000
χ954-4-44-2-24-422-224-42-21-2-20122-122-1-2-20000001-11-1003i−3i00003i−3i3i−3i0000002i3−2i30000000000−2323000000000000000000−i3i30000003−3000000000000
χ964-4-44-2-24-422-224-42-21-2-20122-122-1-2-20000001-11-100−3i3i0000−3i3i−3i3i000000−2i32i30000000000−2323000000000000000000i3−i30000003−3000000000000
χ974-4-44-2-24-422-224-42-21-2-20122-122-1-2-20000001-11-100−3i3i0000−3i3i−3i3i0000002i3−2i3000000000023−23000000000000000000−i3i3000000−33000000000000
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
χ10088-8-8-4-488444-4-8-8-442-4-40-2-4-4-24424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4444-444-442220-222-2-2-22-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4444-444-442220-222-2-2-22-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-448-4-844-4-84-4-42044-2-4-4244-20000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-44-484-84-44-8-42-404-24-42-44-240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-48-8-4-444-88442-4-40-2442-4-4-2440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44-4-4444-4442220-2-2-2222-2-2-2000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-4-4444-4442220-2-2-2222-2-2-2000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-44-8484-44-8-4-4-420-44-244-24-420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-444-8-4-8-4448-42-40-4-244-2442-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-44-444-422202-2-2-2-2-2-222000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-44-444-422202-2-2-2-2-2-222000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

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