Finite Group Databasebeta

← Group #72255318

Character table — Group #72255318

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444448888888888888888888888881616161616161616161616161616161616161616161616161616161616162424242424242424484848484848484848484848
order122222344446666666222222444444121212124444666666121212121212121212121212121222224444446666666612121212121212121212121288888888444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-11-11-11-11-111-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-11-11-11-11-111-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-111-1-11-11-1-111-1-11111-1-1-1-111-1-111iiii−i−i−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-111-1-11-11-1-111-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-11-111-1-1111-1-1-1-111-1-11111-1-1-1-111iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-11-111-1-1111-1-1-1-111-1-11111-1-1-1-111−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-111-1-11-111-1-1-11111-1-1-1-111-1-11111-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-111-1-11-111-1-1-11111-1-1-1-111-1-11111-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ172222222222222222222-2-22-2-222-2-2-2-22222000022-2-2-2-20000000022-2-2-2-200220000-2-20000222200000000-2-2-2-200000000000000000000
χ182222222222222222222-2-22-2-222-2-2-2-22222000022-2-2-2-20000000022-2-2-2-200-2-20000220000-2-2-2-200000000222200000000000000000000
χ19222222222222222222-22-2-22-2-2-222-2-222220000-2-222-2-200000000-2-222-2-2220000-2-200222200000000-2-2-2-2000000000000000000000000
χ20222222222222222222-22-2-22-2-2-222-2-222220000-2-222-2-200000000-2-222-2-2-2-200002200-2-2-2-2000000002222000000000000000000000000
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χ22222222222222222222-2-22-2-22-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22200002200000000000022220000000000000000000000000000
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χ252222222-2-2-2-222222222-222-22-2-222-2-2-2-2-2-2000022-2-22200000000-2-222-2-22-20000-220022-2-200000000-2-222000000000000000000000000
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χ31222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-122-2-2-2-222-2-2-1-1-1-111111111-1-1-1-1111100000000000000000000
χ32222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-1-2-222-2-2-2-2221111-1-1-1-111111111-1-1-1-100000000000000000000
χ33222222-12222-1-1-1-1-1-1-12-2-22-2-222-2-2-2-2-1-1-1-10000-1-11111−i3−i3i3i3−i3−i3i3i3-1-1111100220000-2-2−i3i3−i3i3-1-1-1-1−i3i3−i3i3−i3i3−i3i3111100000000000000000000
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χ36222222-12222-1-1-1-1-1-1-12-2-22-2-222-2-2-2-2-1-1-1-10000-1-11111i3i3−i3−i3i3i3−i3−i3-1-1111100-2-2000022−i3i3−i3i31111i3−i3i3−i3−i3i3−i3i3-1-1-1-100000000000000000000
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χ42222222-12222-1-1-1-1-1-1-1-2-22-2-22-2-2-2-222-1-1-1-122221111-1-1-1-1-1-1-1-1-1-11111-1-10000-2-20000i3−i3i3−i3i3−i3i3−i31111−i3i3−i3i3−i3i3−i3i300000000000000000000
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χ52222222-1-2-2-2-2-1-1-1-1-1-1-12-222-22-2-222-2-211110000-1-111-1-1i3i3−i3−i3−i3−i3i3i311-1-111-2200002-20011-1-1−i3i3i3−i3−i3i3i3−i3-1-111−i3i3i3−i300000000000000000000
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χ874-4-44-44-244-4-42222-2-2-2-4444-4-4-444-4-44-2-22200002-2-222-2000000002-2-222-200000000000000000000000000000000000000000000000000
χ884-4-44-44-244-4-42222-2-2-2-4-4-4444-44-444-4-2-22200002-22-2-22000000002-22-2-2200000000000000000000000000000000000000000000000000
χ894-4-44-44-2-4-4442222-2-2-2444-4-4-4-44-444-422-2-20000-22-222-2000000002-22-2-2200000000000000000000000000000000000000000000000000
χ904-4-44-44-2-4-4442222-2-2-24-4-4-444-444-4-4422-2-20000-222-2-22000000002-2-222-200000000000000000000000000000000000000000000000000
χ914-4-44-44-2-4-4442222-2-2-2-44-44-444-4-44-4422-2-200002-2-22-2200000000-222-22-200000000000000000000000000000000000000000000000000
χ924-4-44-44-2-4-4442222-2-2-2-4-4444-44-44-44-422-2-200002-22-22-200000000-22-22-2200000000000000000000000000000000000000000000000000
χ938888-8-8-48-88-8-4-444-444000000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-8-4-88-88-4-444-4440000000000004-44-400000000000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-800800008-800-8000000000000000000004-400000000004-44-400000000000000000000000000000000000000000000000000000000
χ9688-8-800800008-800-800000000000000000000-440000000000-44-4400000000000000000000000000000000000000000000000000000000
χ9788-8-800-40000-44−4i34i34−4i34i30000000000000000004-40000000000−2−2i32+2i3−2+2i32−2i300000000000000000000000000000000000000000000000000000000
χ9888-8-800-40000-44−4i34i34−4i34i3000000000000000000-4400000000002+2i3−2−2i32−2i3−2+2i300000000000000000000000000000000000000000000000000000000
χ9988-8-800-40000-444i3−4i344i3−4i30000000000000000004-40000000000−2+2i32−2i3−2−2i32+2i300000000000000000000000000000000000000000000000000000000
χ10088-8-800-40000-444i3−4i344i3−4i3000000000000000000-4400000000002−2i3−2+2i32+2i3−2−2i300000000000000000000000000000000000000000000000000000000
χ1018-88-80080000-8800-80000000000000000004-4000000004-44-4000000000000000000000000000000000000000000000000000000000000
χ1028-88-80080000-8800-8000000000000000000-4400000000-44-44000000000000000000000000000000000000000000000000000000000000
χ1038-88-800-400004-4−4i34i344i3−4i300000000000000004-400000000−2+2i32−2i3−2−2i32+2i3000000000000000000000000000000000000000000000000000000000000
χ1048-88-800-400004-4−4i34i344i3−4i30000000000000000-44000000002−2i3−2+2i32+2i3−2−2i3000000000000000000000000000000000000000000000000000000000000
χ1058-88-800-400004-44i3−4i34−4i34i300000000000000004-400000000−2−2i32+2i3−2+2i32−2i3000000000000000000000000000000000000000000000000000000000000
χ1068-88-800-400004-44i3−4i34−4i34i30000000000000000-44000000002+2i3−2−2i32−2i3−2+2i3000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-8-48-8-8844-4-4-444000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-8-4-888-844-4-4-4440000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000000000000

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