Finite Group Databasebeta

← Group #13168445

Character table — Group #13168445

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212124444121212123666121212121212121212244466666666121212121212121212121212121244121212121212121212121212224446666121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111111111111111-1-1111111111-1-1-11111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-111-1-111-1-1-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-11111111111111111111111-111111111-1-1-1-1-1-111111111-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-1-1-111111-1-1-1-1-1-11111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111111111-11-1-111-1-111-1-1-11-11-111-1-111-11-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-11111-1-1-1-111-1-11-11-1-1-1-1111-11-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-111111-1-1-1-11-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-1-111-1-111-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-11111-1-11-111-1-1-111-1-111-1-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-111-1-111-1-11111-1-111111-1-1-1-111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-1-1-1111-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111111111-1-111-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-111-11-11-111-1-111-11-1-11
χ17222222-122-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1200222-1-1-1-1-1-1-1-1-1-1220022-1-1-1-1222000-1-1-1-100002000000-1-1-1-100000
χ18222222-122-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-1-2002-2-2111111-1-1-1-12200-2-21111-2-22000-1-1-1-10000-2000000111100000
χ19222222-122-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1200-222-1-1-1-1-1-11111-2-20022-1-1-1-1-2-2-200011110000-2000000111100000
χ20222222-122-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-200-2-2-21111111111-2-200-2-2111122-2000111100002000000-1-1-1-100000
χ21222222-122-122-1-1222-1-1-22-1-1-12-1-1-1211-2-211112222-1-1-1-1-1-1-1-1-2-2-2111111-200-2-2-2111111-1-111220022-1-1-1-122-2000-1-1110000-200000011-1-100000
χ22222222-122-122-1-1222-1-1-22-1-1-12-1-1-1211-2-2111122-2-21111-1-1-1-1-2-2-2111111200-222-1-1-1-1-1-1-1-1112200-2-21111-2-2-2000-1-11100002000000-1-11100000
χ23222222-122-122-1-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-222-1-1-1-1-1-1-1-1-2-2-2111111-2002-2-211111111-1-1-2-20022-1-1-1-1-2-2200011-1-100002000000-1-11100000
χ24222222-122-122-1-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-2-2-21111-1-1-1-1-2-2-2111111200222-1-1-1-1-1-111-1-1-2-200-2-2111122200011-1-10000-200000011-1-100000
χ2522222-122-12-1222-12-1-122-1-122-1-1-12-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10222000000002222-1-1-1-100000000-122-1-1-1-1-1-1-1-1-102200-1-10000-10000
χ2622222-122-12-1222-12-1-122-1-122-1-1-12-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-22000000002222-1-11100000000-1-2-21-1-1-1-111110-2-20011000010000
χ2722222-122-12-1222-12-1-122-1-122-1-1-12-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1022-200000000-2-2-2-211-1-100000000122-11111-1-1-1-10-2-20011000010000
χ2822222-122-12-1222-12-1-122-1-122-1-1-12-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-200000000-2-2-2-21111000000001-2-211111111102200-1-10000-10000
χ2922222-122-12-1222-12-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-222000000-1-1-1-111111111102-2-20000000022-2-2-1-1-1-10000000012-21-1-111-1-11102-200-1-1000010000
χ3022222-122-12-1222-12-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-222000000-1-1-1-11111111110-22-20000000022-2-2-1-111000000001-22-1-1-11111-1-10-2200110000-10000
χ3122222-122-12-1222-12-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-111111111102-2200000000-2-22211-1-100000000-12-2111-1-1-1-1110-2200110000-10000
χ3222222-122-12-1222-12-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111110-22200000000-2-222111100000000-1-22-111-1-111-1-102-200-1-1000010000
χ332222-122-1222-1222-1-12-12-12-1-1-122-1-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-12220-1-122-1-1-1-100000022-1-1-1-1-1-1000-1-120000-1-1-1-1000220000000-1-100
χ342222-122-1222-1222-1-12-12-12-1-1-122-1-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-12-2-20-1-122-1-1-1-1000000-2-2-1-1-1-1-1-100011-200001111000-2-200000001100
χ352222-122-1222-1222-1-12-12-12-1-1-122-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-222011-2-2111100000022111111000-1-120000-1-1-1-1000-2-200000001100
χ362222-122-1222-1222-1-12-12-12-1-1-122-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-2-2011-2-21111000000-2-211111100011-200001111000220000000-1-100
χ372222-122-1222-1222-1-12-1-2-12-1-1-122-1-1-2-211111100222222-1-1-1-1-211-2-21111-22-2011-2-2111100000022-1-1-1-1-1-1000-11-20000-1-1110002-20000000-1100
χ382222-122-1222-1222-1-12-1-2-12-1-1-122-1-1-2-211111100222222-1-1-1-1-211-2-21111-2-22011-2-21111000000-2-2-1-1-1-1-1-10001-12000011-1-1000-2200000001-100
χ392222-122-1222-1222-1-12-1-2-12-1-1-122-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-2111122-20-1-122-1-1-1-100000022111111000-11-20000-1-111000-2200000001-100
χ402222-122-1222-1222-1-12-1-2-12-1-1-122-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-211112-220-1-122-1-1-1-1000000-2-21111110001-12000011-1-10002-20000000-1100
χ4122-2-2222-2-22-22-2-22-22220-2-22-2-22-2-22000000002-22i−2i2i2i−2i−2i22-2-20000000000000000000002-2002-2002i−2i2i2i−2i−2i2i−2i00002-20000000000000002i−2i00000
χ4222-2-2222-2-22-22-2-22-22220-2-22-2-22-2-22000000002-2−2i2i−2i−2i2i2i22-2-20000000000000000000002-2002-200−2i2i−2i−2i2i2i−2i2i00002-2000000000000000−2i2i00000
χ4322-2-2222-2-22-22-2-22-22220-2-22-2-22-2-2200000000-222i−2i2i2i−2i−2i22-2-2000000000000000000000-2200-22002i−2i2i2i−2i−2i−2i2i0000-22000000000000000−2i2i00000
χ4422-2-2222-2-22-22-2-22-22220-2-22-2-22-2-2200000000-22−2i2i−2i−2i2i2i22-2-2000000000000000000000-2200-2200−2i2i−2i−2i2i2i2i−2i0000-220000000000000002i−2i00000
χ4522-2-222-1-2-2-1-22112-22-1-10-21-11-2-11123−30033−3−32-22i−2i−i−iii-1-1110003−333−3−3000000−i3i3−i3−i3i3i3-113−32-2002i−2i−i−iii2i−2i0000-113−300000000000−i3i3−ii00000
χ4622-2-222-1-2-2-1-22112-22-1-10-21-11-2-11123−30033−3−32-2−2i2iii−i−i-1-1110003−333−3−3000000i3−i3i3i3−i3−i3-113−32-200−2i2iii−i−i−2i2i0000-113−300000000000i3−i3i−i00000
χ4722-2-222-1-2-2-1-22112-22-1-10-21-11-2-11123−30033−3−3-222i−2i−i−iii-1-1110003−333−3−3000000−i3i3−i3−i3i3i31-1−33-22002i−2i−i−iii−2i2i00001-1−3300000000000i3−i3i−i00000
χ4822-2-222-1-2-2-1-22112-22-1-10-21-11-2-11123−30033−3−3-22−2i2iii−i−i-1-1110003−333−3−3000000i3−i3i3i3−i3−i31-1−33-2200−2i2iii−i−i2i−2i00001-1−3300000000000−i3i3−ii00000
χ4922-2-222-1-2-2-1-22112-22-1-10-21-11-2-1112−3300−3−3332-22i−2i−i−iii-1-111000−33−3−333000000i3−i3i3i3−i3−i3-11−332-2002i−2i−i−iii2i−2i0000-11−3300000000000i3−i3−ii00000
χ5022-2-222-1-2-2-1-22112-22-1-10-21-11-2-1112−3300−3−3332-2−2i2iii−i−i-1-111000−33−3−333000000−i3i3−i3−i3i3i3-11−332-200−2i2iii−i−i−2i2i0000-11−3300000000000−i3i3i−i00000
χ5122-2-222-1-2-2-1-22112-22-1-10-21-11-2-1112−3300−3−333-222i−2i−i−iii-1-111000−33−3−333000000i3−i3i3i3−i3−i31-13−3-22002i−2i−i−iii−2i2i00001-13−300000000000−i3i3i−i00000
χ5222-2-222-1-2-2-1-22112-22-1-10-21-11-2-1112−3300−3−333-22−2i2iii−i−i-1-111000−33−3−333000000−i3i3−i3−i3i3i31-13−3-2200−2i2iii−i−i2i−2i00001-13−300000000000i3−i3−ii00000
χ5344444-2-24-2-2-24-2-2-24-21-24-21-2-2-211-2-2-2-244-2-2-2-2440000001111-2-2-2111111000400000000-2-2-2-2-2-20000000000-2000111100000000000000000000
χ5444444-2-24-2-2-24-2-2-24-21-24-21-2-2-211-2-2-2-244-2-2-2-2-4-40000001111-2-2-2111111000-40000000022222200000000002000-1-1-1-100000000000000000000
χ5544444-2-24-2-2-24-2-2-24-21-2-4-21-2-2-211-2-222-4-42222440000001111222-1-1-1-1-1-1000-400000000-2-222-2-20000000000200011-1-100000000000000000000
χ5644444-2-24-2-2-24-2-2-24-21-2-4-21-2-2-211-2-222-4-42222-4-40000001111222-1-1-1-1-1-100040000000022-2-2220000000000-2000-1-11100000000000000000000
χ574444-24-2-24-24-2-2-24-2-2-214-2-211-2-2-21-2-2-2-2-211110044-2-2-2-211114-2-2-2-211114000-2-2-2-2111100000000-2-21111000000000000000000000000000000
χ584444-24-2-24-24-2-2-24-2-2-214-2-211-2-2-21-2-2-2-2-2111100-4-4222211114-2-2-2-21111-40002222-1-1-1-10000000022-1-1-1-1000000000000000000000000000000
χ594444-24-2-24-24-2-2-24-2-2-21-4-2-211-2-2-21-22222-1-1-1-10044-2-2-2-21111-42222-1-1-1-1-40002222-1-1-1-100000000-2-21111000000000000000000000000000000
χ604444-24-2-24-24-2-2-24-2-2-21-4-2-211-2-2-21-22222-1-1-1-100-4-422221111-42222-1-1-1-14000-2-2-2-211110000000022-1-1-1-1000000000000000000000000000000
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χ6944-4-44-2-2-42-22422-2-4-21-202-1-2221-12-2−232300−23−2323234-400000011-1-10003−333−3−3000000000000-22−2323-22000000000000001-13−300000000000000000000
χ7044-4-44-2-2-42-22422-2-4-21-202-1-2221-12-2−232300−23−232323-4400000011-1-10003−333−3−30000000000002-223−232-200000000000000-11−3300000000000000000000
χ7144-4-4-2442-44-4-2-4-442-24-202-4-2224-42-200000000004i−4i4i4i−4i−4i-2-22200000000000000000000000000000−2i2i−2i−2i2i2i000000000000000000000000000000
χ7244-4-4-2442-44-4-2-4-442-24-202-4-2224-42-20000000000−4i4i−4i−4i4i4i-2-222000000000000000000000000000002i−2i2i2i−2i−2i000000000000000000000000000000
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χ7444-4-4-24-22-4-2-4-22242-2-210221-12-22-1-223−2300−3−33300−4i4i2i2i−2i−2i11-1-100023−23−3−3330000002i3−2i3−i3−i3i3i3000000002i−2i−i−iii000000000000000000000000000000
χ7544-4-4-24-22-4-2-4-22242-2-210221-12-22-1-2−23230033−3−3004i−4i−2i−2i2i2i11-1-1000−232333−3−30000002i3−2i3−i3−i3i3i300000000−2i2iii−i−i000000000000000000000000000000
χ7644-4-4-24-22-4-2-4-22242-2-210221-12-22-1-2−23230033−3−300−4i4i2i2i−2i−2i11-1-1000−232333−3−3000000−2i32i3i3i3−i3−i3000000002i−2i−i−iii000000000000000000000000000000
χ774-44-444444-4-4-4-44-4-4444044-44-4-4-4-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
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χ804-44-44-244-2-42-4-442-4-2-240-2-2-44222-420000000000000000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ814-44-44-244-2-42-4-442-4-2-240-2-2-44222-420000000000000000-22-220000000000000000000000000000000000000000000000000000002i3−2i3000000000
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χ854-44-4-24-2-242-422-2-42-2-210-2-2-11222-1200003i−3i3i−3i0000−2323−23231-11-1000003i−3i3i−3i00002i3−2i300−i3i3−i3i300000000003−33−3000000000000000000000000000000
χ864-44-4-24-2-242-422-2-42-2-210-2-2-11222-120000−3i3i−3i3i000023−2323−231-11-100000−3i3i−3i3i00002i3−2i300−i3i3−i3i30000000000−33−33000000000000000000000000000000
χ874-44-4-24-2-242-422-2-42-2-210-2-2-11222-120000−3i3i−3i3i0000−2323−23231-11-100000−3i3i−3i3i0000−2i32i300i3−i3i3−i300000000003−33−3000000000000000000000000000000
χ884-4-44444-4-4-44-44-4-444440-4-4-4-44-444-400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
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χ914-4-444-24-42-4-2-44-424-2-24022-4-4-22-2420000000000000000-222-200000000000000000000000000023−23000000000000000023−23000000000000000000
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χ954-4-44-24-22-4242-22-4-2-2-21022-1-1-22-21200−2i32i3i3−i3−i3i30000−2i32i32i3−2i31-1-110−2i32i300i3−i3−i3i3000000003-3-330000000000i3−i3−i3i3000000000000000000000000000000
χ964-4-44-24-22-4242-22-4-2-2-21022-1-1-22-21200−2i32i3i3−i3−i3i300002i3−2i3−2i32i31-1-110−2i32i300i3−i3−i3i300000000-333-30000000000−i3i3i3−i3000000000000000000000000000000
χ974-4-44-24-22-4242-22-4-2-2-21022-1-1-22-212002i3−2i3−i3i3i3−i30000−2i32i32i3−2i31-1-1102i3−2i300−i3i3i3−i300000000-333-30000000000i3−i3−i3i3000000000000000000000000000000
χ984-4-44-24-22-4242-22-4-2-2-21022-1-1-22-212002i3−2i3−i3i3i3−i300002i3−2i3−2i32i31-1-1102i3−2i300−i3i3i3−i3000000003-3-330000000000−i3i3i3−i3000000000000000000000000000000
χ994-4-44-2-2422-4-224-42-21-2-20-122212-2-2-100−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i300000000000000000023−230000000000000000−333i−3i0000000000000000
χ1004-4-44-2-2422-4-224-42-21-2-20-122212-2-2-100−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i3000000000000000000−232300000000000000003−3−3i3i0000000000000000
χ1014-4-44-2-2422-4-224-42-21-2-20-122212-2-2-1002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i300000000000000000023−230000000000000000−33−3i3i0000000000000000
χ1024-4-44-2-2422-4-224-42-21-2-20-122212-2-2-1002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i3000000000000000000−232300000000000000003−33i−3i0000000000000000
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χ10588-8-8-4-484484-4-8-8-442-4-40-24-44-2-4442000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
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χ10788-8-8-4-4-444-44-444-442220-2-22-2-22-2-22−4343002323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-48-444-84-44-8-42-40-424-44-2-24400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-48-4-4-844-88442-4-402-44-4-2444-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-4-44444-444222022-22-2-2-2-2-200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4-4-44444-444222022-22-2-2-2-2-20000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-844-4-8-4448-42-404-244-4-22-4400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-44-444-42220-2-2-2-22-222-200−4i34i32i3−2i3−2i32i300000000-111-102i3−2i300−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-44-444-42220-2-2-2-22-222-2004i3−4i3−2i32i32i3−2i300000000-111-10−2i32i300i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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