Finite Group Databasebeta

← Group #13168685

Character table — Group #13168685

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212124444121212123666121212121212121212444412121212121212121212121212121212121212121212441212121212121212121212124444412121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-111-1-111111111111111111111-1-11-1-1-1-1-11111-11-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-111-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-111-1-1-1-1-1-11-1111
χ51111111111111111111111111111111111111-1-11111111111111111111-11111111-1-1-1-111-1-11111111111-1-111-111111-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-11-1-111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-11-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-11-1-1-1-1-11111-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11-1-1-11-1-111-1-1-1111-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-111-1-1-1111-1-111-1-1-1-111-11111-1-11-1-1-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-11-1-1-1-1-11111-1-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-111-1111-1-111-1-111-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111-1-1-111-1-111-111-1111-1-111-1-11-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-1-11111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1-111-11111-1-11-1-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111-1-1-11-1-111-1-1-111-11
χ17222222-122-122-12-122-1-122-12-1-1-1-1-12-1-122-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-10222-1-12200002200-1-1-1-1-1-1-1-1-1-1002-10-1-1-1-1-1000000022000000-10-100
χ18222222-122-122-12-122-1-122-12-1-1-1-1-12-1-122-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-102-2-2-1-1-2-200002200-1-1-1-1-1-1-1-1-1-100-210111110000000-2-200000010100
χ19222222-122-122-12-122-1-122-12-1-1-1-1-12-1-122-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-10-22211220000-2-2001111111111002-10-1-1-1-1-10000000-2-200000010100
χ20222222-122-122-12-122-1-122-12-1-1-1-1-12-1-122-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-10-2-2-211-2-20000-2-200111111111100-21011111000000022000000-10-100
χ21222222-122-122-12-122-1-1-22-12-1-1-1-1-1211-2-2111100222222-1-1-1-1-2-2-21111110-22-211-2-20000-2-200-1-1-1-1-1-11111002-10111-1-10000000-2200000010-100
χ22222222-122-122-12-122-1-1-22-12-1-1-1-1-1211-2-2111100222222-1-1-1-1-2-2-21111110-2-2211220000-2-200-1-1-1-1-1-1111100-210-1-1-11100000002-2000000-10100
χ23222222-122-122-12-122-1-1-22-12-1-1-1-1-1211-2-2111100-2-2-2-2-2-2-1-1-1-1-2-2-2111111022-2-1-1-2-200002200111111-1-1-1-1002-10111-1-100000002-2000000-10100
χ24222222-122-122-12-122-1-1-22-12-1-1-1-1-1211-2-2111100-2-2-2-2-2-2-1-1-1-1-2-2-211111102-22-1-12200002200111111-1-1-1-100-210-1-1-1110000000-2200000010-100
χ2522222-122-122-12-122-12-12-1-1-1222-1-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-1202200-1-1222200-1-1000000000000-12-12-1-1-1-1-1-1-1-120200-1-100000-1000
χ2622222-122-122-12-122-12-12-1-1-1222-1-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-120-2-20011222200-1-10000000000001-2-1-21111-1-1-1-1-20-20011000001000
χ2722222-122-122-12-122-12-12-1-1-1222-1-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-202200-1-1-2-2-2-20011000000000000-1212-1-1-1-11111-20-20011000001000
χ2822222-122-122-12-122-12-12-1-1-1222-1-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-20011-2-2-2-200110000000000001-21-21111111120200-1-100000-1000
χ2922222-122-122-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-202-2001122-2-200-1-1000000000000-121-211-1-1-1-11120-2001100000-1000
χ3022222-122-122-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-20-2200-1-122-2-200-1-10000000000001-212-1-111-1-111-20200-1-1000001000
χ3122222-122-122-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111202-20011-2-2220011000000000000-12-1-211-1-111-1-1-20200-1-1000001000
χ3222222-122-122-12-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-111111111120-2200-1-1-2-22200110000000000001-2-12-1-11111-1-120-2001100000-1000
χ332222-122-122-12222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-122002200-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200200000-1-1-1-10200000-1-1-1-100000
χ342222-122-122-12222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-122-2-21111-1-1-1-12-1-122-1-1-1-12-200-2-200-1-1-1-11122-2-211111111-2-200200000-1-1-1-10-200000111100000
χ352222-122-122-12222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-1-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-220022001111-1-1-2-222-1-1-1-1-1-1-1-1-2-200-20000011110-200000111100000
χ362222-122-122-12222-1-1-122-12-1-1-1-122-122-1-1-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-2-200-2-200111111-2-2-2-2111111112200-20000011110200000-1-1-1-100000
χ372222-122-122-12222-1-1-12-2-12-1-1-1-122-1-2-21111112222-1-1-1-1-1-1-1-1-211-2-21111-2-200-2-200-1-111112222-1-1-1-111112200-200000-1-1110-200000-1-11100000
χ382222-122-122-12222-1-1-12-2-12-1-1-1-122-1-2-211111122-2-21111-1-1-1-1-211-2-21111-22002200-1-111-1-122-2-21111-1-1-1-1-2-200-200000-1-111020000011-1-100000
χ392222-122-122-12222-1-1-12-2-12-1-1-1-122-1-2-2111111-2-222-1-1-1-1-1-1-1-1-211-2-211112-200-2-20011-1-111-2-222-1-1-1-11111-2-20020000011-1-1020000011-1-100000
χ402222-122-122-12222-1-1-12-2-12-1-1-1-122-1-2-2111111-2-2-2-21111-1-1-1-1-211-2-211112200220011-1-1-1-1-2-2-2-21111-1-1-1-1220020000011-1-10-200000-1-11100000
χ412-22-2222-2-2-2-222-2-222220-2-222-2-2-22-2000000002i−2i2i−2i2i2i−2i−2i2-2-22000000000000000002i−2i00002i−2i2i−2i2i2i−2i−2i00002-2000000002i−2i0000000002-20000000
χ422-22-2222-2-2-2-222-2-222220-2-222-2-2-22-2000000002i−2i−2i2i−2i−2i2i2i2-2-22000000000000000002i−2i00002i−2i−2i2i−2i−2i2i2i0000-22000000002i−2i000000000-220000000
χ432-22-2222-2-2-2-222-2-222220-2-222-2-2-22-200000000−2i2i2i−2i2i2i−2i−2i2-2-2200000000000000000−2i2i0000−2i2i2i−2i2i2i−2i−2i0000-2200000000−2i2i000000000-220000000
χ442-22-2222-2-2-2-222-2-222220-2-222-2-2-22-200000000−2i2i−2i2i−2i−2i2i2i2-2-2200000000000000000−2i2i0000−2i2i−2i2i−2i−2i2i2i00002-200000000−2i2i0000000002-20000000
χ452-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i32i−2i2i−2i−i−iii-111-10−i3i300−i3−i3i3i300000000−ii3−33−32i−2i2i−2i−i−iii33−3−32-200000000−ii3−30000000-11−i3i300000
χ462-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i32i−2i−2i2iii−i−i-111-10−i3i300−i3−i3i3i300000000−ii3−3−332i−2i−2i2iii−i−i−3−333-2200000000−ii3−300000001-1i3−i300000
χ472-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i3−2i2i2i−2i−i−iii-111-10−i3i300−i3−i3i3i300000000i−i−333−3−2i2i2i−2i−i−iii33−3−3-2200000000i−i−3300000001-1i3−i300000
χ482-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100−i3i3−i3−i3i3i3−2i2i−2i2iii−i−i-111-10−i3i300−i3−i3i3i300000000i−i−33−33−2i2i−2i2iii−i−i−3−3332-200000000i−i−330000000-11−i3i300000
χ492-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i32i−2i2i−2i−i−iii-111-10i3−i300i3i3−i3−i300000000−ii−33−332i−2i2i−2i−i−iii−3−3332-200000000−ii−330000000-11i3−i300000
χ502-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i32i−2i−2i2iii−i−i-111-10i3−i300i3i3−i3−i300000000−ii−333−32i−2i−2i2iii−i−i33−3−3-2200000000−ii−3300000001-1−i3i300000
χ512-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i3−2i2i2i−2i−i−iii-111-10i3−i300i3i3−i3−i300000000i−i3−3−33−2i2i2i−2i−i−iii−3−333-2200000000i−i3−300000001-1−i3i300000
χ522-22-2-1221-2-2122-2-2-1-1-1201-2-1-111-22100i3−i3i3i3−i3−i3−2i2i−2i2iii−i−i-111-10i3−i300i3i3−i3−i300000000i−i3−33−3−2i2i−2i2iii−i−i33−3−32-200000000i−i3−30000000-11i3−i300000
χ5344444-2-24-2-24-2-2-2-24-2-214-21-2-2-2-211-2-2-244-2-2-2-2000000001111-2-2-2111111004400-2-200000000000000000000-2-20-2111100000000000000000000
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χ5544444-2-24-2-24-2-2-2-24-2-21-4-21-2-2-2-211-222-4-42222000000001111222-1-1-1-1-1-1004-4002200000000000000000000-2-202-1-11100000000000000000000
χ5644444-2-24-2-24-2-2-2-24-2-21-4-21-2-2-2-211-222-4-42222000000001111222-1-1-1-1-1-100-4400-2-200000000000000000000220-211-1-100000000000000000000
χ574444-24-2-24-2-24-24-2-2-21-24-2-2-2111-2-2-2-2-2-2-211110044-2-2-2-211114-2-2-2-211110400-2-2000000-2-200-2-211111111000000000000000000000000000000
χ584444-24-2-24-2-24-24-2-2-21-24-2-2-2111-2-2-2-2-2-2-2111100-4-4222211114-2-2-2-211110-40022000000220022-1-1-1-1-1-1-1-1000000000000000000000000000000
χ594444-24-2-24-2-24-24-2-2-21-2-4-2-2-2111-2-2-22222-1-1-1-10044-2-2-2-21111-42222-1-1-1-10-400220000002200-2-21111-1-1-1-1000000000000000000000000000000
χ604444-24-2-24-2-24-24-2-2-21-2-4-2-2-2111-2-2-22222-1-1-1-100-4-422221111-42222-1-1-1-10400-2-2000000-2-20022-1-1-1-11111000000000000000000000000000000
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χ764-44-444-2-4-42-44-2-4244-2-20-424-2222-2-400000000004i−4i4i4i−4i−4i-222-20000000000000000000000000−2i2i−2i−2i2i2i0000000000000000000000000000000000
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χ814-44-4-24-22-4224-2-42-2-21-2022-21-1-12-2200−2i32i3i3i3−i3−i300−4i4i2i2i−2i−2i1-1-110−2i32i300i3i3−i3−i3000000000000−2323002i−2i−i−iii33−3−3000000000000000000000000000000
χ824-44-4-24-22-4224-2-42-2-21-2022-21-1-12-22002i3−2i3−i3−i3i3i3004i−4i−2i−2i2i2i1-1-1102i3−2i300−i3−i3i3i3000000000000−232300−2i2iii−i−i33−3−3000000000000000000000000000000
χ834-44-4-24-22-4224-2-42-2-21-2022-21-1-12-22002i3−2i3−i3−i3i3i300−4i4i2i2i−2i−2i1-1-1102i3−2i300−i3−i3i3i300000000000023−23002i−2i−i−iii−3−333000000000000000000000000000000
χ844-44-4-2-2422-42-242-4-21-2-20-121-2222-2-100−2i32i3−2i3−2i32i32i34i−4i0000001-1-110i3−i300i3i3−i3−i300000000−2i2i23−2300−2i2i00000000000000000000i−i−330000000000000000
χ854-44-4-2-2422-42-242-4-21-2-20-121-2222-2-100−2i32i3−2i3−2i32i32i3−4i4i0000001-1-110i3−i300i3i3−i3−i3000000002i−2i−2323002i−2i00000000000000000000−ii3−30000000000000000
χ864-44-4-2-2422-42-242-4-21-2-20-121-2222-2-1002i3−2i32i32i3−2i3−2i34i−4i0000001-1-110−i3i300−i3−i3i3i300000000−2i2i−232300−2i2i00000000000000000000i−i3−30000000000000000
χ874-44-4-2-2422-42-242-4-21-2-20-121-2222-2-1002i3−2i32i32i3−2i3−2i3−4i4i0000001-1-110−i3i300−i3−i3i3i3000000002i−2i23−23002i−2i00000000000000000000−ii−330000000000000000
χ884-4-4444444-4-4-4-4-44-444404-4-4-4-444-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2442-4-42-4-2-44-2-2042-422-2-22-423−230023−23−232300000000-22-2200023−2323−23−232300000000000000000000000000000000000000000000000000000000
χ904-4-4444-2442-4-42-4-2-44-2-2042-422-2-22-4−232300−232323−2300000000-22-22000−2323−232323−2300000000000000000000000000000000000000000000000000000000
χ914-4-444-244-2-4-42-424-4-24-20-222-4-44-2220000000000000000-22-22000000000000000−2i32i3000000000000000000000000−2i32i30000000000000000000000
χ924-4-444-244-2-4-42-424-4-24-20-222-4-44-2220000000000000000-22-220000000000000002i3−2i30000000000000000000000002i3−2i30000000000000000000000
χ934-4-444-2-24-22-4222-2-4-2-210-2-1222-21-1223−230023−23−2323000000001-11-1000−33−333−3000000−2i32i3000000000000000000000000i3−i33i−3i00000000000000000000
χ944-4-444-2-24-22-4222-2-4-2-210-2-1222-21-1223−230023−23−2323000000001-11-1000−33−333−30000002i3−2i3000000000000000000000000−i3i3−3i3i00000000000000000000
χ954-4-444-2-24-22-4222-2-4-2-210-2-1222-21-12−232300−232323−23000000001-11-10003−33−3−33000000−2i32i3000000000000000000000000i3−i3−3i3i00000000000000000000
χ964-4-444-2-24-22-4222-2-4-2-210-2-1222-21-12−232300−232323−23000000001-11-10003−33−3−330000002i3−2i3000000000000000000000000−i3i33i−3i00000000000000000000
χ974-4-44-244-24-42-4-4-442-2-240-2-4222-24-42000000000000−2i32i32i3−2i3-22-22000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ984-4-44-244-24-42-4-4-442-2-240-2-4222-24-420000000000002i3−2i3−2i32i3-22-220000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ994-4-44-24-2-2422-42-4-22-21-20-222-1-11-22223−2300−333−30000−2i32i32i3−2i31-11-100023−23−333−3000000000000000000i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000
χ1004-4-44-24-2-2422-42-4-22-21-20-222-1-11-22223−2300−333−300002i3−2i3−2i32i31-11-100023−23−333−3000000000000000000−i3i3i3−i33i−3i−3i3i000000000000000000000000000000
χ1014-4-44-24-2-2422-42-4-22-21-20-222-1-11-222−2323003−3−330000−2i32i32i3−2i31-11-1000−23233−3−33000000000000000000i3−i3−i3i33i−3i−3i3i000000000000000000000000000000
χ1024-4-44-24-2-2422-42-4-22-21-20-222-1-11-222−2323003−3−3300002i3−2i3−2i32i31-11-1000−23233−3−33000000000000000000−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-88-4-4-84-4844-44-8-4-4204244-44-2-2-4000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-48448-44-8-4-842-4-40-2-4-24-44442000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-4-444-4442220-22-2-22-2-2-2200006i−6i6i−6i00000000-1-11100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-4-444-4-444-4442220-22-2-22-2-2-220000−6i6i−6i6i00000000-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1098-88-88-4-4-844-8-4-4448-4-4204-2-4-444-22400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44444-4-444-42220-2-222-2-2-22-200−4i34i32i32i3−2i3−2i300000000-111-102i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44444-4-444-42220-2-222-2-2-22-2004i3−4i3−2i3−2i32i32i300000000-111-10−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-4-4-844-84842-4-4024-244-4-44-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-4-444444-4422202-2-2-2-222-2-243−4300−232323−2300000000-11-11000−23233−3−3300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-4-444444-4422202-2-2-2-222-2-2−43430023−23−232300000000-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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