Finite Group Databasebeta

← Group #13172903

Character table — Group #13172903

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order12223336666666662333666666666664444443666666666666666244121212121212121212121212121212122222666666661212121212121212121212122444666612122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111111111111111111-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11111111-1-1-1-1-11-11-1-1-1-111-1-1-11-1
χ3111111111111111111111111111111111-1-1111111111111111111-111111111-1-1111111-1-111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-11-111-1-1-1-1111-11
χ51111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-11111111-11-111-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-11-11-1-1-1-11111-111
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1111111-1-1-1-11
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-11-11111-1-111-1-1-1-11111-1-1111111-1-1-1-11-111-1-111-1-111-111-1-1-1-1-111111-1-1
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-111-1-11111-1
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-1-1-111111111111-111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-111
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1-1-1-111111111-1-111-1-1111111-1-1-1-1-11-1-1111111-1-11-1-1111-1-1-1-111-11-1
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-1-1-1111
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-1-1-111-1-11111-1-1-1-1-1-11111111111-11-1-111-1-111-1-1-111-1-1-1-1-111-1-11-11
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111111111-1-1-1
χ17222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-12220022-122-1-1-1-122-1-1-1-1-1-1-102222-1-1-1-10022-1-1-1-1002222-1-1-1-1000022-1-1-1-100-1-1-1-1000000-1-10000000
χ18222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-122200-2-2-122-1-1-1-122-1-1-1-1-1-1-10-2222-1-1-1-100-2-2111100-2-2-2-211110000-22-1-1-1-1001111000000110000000
χ19222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-12-2-20022-122-1-1-1-122-1-1-1-1-1-1-102-2-2-211110022-1-1-1-100-2-2-2-2111100002-2111100-1-1-1-1000000110000000
χ20222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-12-2-200-2-2-122-1-1-1-122-1-1-1-1-1-1-10-2-2-2-2111100-2-21111002222-1-1-1-10000-2-21111001111000000-1-10000000
χ21222222-12-122-1-1222-2-1-1211-1-122-1-1-1-12220022-1-2-21111-2-2-1-1-111110-2-222-1-1110022-1-1110022-2-211110000-2-2-1-11100-1-111000000-1-10000000
χ22222222-12-122-1-1222-2-1-1211-1-122-1-1-1-122200-2-2-1-2-21111-2-2-1-1-1111102-222-1-11100-2-211-1-100-2-222-1-1-1-100002-2-1-1110011-1-1000000110000000
χ23222222-12-122-1-1222-2-1-1211-1-122-1-1-1-12-2-20022-1-2-21111-2-2-1-1-111110-22-2-211-1-10022-1-11100-2-222-1-1-1-10000-2211-1-100-1-111000000110000000
χ24222222-12-122-1-1222-2-1-1211-1-122-1-1-1-12-2-200-2-2-1-2-21111-2-2-1-1-11111022-2-211-1-100-2-211-1-10022-2-2111100002211-1-10011-1-1000000-1-10000000
χ2522222-12-122-1222-1222-1-1222-1-1-122-1-1-1002222-12-122-1-1-1-1-1-1-1-1-1-1-1220000000-1-1-1-1222222000000002-1-1-1-100000-1-1-1-1-1-12020-1-1000000-100
χ2622222-12-122-1222-1222-1-1222-1-1-122-1-1-10022-2-2-12-122-1-1-1-1-1-1-1-1-1-1-12-20000000-1-111-2-2-2-222000000002-1-1-1100000-1-11111-20-2011000000100
χ2722222-12-122-1222-1222-1-1222-1-1-122-1-1-100-2-222-12-122-1-1-1-1-1-1-1-1-1-1-1-22000000011-1-12222-2-200000000-2111-10000011-1-1-1-1-20-2011000000100
χ2822222-12-122-1222-1222-1-1222-1-1-122-1-1-100-2-2-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-2-200000001111-2-2-2-2-2-200000000-21111000001111112020-1-1000000-100
χ2922222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-1002222-1-21-2-21111-1-1-11111-2-20000000-1-1-1-122-2-22200000000-2111100000-1-1-1-11120-20-1-1000000100
χ3022222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-10022-2-2-1-21-2-21111-1-1-11111-220000000-1-111-2-2222200000000-2111-100000-1-111-1-1-202011000000-100
χ3122222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-100-2-222-1-21-2-21111-1-1-111112-2000000011-1-122-2-2-2-2000000002-1-1-110000011-1-111-202011000000-100
χ3222222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-100-2-2-2-2-1-21-2-21111-1-1-111112200000001111-2-222-2-2000000002-1-1-1-1000001111-1-120-20-1-1000000100
χ332222-12222-1222-12-12-12-122-12-1-1-1-122-1222200-1-12-1-122-1-1-1-1-1-1-1-1-1202-1-1222222000000-1-100000000-12-1-10-1-1-1-1-1-1-1000002020000-1-1000-10
χ342222-12222-1222-12-12-12-122-12-1-1-1-122-122-2-200-1-12-1-122-1-1-1-1-1-1-1-1-1-202-1-12222-2-200000011000000001-2110-1-1-1-1-11100000-20-200001100010
χ352222-12222-1222-12-12-12-122-12-1-1-1-122-1-2-22200-1-12-1-122-1-1-1-1-1-1-1-1-120-211-2-2-2-222000000-1-100000000-12-1-1011111-1-100000-20-200001100010
χ362222-12222-1222-12-12-12-122-12-1-1-1-122-1-2-2-2-200-1-12-1-122-1-1-1-1-1-1-1-1-1-20-211-2-2-2-2-2-200000011000000001-21101111111000002020000-1-1000-10
χ372222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-1222200-11-211-2-211-1-1-11111-20-2-1-122-2-222000000-1-1000000001-21101-1-111-1-10000020-20000-1-100010
χ382222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-122-2-200-11-211-2-211-1-1-1111120-2-1-122-2-2-2-20000001100000000-12-1-101-1-1111100000-202000011000-10
χ392222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-1-2-22200-11-211-2-211-1-1-11111-20211-2-22222000000-1-1000000001-2110-111-1-1-1-100000-202000011000-10
χ402222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-1-2-2-2-200-11-211-2-211-1-1-1111120211-2-222-2-20000001100000000-12-1-10-111-1-1110000020-20000-1-100010
χ4122-2-222222-2-2-2-22-2-2022200222-2-2-2-2-2-22i−2i002i−2i2000000002-2-200000002i−2i2i−2i00002i−2i2i−2i00002-20000000000002i−2i00002i−2i000000002-20000000
χ4222-2-222222-2-2-2-22-2-2022200222-2-2-2-2-2-22i−2i00−2i2i2000000002-2-200000002i−2i2i−2i0000−2i2i−2i2i0000-220000000000002i−2i0000−2i2i00000000-220000000
χ4322-2-222222-2-2-2-22-2-2022200222-2-2-2-2-2-2−2i2i002i−2i2000000002-2-20000000−2i2i−2i2i00002i−2i2i−2i0000-22000000000000−2i2i00002i−2i00000000-220000000
χ4422-2-222222-2-2-2-22-2-2022200222-2-2-2-2-2-2−2i2i00−2i2i2000000002-2-20000000−2i2i−2i2i0000−2i2i−2i2i00002-2000000000000−2i2i0000−2i2i000000002-20000000
χ4522-2-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-22i−2i002i−2i-100−i3i3−i3i300-111−i3−i3i3i30002i−2i−ii3−3002i−2i−ii3−3002-200−i3−i3i3i3000000−ii3−300−ii3−3000000-110000000
χ4622-2-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-22i−2i00−2i2i-100−i3i3−i3i300-111−i3−i3i3i30002i−2i−ii3−300−2i2ii−i−3300-2200i3i3−i3−i3000000−ii3−300i−i−330000001-10000000
χ4722-2-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-2−2i2i002i−2i-100−i3i3−i3i300-111−i3−i3i3i3000−2i2ii−i−33002i−2i−ii3−300-2200i3i3−i3−i3000000i−i−3300−ii3−30000001-10000000
χ4822-2-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-2−2i2i00−2i2i-100−i3i3−i3i300-111−i3−i3i3i3000−2i2ii−i−3300−2i2ii−i−33002-200−i3−i3i3i3000000i−i−3300i−i−33000000-110000000
χ4922-2-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-22i−2i002i−2i-100i3−i3i3−i300-111i3i3−i3−i30002i−2i−ii−33002i−2i−ii−33002-200i3i3−i3−i3000000−ii−3300−ii−33000000-110000000
χ5022-2-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-22i−2i00−2i2i-100i3−i3i3−i300-111i3i3−i3−i30002i−2i−ii−3300−2i2ii−i3−300-2200−i3−i3i3i3000000−ii−3300i−i3−30000001-10000000
χ5122-2-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-2−2i2i002i−2i-100i3−i3i3−i300-111i3i3−i3−i3000−2i2ii−i3−3002i−2i−ii−3300-2200−i3−i3i3i3000000i−i3−300−ii−330000001-10000000
χ5222-2-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-2−2i2i00−2i2i-100i3−i3i3−i300-111i3i3−i3−i3000−2i2ii−i3−300−2i2ii−i3−3002-200i3i3−i3−i3000000i−i3−300i−i3−3000000-110000000
χ532-2-22222-2-2-222-2-2-22022200-2-2-2-22-22-22002-200200000000-22-200000000000002-20000002-2002-22-22-200000000002-2000000000000002-2000
χ542-2-22222-2-2-222-2-2-22022200-2-2-2-22-22-22002-200200000000-22-200000000000002-20000002-200-22-22-2200000000002-200000000000000-22000
χ552-2-22222-2-2-222-2-2-22022200-2-2-2-22-22-2200-2200200000000-22-20000000000000-22000000-22002-22-22-20000000000-2200000000000000-22000
χ562-2-22222-2-2-222-2-2-22022200-2-2-2-22-22-2200-2200200000000-22-20000000000000-22000000-2200-22-22-220000000000-22000000000000002-2000
χ5744444-2-2-2-24-2-2-24-244-21-2-2-2-21-2-2-2-211-200004414-2-2-211-2-2111111104000000000-2-2-2-2-2-200000000000000-200000001111000000000000000
χ5844444-2-2-2-24-2-2-24-244-21-2-2-2-21-2-2-2-211-20000-4-414-2-2-211-2-211111110-40000000002222220000000000000020000000-1-1-1-1000000000000000
χ5944444-2-2-2-24-2-2-24-24-4-21-222-21-2-2-2-211-20000441-4222-1-122111-1-1-1-10-4000000000-2-2-2-222000000000000002000000011-1-1000000000000000
χ6044444-2-2-2-24-2-2-24-24-4-21-222-21-2-2-2-211-20000-4-41-4222-1-122111-1-1-1-1040000000002222-2-200000000000000-20000000-1-111000000000000000
χ614444-24-24-2-24-2-2-24-241-2-2-2-21-2-2-211-2-2-24400001-2411-2-2-2-21111111004-2-2-2-2-2-200000000000000000000000-21111000000000000000000000
χ624444-24-24-2-24-2-2-24-241-2-2-2-21-2-2-211-2-2-2-4-400001-2411-2-2-2-2111111100-4222222000000000000000000000002-1-1-1-1000000000000000000000
χ634444-24-24-2-24-2-2-24-2-41-2-2221-2-2-211-2-2-244000012-4-1-12222111-1-1-1-100-4-2-2-2-22200000000000000000000000211-1-1000000000000000000000
χ644444-24-24-2-24-2-2-24-2-41-2-2221-2-2-211-2-2-2-4-4000012-4-1-12222111-1-1-1-10042222-2-200000000000000000000000-2-1-111000000000000000000000
χ654444-2-24-24-2-244-2-2-24-2-2144-2-211-2-2-2-210044001-2-2-2-2-2-2111111111400000000-2-2000000-2-200000000-2-211000000110000000000000000000
χ664444-2-24-24-2-244-2-2-24-2-2144-2-211-2-2-2-2100-4-4001-2-2-2-2-2-2111111111-40000000022000000220000000022-1-1000000-1-10000000000000000000
χ674444-2-24-24-2-244-2-2-2-4-2-21-4-4-2-211-2-2-2-210044001222222-1-1111-1-1-1-1-400000000-2-2000000-2-20000000022-1-1000000110000000000000000000
χ684444-2-24-24-2-244-2-2-2-4-2-21-4-4-2-211-2-2-2-2100-4-4001222222-1-1111-1-1-1-1400000000220000002200000000-2-211000000-1-10000000000000000000
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χ7344-4-44-2-2-2-2-422242-40-21-22i3−2i3-21-2222-1-1200004i−4i1002i3−2i3−i3i3001-1-1−i3−i3i3i300000000000−2i2i−2i2i−23230000000000000000000000i−i3−3000000000000000
χ7444-4-44-2-2-2-2-422242-40-21-22i3−2i3-21-2222-1-120000−4i4i1002i3−2i3−i3i3001-1-1−i3−i3i3i3000000000002i−2i2i−2i23−230000000000000000000000−ii−33000000000000000
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χ7744-4-4-24-24-22-422-2-4201-2-2−2i32i31-2-22-1-12224i−4i0000100i3−i3−2i32i3001-1-1i3i3−i3−i3000−2i2i−2i2i23−23000000000000000000000000i−i−33000000000000000000000
χ7844-4-4-24-24-22-422-2-4201-2-2−2i32i31-2-22-1-1222−4i4i0000100i3−i3−2i32i3001-1-1i3i3−i3−i30002i−2i2i−2i−2323000000000000000000000000−ii3−3000000000000000000000
χ7944-4-4-24-24-22-422-2-4201-2-22i3−2i31-2-22-1-12224i−4i0000100−i3i32i3−2i3001-1-1−i3−i3i3i3000−2i2i−2i2i−2323000000000000000000000000i−i3−3000000000000000000000
χ8044-4-4-24-24-22-422-2-4201-2-22i3−2i31-2-22-1-1222−4i4i0000100−i3i32i3−2i3001-1-1−i3−i3i3i30002i−2i2i−2i23−23000000000000000000000000−ii−33000000000000000000000
χ814-44-4444-4-44-4-44-44-4044400-4-4-44-44-44-4000000400000000-4-4400000000000000000000000000000000000000000000000000000000000000
χ824-44-444-2-424-42-2-44-40-2-240022-442-22-2-4000000-20000000022-2000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
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χ864-44-4-244-4-4-2-4-442420-24-2002-42-22-2-442000000-20000000022-2000000000000000000000000000000000000000000000000000000023−2300000
χ874-44-4-244-4-4-2-4-442420-24-2002-42-22-2-442000000-20000000022-20000000000000000000000000000000000000000000000000000000−232300000
χ884-4-4444-2-42-44-22-4-440-2-240022-4-4-22-224000000-2000000002-2200000000000000000000000004-4-22-220000000000000000000000000000000
χ894-4-4444-2-42-44-22-4-440-2-240022-4-4-22-224000000-2000000002-220000000000000000000000000-442-22-20000000000000000000000000000000
χ904-4-444-242-4-4-24-4-42404-2-200-42224-4-22-2004-400-2000000002-220000000000000-220000004-4000000000000000000-220000000000000000000
χ914-4-444-242-4-4-24-4-42404-2-200-42224-4-22-200-4400-2000000002-2200000000000002-2000000-440000000000000000002-20000000000000000000
χ924-4-44-244-4-4244-42-4-20-24-2002-422-224-4-2004-400-2000000002-2200000000000004-4000000-22000000000000000000-220000000000000000000
χ934-4-44-244-4-4244-42-4-20-24-2002-422-224-4-200-4400-2000000002-220000000000000-440000002-20000000000000000002-20000000000000000000
χ944-4-44-2-242-42-24-422-20-2-210022-1-1-22-221004-40010000003-3-11-13-33-3000000000-22000000-2200000000003-30000001-10000000000000000000
χ954-4-44-2-242-42-24-422-20-2-210022-1-1-22-221004-4001000000-33-11-1-33-33000000000-22000000-220000000000-330000001-10000000000000000000
χ964-4-44-2-242-42-24-422-20-2-210022-1-1-22-22100-440010000003-3-11-13-33-30000000002-20000002-20000000000-33000000-110000000000000000000
χ974-4-44-2-242-42-24-422-20-2-210022-1-1-22-22100-44001000000-33-11-1-33-330000000002-20000002-200000000003-3000000-110000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222000000-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222000000-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-48-4844-8-8-4440-4-4200-4-42-24444-20000002000000002-2-200000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-44444-4440222−4i34i3222-2-2-2-2-2-2000000-1002i3−2i32i3−2i300-111−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-44444-44402224i3−4i3222-2-2-2-2-2-2000000-100−2i32i3−2i32i300-111i3i3−i3−i30000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-444844-4-8-4-80-42-4004-24-44-4-224000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-4-84-4-84-448402-4-400-244-4-224-44000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-484-8-44-884-440-4-420044-224-44-4-2000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-444-44-44022200-2-2-22-22-22-2000000-10000000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-444-44-44022200-2-2-22-22-22-2000000-10000000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-444-8-4-44-8480-42-4004-244-442-2-4000000200000000-22-200000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-8448-444-8-402-4-400-24442-2-44-4000000200000000-22-200000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-4-4444-4022200-2-2-2-22-22-22000000-10000006-61-11-33-330000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-4-4444-4022200-2-2-2-22-22-22000000-1000000-661-113-33-30000000000000000000000000000000000000000000000000000000000

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