Finite Group Databasebeta

← Group #13171969

Character table — Group #13171969

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666662333666666666664444366666666666666624446612121212121212121212121212124444444412121212666121212121212121212121212122412121212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-1111111111111-1-1-1-11111-1-11111-1-1-11-1111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-1111111-1-1-1-111-1111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-1-111-1-11-111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111111-1-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1111-1-1-1-1-1111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111111-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
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
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-1-1-1-11-1-11111-111-1
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11-111-1-111-1-1111-111-1-1111-1-11
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-11
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-111111111-1-1-111-111-1-1-1-11111-1-11111-1-1-1-11-1
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-11
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1111-1
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-11-1-111-1-111-1-11-111-1-1111-11-1
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11111-11-1-11111-11-11
χ17222222-1-1222-12-12222-1-1222-1-1-122-1-1-10022-12-122-1-1-1-1-1-1-1-1-1-1-12022-1-10000002222-1-1222200000000002-1-1-1-100000-1-1-1-1-1-12000-1-100-1000
χ18222222-1-1222-12-12222-1-1222-1-1-122-1-1-10022-12-122-1-1-1-1-1-1-1-1-1-1-1-202-2110000002222-1-1-2-2-2-20000000000-211-1100000-1-1-1-111-200011001000
χ19222222-1-1222-12-12222-1-1222-1-1-122-1-1-100-2-2-12-122-1-1-1-1-1-1-1-1-1-1-120-22-1-1000000-2-2-2-21122-2-200000000002-1-11-1000001111-1-1-200011001000
χ20222222-1-1222-12-12222-1-1222-1-1-122-1-1-100-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20-2-211000000-2-2-2-211-2-2220000000000-21111000001111112000-1-100-1000
χ21222222-1-1222-12-122-22-1-1-2-22-1-1-122-1-1-10022-1-21-2-21111-1-1-1111120-2-2-1-100000022-2-2-1-1-2-22200000000002-1-11100000-1-11111-2000-1-1001000
χ22222222-1-1222-12-122-22-1-1-2-22-1-1-122-1-1-10022-1-21-2-21111-1-1-11111-20-221100000022-2-2-1-122-2-20000000000-2111-100000-1-111-1-120001100-1000
χ23222222-1-1222-12-122-22-1-1-2-22-1-1-122-1-1-100-2-2-1-21-2-21111-1-1-11111202-2-1-1000000-2-22211-2-2-2-200000000002-1-1-110000011-1-11120001100-1000
χ24222222-1-1222-12-122-22-1-1-2-22-1-1-122-1-1-100-2-2-1-21-2-21111-1-1-11111-202211000000-2-2221122220000000000-211-1-10000011-1-1-1-1-2000-1-1001000
χ2522222-122-1222-12-122-12-122-12-1-1-1-122-12200-1-12-1-122-1-1-1-1-1-1-1-1-1220222-1-12222000000-1-1000000220000-1-1-102-1-1-1-1-10000-1-102-1-100000-100
χ2622222-122-1222-12-122-12-122-12-1-1-1-122-12200-1-12-1-122-1-1-1-1-1-1-1-1-1-220-2-2-2-1-1222200000011000000-2-200001110-2-1-1-1-1-10000110-21100000100
χ2722222-122-1222-12-122-12-122-12-1-1-1-122-1-2-200-1-12-1-122-1-1-1-1-1-1-1-1-12-2022211-2-2-2-2000000-1-1000000-2-20000-1-1-102111110000-1-10-21100000100
χ2822222-122-1222-12-122-12-122-12-1-1-1-122-1-2-200-1-12-1-122-1-1-1-1-1-1-1-1-1-2-20-2-2-211-2-2-2-2000000110000002200001110-21111100001102-1-100000-100
χ2922222-122-1222-12-12-2-12-1-2-2-12-1-1-1-122-12200-11-211-2-211-1-1-111112-20-222-1-122-2-200000011000000-2-20000-1-1-10-21-1-111000011021100000-100
χ3022222-122-1222-12-12-2-12-1-2-2-12-1-1-1-122-12200-11-211-2-211-1-1-11111-2-202-2-2-1-122-2-2000000-1-1000000220000111021-1-1110000-1-10-2-1-100000100
χ3122222-122-1222-12-12-2-12-1-2-2-12-1-1-1-122-1-2-200-11-211-2-211-1-1-11111220-22211-2-22200000011000000220000-1-1-10-2-111-1-10000110-2-1-100000100
χ3222222-122-1222-12-12-2-12-1-2-2-12-1-1-1-122-1-2-200-11-211-2-211-1-1-11111-2202-2-211-2-222000000-1-1000000-2-2000011102-111-1-10000-1-1021100000-100
χ332222-12222-1-12222-12-1-12-1-1-1-122-1-1-1-122222-122-1-1-1-122-1-1-1-1-1-1-102200022-1-1-1-1-1-1-1-1220000222200-1-1-1-1000202-1-1-1-1-1-1-1-100000000-1-10000
χ342222-12222-1-12222-12-1-12-1-1-1-122-1-1-1-1222-2-2-122-1-1-1-122-1-1-1-1-1-1-102-200022-1-1-1-11111-2-20000-2-2-2-2001111000-202-1-1-1-1111100000000110000
χ352222-12222-1-12222-12-1-12-1-1-1-122-1-1-1-12-2-222-122-1-1-1-122-1-1-1-1-1-1-10-22000-2-21111-1-1-1-1220000-2-2-2-200111100020-21111-1-1-1-100000000110000
χ362222-12222-1-12222-12-1-12-1-1-1-122-1-1-1-12-2-2-2-2-122-1-1-1-122-1-1-1-1-1-1-10-2-2000-2-211111111-2-20000222200-1-1-1-1000-20-21111111100000000-1-10000
χ372222-12222-1-12222-1-2-1-1211-1-122-1-1-1-122222-1-2-21111-2-2-1-1-111110-2-200022-1-111-1-11122000022-2-2001111000-20-2-1-111-1-11100000000-1-10000
χ382222-12222-1-12222-1-2-1-1211-1-122-1-1-1-1222-2-2-1-2-21111-2-2-1-1-111110-2200022-1-11111-1-1-2-20000-2-22200-1-1-1-100020-2-1-11111-1-100000000110000
χ392222-12222-1-12222-1-2-1-1211-1-122-1-1-1-12-2-222-1-2-21111-2-2-1-1-1111102-2000-2-211-1-1-1-111220000-2-22200-1-1-1-1000-20211-1-1-1-11100000000110000
χ402222-12222-1-12222-1-2-1-1211-1-122-1-1-1-12-2-2-2-2-1-2-21111-2-2-1-1-11111022000-2-211-1-111-1-1-2-2000022-2-200111100020211-1-111-1-100000000-1-10000
χ4122-2-2222-222-2-2-22-2-2022200-2-22-22-22-2-200002000000002-2-20000000000000000000000002-2002i−2i2i−2i2i2i−2i−2i0000000000000000002i−2i2-2000000
χ4222-2-2222-222-2-2-22-2-2022200-2-22-22-22-2-200002000000002-2-20000000000000000000000002-200−2i2i−2i2i−2i−2i2i2i000000000000000000−2i2i2-2000000
χ4322-2-2222-222-2-2-22-2-2022200-2-22-22-22-2-200002000000002-2-2000000000000000000000000-22002i−2i−2i2i2i2i−2i−2i000000000000000000−2i2i-22000000
χ4422-2-2222-222-2-2-22-2-2022200-2-22-22-22-2-200002000000002-2-2000000000000000000000000-2200−2i2i2i−2i−2i−2i2i2i0000000000000000002i−2i-22000000
χ452-22-22222-2-2-2-22-2-2202220022-22-2-2-2-2-22i−2i2i−2i200000000-22-200000000002i−2i2i−2i002i−2i002i−2i00002-2000000000000002i−2i002i−2i00000000002-20000
χ462-22-22222-2-2-2-22-2-2202220022-22-2-2-2-2-22i−2i−2i2i200000000-22-200000000002i−2i2i−2i00−2i2i00−2i2i0000-22000000000000002i−2i00−2i2i0000000000-220000
χ472-22-22222-2-2-2-22-2-2202220022-22-2-2-2-2-2−2i2i2i−2i200000000-22-20000000000−2i2i−2i2i002i−2i002i−2i0000-2200000000000000−2i2i002i−2i0000000000-220000
χ482-22-22222-2-2-2-22-2-2202220022-22-2-2-2-2-2−2i2i−2i2i200000000-22-20000000000−2i2i−2i2i00−2i2i00−2i2i00002-200000000000000−2i2i00−2i2i00000000002-20000
χ492-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-221111-22i−2i2i−2i-100−i3i3−i3i3001-11−i3−i3i3i30000002i−2i−ii3−3−ii3−32i−2i00002-20000−i3i3−i3i3000000−ii3−3−ii3−300000000-110000
χ502-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-221111-22i−2i−2i2i-100−i3i3−i3i3001-11−i3−i3i3i30000002i−2i−ii3−3i−i−33−2i2i0000-220000i3−i3i3−i3000000−ii3−3i−i−33000000001-10000
χ512-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-221111-2−2i2i2i−2i-100−i3i3−i3i3001-11−i3−i3i3i3000000−2i2ii−i−33−ii3−32i−2i0000-220000i3−i3i3−i3000000i−i−33−ii3−3000000001-10000
χ522-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-221111-2−2i2i−2i2i-100−i3i3−i3i3001-11−i3−i3i3i3000000−2i2ii−i−33i−i−33−2i2i00002-20000−i3i3−i3i3000000i−i−33i−i−3300000000-110000
χ532-22-2-1222-211-22-2-2-10-1-12i3−i3-1-1-221111-22i−2i2i−2i-100i3−i3i3−i3001-11i3i3−i3−i30000002i−2i−ii−33−ii−332i−2i00002-20000i3−i3i3−i3000000−ii−33−ii−3300000000-110000
χ542-22-2-1222-211-22-2-2-10-1-12i3−i3-1-1-221111-22i−2i−2i2i-100i3−i3i3−i3001-11i3i3−i3−i30000002i−2i−ii−33i−i3−3−2i2i0000-220000−i3i3−i3i3000000−ii−33i−i3−3000000001-10000
χ552-22-2-1222-211-22-2-2-10-1-12i3−i3-1-1-221111-2−2i2i2i−2i-100i3−i3i3−i3001-11i3i3−i3−i3000000−2i2ii−i3−3−ii−332i−2i0000-220000−i3i3−i3i3000000i−i3−3−ii−33000000001-10000
χ562-22-2-1222-211-22-2-2-10-1-12i3−i3-1-1-221111-2−2i2i−2i2i-100i3−i3i3−i3001-11i3i3−i3−i3000000−2i2ii−i3−3i−i3−3−2i2i00002-20000i3−i3i3−i3000000i−i3−3i−i3−300000000-110000
χ5744444-2-2-2-244-2-2-2-244-2-2144-2-211-2-2-2-2100001-2-2-2-2-2-21111111114004-2-2000000000000-2-2000000000000-2110-200000000011000000000000
χ5844444-2-2-2-244-2-2-2-244-2-2144-2-211-2-2-2-2100001-2-2-2-2-2-2111111111-400-422000000000000220000000000002-1-102000000000-1-1000000000000
χ5944444-2-2-2-244-2-2-2-24-4-2-21-4-4-2-211-2-2-2-2100001222222-1-1111-1-1-1-1400-4-2-200000000000022000000000000-21102000000000-1-1000000000000
χ6044444-2-2-2-244-2-2-2-24-4-2-21-4-4-2-211-2-2-2-2100001222222-1-1111-1-1-1-1-400422000000000000-2-20000000000002-1-10-200000000011000000000000
χ614444-24-2-24-2-2-24-24-24-21-2-2-2-21-2-2-2-211-2004414-2-2-211-2-21111111004000000000-2-2-2-2-2-200000000000000000-2000000111100000000000000
χ624444-24-2-24-2-2-24-24-24-21-2-2-2-21-2-2-2-211-200-4-414-2-2-211-2-2111111100-4000000000222222000000000000000002000000-1-1-1-100000000000000
χ634444-24-2-24-2-2-24-24-2-4-21-222-21-2-2-2-211-200441-4222-1-122111-1-1-1-100-4000000000-2-222-2-200000000000000000200000011-1-100000000000000
χ644444-24-2-24-2-2-24-24-2-4-21-222-21-2-2-2-211-200-4-41-4222-1-122111-1-1-1-100400000000022-2-22200000000000000000-2000000-1-11100000000000000
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χ804-44-4-24-2-2-422242-4-20-21-2−2i32i3-212-222-1-1200−4i4i100−2i32i3i3−i300-11-1i3i3−i3−i30000000000002i−2i−23232i−2i000000000000000000000000−ii3−300000000000000
χ814-44-4-24-2-2-422242-4-20-21-22i3−2i3-212-222-1-12004i−4i1002i3−2i3−i3i300-11-1−i3−i3i3i3000000000000−2i2i−2323−2i2i000000000000000000000000i−i3−300000000000000
χ824-44-4-24-2-2-422242-4-20-21-22i3−2i3-212-222-1-1200−4i4i1002i3−2i3−i3i300-11-1−i3−i3i3i30000000000002i−2i23−232i−2i000000000000000000000000−ii−3300000000000000
χ834-44-4-2-244222-4-2-42-201-2-2−2i32i31-22-2-1-12224i−4i00100i3−i3−2i32i300-11-1i3i3−i3−i3000000−2i2i−2i2i23−2300000000000000000000000000i−i−33000000000000000000
χ844-44-4-2-244222-4-2-42-201-2-2−2i32i31-22-2-1-1222−4i4i00100i3−i3−2i32i300-11-1i3i3−i3−i30000002i−2i2i−2i−232300000000000000000000000000−ii3−3000000000000000000
χ854-44-4-2-244222-4-2-42-201-2-22i3−2i31-22-2-1-12224i−4i00100−i3i32i3−2i300-11-1−i3−i3i3i3000000−2i2i−2i2i−232300000000000000000000000000i−i3−3000000000000000000
χ864-44-4-2-244222-4-2-42-201-2-22i3−2i31-22-2-1-1222−4i4i00100−i3i32i3−2i300-11-1−i3−i3i3i30000002i−2i2i−2i23−2300000000000000000000000000−ii−33000000000000000000
χ874-4-44444-4-4-444-4-44-4044400-4-4-4-4-44-4440000400000000-4-440000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-22-4-44-2-424-404-2-200-4222-442-2-20000-20000000022-200000000−2i32i3000000000000000000000000000−2i32i30000000000000000000000000
χ894-4-4444-22-4-44-2-424-404-2-200-4222-442-2-20000-20000000022-2000000002i3−2i30000000000000000000000000002i3−2i30000000000000000000000000
χ904-4-444-24-42-4442-4-2-40-24-2002-4222-2-44-20000-20000000022-20000000000000000000000−2i32i300000000000000000000000000−2i32i3000000000000
χ914-4-444-24-42-4442-4-2-40-24-2002-4222-2-44-20000-20000000022-200000000000000000000002i3−2i3000000000000000000000000002i3−2i3000000000000
χ924-4-444-2-222-44-222-2-40-2-210022-1-12-22-21000010000003-3-1-113-33-30000−2i32i3000000000000−2i32i30000000000000i3−i300000000000i3−i3000000000000
χ934-4-444-2-222-44-222-2-40-2-210022-1-12-22-21000010000003-3-1-113-33-300002i3−2i30000000000002i3−2i30000000000000−i3i300000000000−i3i3000000000000
χ944-4-444-2-222-44-222-2-40-2-210022-1-12-22-2100001000000-33-1-11-33-330000−2i32i30000000000002i3−2i30000000000000i3−i300000000000−i3i3000000000000
χ954-4-444-2-222-44-222-2-40-2-210022-1-12-22-2100001000000-33-1-11-33-3300002i3−2i3000000000000−2i32i30000000000000−i3i300000000000i3−i3000000000000
χ964-4-44-244-4-42-24-4-4420-2-240022-4-42-22-240000-20000000022-20000000000000000000000000000000023−23−23230000000000000000000000000000
χ974-4-44-244-4-42-24-4-4420-2-240022-4-42-22-240000-20000000022-200000000000000000000000000000000−232323−230000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-44-48-844-44-80-4-4200442-2-44-44-200002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-448-444-8-4-840-42-4004-2-44-442-2400002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48-8-4-44-8484402-4-400-24-442-2-44400002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-4-4444-444022200-2-22-22-22-2-20000-100000000-111−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44-4-4444-444022200-2-22-22-22-2-20000-100000000-1113i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-4-44-8-84-44480-4-4200-4-4-224444-20000200000000-22-20000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4-44444-444-40222−4i34i322-22-2-2-2-2-20000-1002i3−2i32i3−2i3001-11−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-44444-444-402224i3−4i322-22-2-2-2-2-20000-100−2i32i3−2i32i3001-11i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-44-84-4-4-84840-42-4004-2444-4-22-40000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-844-484-8-4402-4-400-2444-224-4-40000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-4-444-44022200-2-2-2-2-22-2220000-10000006-611-1-33-33000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-4-444-44022200-2-2-2-2-22-2220000-1000000-6611-13-33-3000000000000000000000000000000000000000000000000000000000000

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