Finite Group Databasebeta

← Group #13169270

Character table — Group #13169270

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212444412121212121212121212121212121212222244441212121212121212121212121212121212121212246666121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-11-1-1111111111111-1-111-1-111-1-11111-11-11-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-11111111111-1-1-1-1-11-1-111-1-1-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11-1-1-1-1-1111-111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1111-11111-1-1-1-111111-1-1-1-1-1111-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-1-1111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111-11-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-111-1-111-1-1-1-111-1-1-1-11-1-1-1-1-11111-1-111-1-1-1111-1-111-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11-11111-1-11-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-11111111111-111-111-1-111-1-1-1-111-1-1-1-11111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1-111-1-111-1-1111-11111-1-11-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-111111-1-1-1-111-1-111-1111-1-111-11-11
χ17222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1020200-1-1-1-122-1-1-1-1220022002200-1-1-1-102020000-1-1-1-1-1-1-1-100-1-100000000
χ18222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-1020-200-1-1-1-1-2-211112200-2-200-2-20011110-2020000-1-1-1-11111001100000000
χ19222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-10-20200111122-1-1-1-1-2-200-2-200-2-2001111020-200001111-1-1-1-1001100000000
χ20222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-10-20-2001111-2-21111-2-20022002200-1-1-1-10-20-200001111111100-1-100000000
χ21222222-12222-1-1-1222-1-1-22-1-1-1-122-1-1112222-1-1-1-1-2-21111-2-211110-20-200-1-11122-1-11122002200-2-20011110-20-20000-1-111-1-11100-1-100000000
χ22222222-12222-1-1-1222-1-1-22-1-1-1-122-1-11122-2-2-1-1-1-1-2-21111-2-211110-20200-1-111-2-211-1-12200-2-2002200-1-1-1-1020-20000-1-11111-1-1001100000000
χ23222222-12222-1-1-1222-1-1-22-1-1-1-122-1-111-2-222-1-1-1-1-2-21111-2-21111020-20011-1-122-1-111-2-200-2-2002200-1-1-1-10-202000011-1-1-1-111001100000000
χ24222222-12222-1-1-1222-1-1-22-1-1-1-122-1-111-2-2-2-2-1-1-1-1-2-21111-2-2111102020011-1-1-2-211-1-1-2-2002200-2-20011110202000011-1-111-1-100-1-100000000
χ2522222-1222-1-1222-12-12-12-12-12-1-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12022-1-10000-1-1222200220000002200002-1-10-1-1-1-10000-1-1-1-1200000-1-1-1000
χ2622222-1222-1-1222-12-12-12-12-12-1-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1-20-22110000-1-1222200-2-2000000-2-20000-2-11011110000-1-1-1-1-200000111000
χ2722222-1222-1-1222-12-12-12-12-12-1-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1202-2-1-1000011-2-2-2-20022000000-2-2000021-10-1-1-1-100001111-200000111000
χ2822222-1222-1-1222-12-12-12-12-12-1-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-211000011-2-2-2-200-2-2000000220000-2110111100001111200000-1-1-1000
χ2922222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-20022-1-1-1-1-21-2-21111111120-2-2-1-10000-1-122-2-200-2-2000000220000211011-1-10000-1-111-200000-1-11000
χ3022222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-20022-1-1-1-1-21-2-211111111-202-2110000-1-122-2-20022000000-2-20000-21-10-1-1110000-1-11120000011-1000
χ3122222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-200-2-2-1-1-1-1-21-2-21111111120-22-1-1000011-2-22200-2-2000000-2-200002-11011-1-1000011-1-120000011-1000
χ3222222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111-202211000011-2-2220022000000220000-2-1-10-1-111000011-1-1-200000-1-11000
χ332222-122-1-1222222-1-1-122-1-12-12-1-1-12222200-1-1-1-1-12-1-122-1-1-1-1-1-12220222222000000-1-1-1-1002200000000-102-1-1-1-1-1-1-1-1-100000200-1-1000-100
χ342222-122-1-1222222-1-1-122-1-12-12-1-1-12222200-1-1-1-1-12-1-122-1-1-1-1-1-1-22-20-2-22222000000-1-11100-2-20000000010-2-11111-1-1-1-100000-20011000100
χ352222-122-1-1222222-1-1-122-1-12-12-1-1-1222-2-200-1-1-1-1-12-1-122-1-1-1-1-1-12-22022-2-2-2-200000011-1-100-2-200000000-1021-1-1-1-1111100000-20011000100
χ362222-122-1-1222222-1-1-122-1-12-12-1-1-1222-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2-2-20-2-2-2-2-2-2000000111100220000000010-211111111100000200-1-1000-100
χ372222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-22200-1-1-1-11-211-2-21111112-2-202222-2-2000000-1-11100-2-200000000-10-2111-1-1-1-1110000020011000-100
χ382222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-22200-1-1-1-11-211-2-2111111-2-220-2-222-2-2000000-1-1-1-10022000000001021-1-111-1-11100000-200-1-1000100
χ392222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-2-2-200-1-1-1-11-211-2-211111122-2022-2-2220000001111002200000000-10-2-111-1-111-1-100000-200-1-1000100
χ402222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-2-2-200-1-1-1-11-211-2-2111111-2220-2-2-2-22200000011-1-100-2-200000000102-1-1-11111-1-10000020011000-100
χ4122-2-2222-222-2-2-22-2-22220-2-2-222-22-2-2002i−2i2i−2i2-2-220000000000000000002i−2i002i−2i2i−2i002i−2i002-20000000000000000002i−2i002i−2i00002-200000000
χ4222-2-2222-222-2-2-22-2-22220-2-2-222-22-2-2002i−2i−2i2i2-2-220000000000000000002i−2i00−2i2i−2i2i002i−2i00-220000000000000000002i−2i00−2i2i0000-2200000000
χ4322-2-2222-222-2-2-22-2-22220-2-2-222-22-2-200−2i2i2i−2i2-2-22000000000000000000−2i2i002i−2i2i−2i00−2i2i00-22000000000000000000−2i2i002i−2i0000-2200000000
χ4422-2-2222-222-2-2-22-2-22220-2-2-222-22-2-200−2i2i−2i2i2-2-22000000000000000000−2i2i00−2i2i−2i2i00−2i2i002-2000000000000000000−2i2i00−2i2i00002-200000000
χ4522-2-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i32i−2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000−ii3−32i−2i−ii3−32i−2i002-2000000−i3−i3i3i300000000−ii3−3−ii3−300-1100000000
χ4622-2-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i32i−2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000−ii3−3−2i2ii−i−332i−2i00-22000000i3i3−i3−i300000000−ii3−3i−i−33001-100000000
χ4722-2-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i3−2i2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000i−i−332i−2i−ii3−3−2i2i00-22000000i3i3−i3−i300000000i−i−33−ii3−3001-100000000
χ4822-2-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i3−2i2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000i−i−33−2i2ii−i−33−2i2i002-2000000−i3−i3i3i300000000i−i−33i−i−3300-1100000000
χ4922-2-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i32i−2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000−ii−332i−2i−ii−332i−2i002-2000000i3i3−i3−i300000000−ii−33−ii−3300-1100000000
χ5022-2-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i32i−2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000−ii−33−2i2ii−i3−32i−2i00-22000000−i3−i3i3i300000000−ii−33i−i3−3001-100000000
χ5122-2-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i3−2i2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000i−i3−32i−2i−ii−33−2i2i00-22000000−i3−i3i3i300000000i−i3−3−ii−33001-100000000
χ5222-2-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i3−2i2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000i−i3−3−2i2ii−i3−3−2i2i002-2000000i3i3−i3−i300000000i−i3−3i−i3−300-1100000000
χ532-2-222222-2-222-2-2-2-2222022-2-2-2-2-2-2200000022-2-200000000000000000000000000000000002-22i−2i2i−2i2i−2i2i−2i000000000000000000002-22i−2i0000
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χ552-2-222222-2-222-2-2-2-2222022-2-2-2-2-2-2200000022-2-20000000000000000000000000000000000-222i−2i−2i2i2i−2i2i−2i00000000000000000000-22−2i2i0000
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χ5744444-2-244-2-2-2-2-2-24-2-214-2-21-21-2-2-21-2-2004411114-2-2-211-2-211110004000000-2-2-2-2-2-200000000000000000-200000000001111000000000000
χ5844444-2-244-2-2-2-2-2-24-2-214-2-21-21-2-2-21-2-200-4-411114-2-2-211-2-21111000-40000002222220000000000000000020000000000-1-1-1-1000000000000
χ5944444-2-244-2-2-2-2-2-24-2-21-4-2-21-21-2-2-212200441111-4222-1-122-1-1-1-1000-4000000-2-2-2-222000000000000000002000000000011-1-1000000000000
χ6044444-2-244-2-2-2-2-2-24-2-21-4-2-21-21-2-2-212200-4-41111-4222-1-122-1-1-1-100040000002222-2-200000000000000000-20000000000-1-111000000000000
χ614444-24-2-2-244-2-2-24-2-21-24-21-21-2-2-21-2-2-244001111-2411-2-2-2-21111040000-2-2-2-2000000-2-200000000000000000-2000011110000000000000000
χ624444-24-2-2-244-2-2-24-2-21-24-21-21-2-2-21-2-2-2-4-4001111-2411-2-2-2-211110-400002222000000220000000000000000020000-1-1-1-10000000000000000
χ634444-24-2-2-244-2-2-24-2-21-2-4-21-21-2-2-21-222440011112-4-1-12222-1-1-1-10-40000-2-222000000-2-2000000000000000002000011-1-10000000000000000
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χ7744-4-4-24-22-24-422-2-42-21-202-121-22-2-12−2i32i34i−4i001-1-1100i3−i3−2i32i300i3i3−i3−i3000000−2i2i23−23000000−2i2i0000000000000000000000i−i−330000000000000000
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χ854-44-44-24-4-422-44-4-24-24-202-4-2-42-2242000000-22-220000000000000000−232300000000000000000000000000000000−232300000000000000000000
χ864-44-4-24422-4-4-44-44-2-2-2402242-4-22-2-4000000-22-22000000000000000000000000000000−2i32i30000000000000000−2i32i30000000000000000000000
χ874-44-4-24422-4-4-44-44-2-2-2402242-4-22-2-4000000-22-220000000000000000000000000000002i3−2i300000000000000002i3−2i30000000000000000000000
χ884-44-4-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-10000003i−3i3i−3i3i−3i000023−23000000000000−2i32i30000000000000000i3−i3−3300000000000000000000
χ894-44-4-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-10000003i−3i3i−3i3i−3i0000−23230000000000002i3−2i30000000000000000−i3i33−300000000000000000000
χ904-44-4-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-1000000−3i3i−3i3i−3i3i000023−230000000000002i3−2i30000000000000000−i3i3−3300000000000000000000
χ914-44-4-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-1000000−3i3i−3i3i−3i3i0000−2323000000000000−2i32i30000000000000000i3−i33−300000000000000000000
χ924-4-4444-24-4-44-222-4-44-2-204-2222-4-42-2000000-2-2220000000000000000000000000000000000004i−4i00−2i2i−2i2i0000000000000000000000000000
χ934-4-4444-24-4-44-222-4-44-2-204-2222-4-42-2000000-2-222000000000000000000000000000000000000−4i4i002i−2i2i−2i0000000000000000000000000000
χ944-4-444-244-42-24-4-42-4-24-20-242-4222-4-2000000-2-222000000000000000000000000000000000000004i−4i00000000000000000000000000−2i2i0000
χ954-4-444-244-42-24-4-42-4-24-20-242-4222-4-2000000-2-22200000000000000000000000000000000000000−4i4i000000000000000000000000002i−2i0000
χ964-4-44-244-22-444-4-4-42-2-240-2-2-42-42224000000-2-22200000000000000000000000000000000004-40000000000000000000000000000-22000000
χ974-4-44-244-22-444-4-4-42-2-240-2-2-42-42224000000-2-2220000000000000000000000000000000000-4400000000000000000000000000002-2000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-484-4-44-8-88442-4-40-244-4-4-22440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-4-4444-4442220-2-2-222-22-2-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-4-4444-4442220-2-2-222-22-2-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-4-8-8444-44-48-4-4204424-2-44-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-444-8-84-448-4-42-404-2-4-24-44240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444444-44-4-42220-2-22-2-22-22-2000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444444-44-4-42220-2-22-2-22-22-2000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-48-84-4-4444-8-4-420-4-4-24-2444200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-44-88-444-84-42-40-424-2444-2-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-444-48-8-8442-4-402-4444-2-24-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-444-4-44444222022-2-2-2-2-2-22000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-444-4-44444222022-2-2-2-2-2-22000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000

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