Finite Group Databasebeta

← Group #13172021

Character table — Group #13172021

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666662333666666666662244366666666666666624446666661212121212121212121244444444121212126666612121212121212121212122412121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111111-1-1111111-1-1111111-1-1-1-11111-111-1-11-11111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-11111-1-1-1-111-1111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-11-1-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-11-1-11111-1-1-11111111-1-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1111-1-1-1-1-1111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111-1-111-11-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
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
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-1-1-1-11-1-11111-111-1
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-111-1-1-11-1-1-111-1-1111-111-1-1111-1-11
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-11
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-11111111111-111-1-111-1-1-1-1-11111-1-11111-1-1-1-11-1
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-111111111111-1-111-1-111111-1-1-1-1-1-11111-1-1-1-1-11
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111-1
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-1111-1111-1-111-1-11-111-1-1111-11-1
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-11111-11-1-11111-11-11
χ17222222-12-122-122-122-12-122-122-1-1-1-12-10022-12-1-1-122-1-1-1-1-1-1-1-1-122200000-1-10022-1-12222000000220000200-1-1-1-1000-1-1-1-1-1-12000-1-100-1000
χ18222222-12-122-122-122-12-122-122-1-1-1-12-10022-12-1-1-122-1-1-1-1-1-1-1-1-1-22-200000110022-1-1-2-222000000-2-20000-20011-11000-1-1-1-111-200011001000
χ19222222-12-122-122-122-12-122-122-1-1-1-12-100-2-2-12-1-1-122-1-1-1-1-1-1-1-1-12-2200000-1-100-2-21122-2-2000000-2-20000200-1-11-10001111-1-1-200011001000
χ20222222-12-122-122-122-12-122-122-1-1-1-12-100-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2000001100-2-211-2-2-2-2000000220000-20011110001111112000-1-100-1000
χ21222222-12-122-122-12-2-12-1-2-2-122-1-1-1-12-10022-1-2111-2-211-1-1-111112-2-200000-1-10022-1-1-2-2-2-2000000220000200-1-111000-1-11111-2000-1-1001000
χ22222222-12-122-122-12-2-12-1-2-2-122-1-1-1-12-10022-1-2111-2-211-1-1-11111-2-2200000110022-1-122-2-2000000-2-20000-200111-1000-1-111-1-120001100-1000
χ23222222-12-122-122-12-2-12-1-2-2-122-1-1-1-12-100-2-2-1-2111-2-211-1-1-1111122-200000-1-100-2-211-2-222000000-2-20000200-1-1-1100011-1-11120001100-1000
χ24222222-12-122-122-12-2-12-1-2-2-122-1-1-1-12-100-2-2-1-2111-2-211-1-1-11111-222000001100-2-2112222000000220000-20011-1-100011-1-1-1-1-2000-1-1001000
χ2522222-12-12222-1-12222-1-1222-1-1-1-122-1-12200-1-1222-1-1-1-1-1-1-1-1-1-1-1202222-1-122220000-1-100000022000000-1-1-1-1-102-1-1-10000-1-102-1-100000-100
χ2622222-12-12222-1-12222-1-1222-1-1-1-122-1-12200-1-1222-1-1-1-1-1-1-1-1-1-1-1-20-2222-1-1-2-222000011000000-2-20000001-1-1110-2-1-1-10000110-21100000100
χ2722222-12-12222-1-12222-1-1222-1-1-1-122-1-1-2-200-1-1222-1-1-1-1-1-1-1-1-1-1-1202-2-2-21122-2-20000-1-1000000-2-2000000-111-1-1021110000-1-10-21100000100
χ2822222-12-12222-1-12222-1-1222-1-1-1-122-1-1-2-200-1-1222-1-1-1-1-1-1-1-1-1-1-1-20-2-2-2-211-2-2-2-200001100000022000000111110-211100001102-1-100000-100
χ2922222-12-12222-1-122-22-1-1-2-22-1-1-1-122-1-12200-11-2-2-21111-1-1-1111120-2-222-1-122-2-2000011000000-2-2000000-1-1-1-1-10-2111000011021100000-100
χ3022222-12-12222-1-122-22-1-1-2-22-1-1-1-122-1-12200-11-2-2-21111-1-1-11111-202-222-1-1-2-2-2-20000-1-1000000220000001-1-111021110000-1-10-2-1-100000100
χ3122222-12-12222-1-122-22-1-1-2-22-1-1-1-122-1-1-2-200-11-2-2-21111-1-1-1111120-22-2-211222200001100000022000000-111-1-10-2-1-1-10000110-2-1-100000100
χ3222222-12-12222-1-122-22-1-1-2-22-1-1-1-122-1-1-2-200-11-2-2-21111-1-1-11111-2022-2-211-2-2220000-1-1000000-2-20000001111102-1-1-10000-1-1021100000-100
χ332222-12222-1-12222-12-1-12-1-1-1-1-122-1-1-122222-122-1-1-1-122-1-1-1-1-1-1-10202-1-12200-1-1-1-12200-1-122220000-1-1-1-10-1-100202-1-1-1-1-1-100000000-1-10000
χ342222-12222-1-12222-12-1-12-1-1-1-1-122-1-1-1222-2-2-122-1-1-1-122-1-1-1-1-1-1-10-202-1-12200-1-111-2-20011-2-2-2-2000011110-1-100-202-1-1111100000000110000
χ352222-12222-1-12222-12-1-12-1-1-1-1-122-1-1-12-2-222-122-1-1-1-122-1-1-1-1-1-1-1020-211-2-20011-1-12200-1-1-2-2-2-2000011110110020-211-1-1-1-100000000110000
χ362222-12222-1-12222-12-1-12-1-1-1-1-122-1-1-12-2-2-2-2-122-1-1-1-122-1-1-1-1-1-1-10-20-211-2-2001111-2-2001122220000-1-1-1-101100-20-211111100000000-1-10000
χ372222-12222-1-12222-1-2-1-1211-1-1-122-1-1-122222-1-2-21111-2-2-1-1-111110-20-2-1-1220011-1-122001122-2-2000011110-1-100-20-211-1-11100000000-1-10000
χ382222-12222-1-12222-1-2-1-1211-1-1-122-1-1-1222-2-2-1-2-21111-2-2-1-1-11111020-2-1-122001111-2-200-1-1-2-2220000-1-1-1-10-1-10020-21111-1-100000000110000
χ392222-12222-1-12222-1-2-1-1211-1-1-122-1-1-12-2-222-1-2-21111-2-2-1-1-111110-20211-2-200-1-1-1-1220011-2-2220000-1-1-1-101100-202-1-1-1-11100000000110000
χ402222-12222-1-12222-1-2-1-1211-1-1-122-1-1-12-2-2-2-2-1-2-21111-2-2-1-1-11111020211-2-200-1-111-2-200-1-122-2-20000111101100202-1-111-1-100000000-1-10000
χ412-22-22222-22-2-2-2-22-2022200-22-22-22-2-2-200002000000002-2-2000000000000000000000000002i−2i2i−2i2-22i2i−2i−2i0000000000000000002i−2i2-2000000
χ422-22-22222-22-2-2-2-22-2022200-22-22-22-2-2-200002000000002-2-2000000000000000000000000002i−2i−2i2i-222i2i−2i−2i000000000000000000−2i2i-22000000
χ432-22-22222-22-2-2-2-22-2022200-22-22-22-2-2-200002000000002-2-200000000000000000000000000−2i2i2i−2i-22−2i−2i2i2i0000000000000000002i−2i-22000000
χ442-22-22222-22-2-2-2-22-2022200-22-22-22-2-2-200002000000002-2-200000000000000000000000000−2i2i−2i2i2-2−2i−2i2i2i000000000000000000−2i2i2-2000000
χ452-2-22222-22-22-22-2-2-20222002-2-2-22-2-22-22-22i−2i200000000-22-2000000002-22-200002i−2i2i−2i00002i−2i000000000002-200000002i−2i00000000002i−2i0000
χ462-2-22222-22-22-22-2-2-20222002-2-2-22-2-22-22-2−2i2i200000000-22-2000000002-22-20000−2i2i−2i2i0000−2i2i000000000002-20000000−2i2i0000000000−2i2i0000
χ472-2-22222-22-22-22-2-2-20222002-2-2-22-2-22-2-222i−2i200000000-22-200000000-22-2200002i−2i2i−2i0000−2i2i00000000000-2200000002i−2i0000000000−2i2i0000
χ482-2-22222-22-22-22-2-2-20222002-2-2-22-2-22-2-22−2i2i200000000-22-200000000-22-220000−2i2i−2i2i00002i−2i00000000000-220000000−2i2i00000000002i−2i0000
χ492-2-22-122-221-1-22-2-210-1-12−i3i3-111-2211-1-22-22i−2i-100−i3i3−i3i3001-11−i3−i3i3i30000-112-200−i3i3−ii2i−2i003−32i−2i0000003−33−30-1100000−i3i3−ii3−300000000−ii0000
χ502-2-22-122-221-1-22-2-210-1-12−i3i3-111-2211-1-22-2−2i2i-100−i3i3−i3i3001-11−i3−i3i3i30000-112-200−i3i3i−i−2i2i00−33−2i2i000000−33−330-1100000−i3i3i−i−3300000000i−i0000
χ512-2-22-122-221-1-22-2-210-1-12−i3i3-111-2211-1-2-222i−2i-100−i3i3−i3i3001-11−i3−i3i3i300001-1-2200i3−i3−ii2i−2i003−3−2i2i000000−33−3301-100000i3−i3−ii3−300000000i−i0000
χ522-2-22-122-221-1-22-2-210-1-12−i3i3-111-2211-1-2-22−2i2i-100−i3i3−i3i3001-11−i3−i3i3i300001-1-2200i3−i3i−i−2i2i00−332i−2i0000003−33−301-100000i3−i3i−i−3300000000−ii0000
χ532-2-22-122-221-1-22-2-210-1-12i3−i3-111-2211-1-22-22i−2i-100i3−i3i3−i3001-11i3i3−i3−i30000-112-200i3−i3−ii2i−2i00−332i−2i000000−33−330-1100000i3−i3−ii−3300000000−ii0000
χ542-2-22-122-221-1-22-2-210-1-12i3−i3-111-2211-1-22-2−2i2i-100i3−i3i3−i3001-11i3i3−i3−i30000-112-200i3−i3i−i−2i2i003−3−2i2i0000003−33−30-1100000i3−i3i−i3−300000000i−i0000
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χ5744444-2-2-2-244-2-2-2-244-2-2144-2-2-211-2-2-2100001-2-2-2-2-2-211111111140400000-2-2000000-2-200000000000000-200110-2000000011000000000000
χ5844444-2-2-2-244-2-2-2-244-2-2144-2-2-211-2-2-2100001-2-2-2-2-2-2111111111-40-400000220000002200000000000000200-1-1020000000-1-1000000000000
χ5944444-2-2-2-244-2-2-2-24-4-2-21-4-4-2-2-211-2-2-2100001222222-1-1111-1-1-1-140-400000-2-20000002200000000000000-20011020000000-1-1000000000000
χ6044444-2-2-2-244-2-2-2-24-4-2-21-4-4-2-2-211-2-2-2100001222222-1-1111-1-1-1-1-4040000022000000-2-200000000000000200-1-10-2000000011000000000000
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χ624444-24-24-2-2-2-244-2-241-2-2-2-21-2-2-2-211-2-200-4-414-211-2-2-2-211111110-40000000000222200220000000000000000020000-1-1-1-100000000000000
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χ884-4-444-2424-44-4-22-4-404-2-2004222-2-4-4-224-400-2000000002-22000000004-4-220000000000000000000000000-220000000000000000000000000
χ894-4-444-2424-44-4-22-4-404-2-2004222-2-4-4-22-4400-2000000002-2200000000-442-200000000000000000000000002-20000000000000000000000000
χ904-4-44-24-2-4-22-224-42201-2-2−2i32i31222-2-1-1-22004i−4i100i3−i3−2i32i300-11-1i3i3−i3−i3000000000000−2i2i−2i2i0023−230000000000000000000000i−i−3300000000000000
χ914-4-44-24-2-4-22-224-42201-2-2−2i32i31222-2-1-1-2200−4i4i100i3−i3−2i32i300-11-1i3i3−i3−i30000000000002i−2i2i−2i00−23230000000000000000000000−ii3−300000000000000
χ924-4-44-24-2-4-22-224-42201-2-22i3−2i31222-2-1-1-22004i−4i100−i3i32i3−2i300-11-1−i3−i3i3i3000000000000−2i2i−2i2i00−23230000000000000000000000i−i3−300000000000000
χ934-4-44-24-2-4-22-224-42201-2-22i3−2i31222-2-1-1-2200−4i4i100−i3i32i3−2i300-11-1−i3−i3i3i30000000000002i−2i2i−2i0023−230000000000000000000000−ii−3300000000000000
χ944-4-44-2-24242-2-4-22-420-21-2−2i32i3-2-1-12-222124-400100−2i32i3i3−i300-11-1i3i3−i3−i30000-22-2200−2i32i30000000000000000000001-100000i3−i3000000000000000000
χ954-4-44-2-24242-2-4-22-420-21-2−2i32i3-2-1-12-22212-4400100−2i32i3i3−i300-11-1i3i3−i3−i300002-22-2002i3−2i3000000000000000000000-1100000−i3i3000000000000000000
χ964-4-44-2-24242-2-4-22-420-21-22i3−2i3-2-1-12-222124-4001002i3−2i3−i3i300-11-1−i3−i3i3i30000-22-22002i3−2i30000000000000000000001-100000−i3i3000000000000000000
χ974-4-44-2-24242-2-4-22-420-21-22i3−2i3-2-1-12-22212-44001002i3−2i3−i3i300-11-1−i3−i3i3i300002-22-200−2i32i3000000000000000000000-1100000i3−i3000000000000000000
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
χ10088-8-8-48-4-8444-4-884-402-4-400-24-444-224-40000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-484-84484-4-8-40-42-4004-22444-4-2-40000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44444-44-44-4022200-2-22-2-2-22-220000-10000006-611-1-33-33000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44444-44-44-4022200-2-22-2-2-22-220000-1000000-6611-13-33-3000000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4-448-8444-4-80-4-42004-442-2-444-200002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-484-444-8-8-4402-4-400-2-44-442-24400002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-48-4-8-44-844840-42-40042-2-44-44-2400002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-44-44444-44022200-22-22-22-2-2-20000-100000000-111−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-44-44444-44022200-22-22-22-2-2-20000-100000000-1113i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1098-8-888-4-44-4-884-444-80-4-4200-444-2244-4-20000200000000-22-20000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44-44-44-44440222−4i34i32-2-2-22-2-22-20000-1002i3−2i32i3−2i3001-11−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44-44-44-444402224i3−4i32-2-2-22-2-22-20000-100−2i32i3−2i32i3001-11i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000

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