Finite Group Databasebeta

← Group #13172223

Character table — Group #13172223

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666662333666666666664444366666666666666624446612121212121212121212121212124444444412121212666121212121212121212121212122412121212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111-1-11111-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111-11111-1-1-1-11111-1111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
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
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-11-1-11111-11-11
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-111111-1-1-1-1111-111-1-1111-11-1
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-11111-1-1-111-111-1-11111-1-111-1-1-1-1-1-1111-1
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-111-1-111-1-11111-1-111-1-111111111-1-1-11-1111-1-111-1-111-1-11111-1-1-1-1-11
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-11-111-1-111-1-111-1-1-1-11111-1-111111111111-11-1-1-111-1-111-1-1-1-11111-1-1-1-11-1
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1111-1-111-1-1-1-111-1-111-1-1-1-111-1-11111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-111-11
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-1-1-1-11111-1-11-111-1-1111-1-11
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-111-11-1-11111-111-1
χ17222222-1222-1-122-122-1-1222-1-122-1-1-1-120022-12-1-1-1-1-122-1-1-1-1-1-1-102220000-1-122-1-1220022220000000000000-12-100-1-1-1-1-1-1-1-12000-1-100-1000
χ18222222-1222-1-122-122-1-1222-1-122-1-1-1-120022-12-1-1-1-1-122-1-1-1-1-1-1-102-2-20000-1-12211-2-20022-2-20000000000000-1-2100-1-1-1-11111-200011001000
χ19222222-1222-1-122-122-1-1222-1-122-1-1-1-1200-2-2-12-1-1-1-1-122-1-1-1-1-1-1-10-222000011-2-2-1-12200-2-2-2-2000000000000012-1001111-1-1-1-1-200011001000
χ20222222-1222-1-122-122-1-1222-1-122-1-1-1-1200-2-2-12-1-1-1-1-122-1-1-1-1-1-1-10-2-2-2000011-2-211-2-200-2-22200000000000001-2100111111112000-1-100-1000
χ21222222-1222-1-122-12-2-1-12-2-2-1-122-1-1-1-120022-1-211111-2-2-1-1-111110-22-20000-1-1-2-2-1-1-2-2002222000000000000012100-1-111-1-111-2000-1-1001000
χ22222222-1222-1-122-12-2-1-12-2-2-1-122-1-1-1-120022-1-211111-2-2-1-1-111110-2-220000-1-1-2-211220022-2-200000000000001-2-100-1-11111-1-120001100-1000
χ23222222-1222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-2-1-211111-2-2-1-1-11111022-200001122-1-1-2-200-2-2-2-20000000000000-1210011-1-1-1-11120001100-1000
χ24222222-1222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-2-1-211111-2-2-1-1-1111102-2200001122112200-2-2220000000000000-1-2-10011-1-111-1-1-2000-1-1001000
χ2522222-1222-122-1-12222-1-1222-1-1-122-1-1-12200-1-1222-1-1-1-1-1-1-1-1-1-1-120222222000022-1-1-1-100000000220000-1-1-10-12-1-10000-1-1-1-102-1-100000-100
χ2622222-1222-122-1-12222-1-1222-1-1-122-1-1-12200-1-1222-1-1-1-1-1-1-1-1-1-1-120-2-222220000-2-211-1-100000000-2-20000-1-1-101-2-1-1000011110-21100000100
χ2722222-1222-122-1-12222-1-1222-1-1-122-1-1-1-2-200-1-1222-1-1-1-1-1-1-1-1-1-1-1-2022-2-2-2-2000022-1-11100000000-2-200001110-12110000-1-1-1-10-21100000100
χ2822222-1222-122-1-12222-1-1222-1-1-122-1-1-1-2-200-1-1222-1-1-1-1-1-1-1-1-1-1-1-20-2-2-2-2-2-20000-2-211110000000022000011101-2110000111102-1-100000-100
χ2922222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-12200-11-2-2-21111-1-1-11111-202-2-2-22200002211-1-100000000-2-200001110-1-2-1-10000-1-111021100000-100
χ3022222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-12200-11-2-2-21111-1-1-11111-20-22-2-2220000-2-2-1-1-1-100000000220000111012-1-1000011-1-10-2-1-100000100
χ3122222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-1-2-200-11-2-2-21111-1-1-11111202-222-2-2000022111100000000220000-1-1-10-1-2110000-1-1110-2-1-100000100
χ3222222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-1-2-200-11-2-2-21111-1-1-1111120-2222-2-20000-2-2-1-11100000000-2-20000-1-1-101211000011-1-1021100000-100
χ332222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-12222-122-1-122-1-1-1-1-1-1-1-1-12200-1-1-1-122-1-1000022-1-100222200-1-1-1-12-1-1200-1-1-1-1-1-10000000000-1-10000
χ342222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-122-2-2-122-1-122-1-1-1-1-1-1-1-1-12-200-1-1-1-1-2-2110000221100-2-2-2-20011112-1-1-200-1-111110000000000110000
χ352222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-1-2-222-122-1-122-1-1-1-1-1-1-1-1-1-2200111122-1-10000-2-2-1-100-2-2-2-2001111-21120011-1-1-1-10000000000110000
χ362222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-1-2-2-2-2-122-1-122-1-1-1-1-1-1-1-1-1-2-2001111-2-2110000-2-21100222200-1-1-1-1-211-2001111110000000000-1-10000
χ372222-122-1-1222222-1-2-12-111-12-1-1-1-122-12222-1-2-211-2-211-1-1-11111-2-20011-1-12211000022-1-10022-2-2001111-211-200-1-1-1-1110000000000-1-10000
χ382222-122-1-1222222-1-2-12-111-12-1-1-1-122-122-2-2-1-2-211-2-211-1-1-11111-220011-1-1-2-2-1-10000221100-2-22200-1-1-1-1-211200-1-111-1-10000000000110000
χ392222-122-1-1222222-1-2-12-111-12-1-1-1-122-1-2-222-1-2-211-2-211-1-1-111112-200-1-11122110000-2-2-1-100-2-22200-1-1-1-12-1-1-20011-1-1110000000000110000
χ402222-122-1-1222222-1-2-12-111-12-1-1-1-122-1-2-2-2-2-1-2-211-2-211-1-1-111112200-1-111-2-2-1-10000-2-2110022-2-20011112-1-12001111-1-10000000000-1-10000
χ4122-2-22222-22-2-2-2-22-2022200-2-22-22-22-2-200002000000002-2-20000000000000000000000002-2002i−2i2i−2i2i2i−2i−2i0000000000000000002i−2i2-2000000
χ4222-2-22222-22-2-2-2-22-2022200-2-22-22-22-2-200002000000002-2-20000000000000000000000002-200−2i2i−2i2i−2i−2i2i2i000000000000000000−2i2i2-2000000
χ4322-2-22222-22-2-2-2-22-2022200-2-22-22-22-2-200002000000002-2-2000000000000000000000000-22002i−2i−2i2i2i2i−2i−2i000000000000000000−2i2i-22000000
χ4422-2-22222-22-2-2-2-22-2022200-2-22-22-22-2-200002000000002-2-2000000000000000000000000-2200−2i2i2i−2i−2i−2i2i2i0000000000000000002i−2i-22000000
χ452-22-2222-22-22-2-22-2-20222002-2-2-2-2-2-2222-22i−2i200000000-22-200000000002-22i−2i0000002-22i−2i002i−2i000000000000002-22i−2i0000000000002i−2i0000
χ462-22-2222-22-22-2-22-2-20222002-2-2-2-2-2-2222-2−2i2i200000000-22-200000000002-2−2i2i0000002-2−2i2i00−2i2i000000000000002-2−2i2i000000000000−2i2i0000
χ472-22-2222-22-22-2-22-2-20222002-2-2-2-2-2-222-222i−2i200000000-22-20000000000-222i−2i000000-222i−2i00−2i2i00000000000000-222i−2i000000000000−2i2i0000
χ482-22-2222-22-22-2-22-2-20222002-2-2-2-2-2-222-22−2i2i200000000-22-20000000000-22−2i2i000000-22−2i2i002i−2i00000000000000-22−2i2i0000000000002i−2i0000
χ492-22-2-1221-1-22-2-22-210-12-1−i3i3-1-21111-22-12-22i−2i-100−i3i300−i3i31-11−i3−i3i3i30000−i3i3-112i−2i3−300002-2−ii002i−2i00003−33−30−i3i3000-11−ii3−30000000000−ii0000
χ502-22-2-1221-1-22-2-22-210-12-1−i3i3-1-21111-22-12-2−2i2i-100−i3i300−i3i31-11−i3−i3i3i30000−i3i3-11−2i2i−3300002-2i−i00−2i2i0000−33−330−i3i3000-11i−i−330000000000i−i0000
χ512-22-2-1221-1-22-2-22-210-12-1−i3i3-1-21111-22-1-222i−2i-100−i3i300−i3i31-11−i3−i3i3i30000i3−i31-12i−2i3−30000-22−ii00−2i2i0000−33−330i3−i30001-1−ii3−30000000000i−i0000
χ522-22-2-1221-1-22-2-22-210-12-1−i3i3-1-21111-22-1-22−2i2i-100−i3i300−i3i31-11−i3−i3i3i30000i3−i31-1−2i2i−330000-22i−i002i−2i00003−33−30i3−i30001-1i−i−330000000000−ii0000
χ532-22-2-1221-1-22-2-22-210-12-1i3−i3-1-21111-22-12-22i−2i-100i3−i300i3−i31-11i3i3−i3−i30000i3−i3-112i−2i−3300002-2−ii002i−2i0000−33−330i3−i3000-11−ii−330000000000−ii0000
χ542-22-2-1221-1-22-2-22-210-12-1i3−i3-1-21111-22-12-2−2i2i-100i3−i300i3−i31-11i3i3−i3−i30000i3−i3-11−2i2i3−300002-2i−i00−2i2i00003−33−30i3−i3000-11i−i3−30000000000i−i0000
χ552-22-2-1221-1-22-2-22-210-12-1i3−i3-1-21111-22-1-222i−2i-100i3−i300i3−i31-11i3i3−i3−i30000−i3i31-12i−2i−330000-22−ii00−2i2i00003−33−30−i3i30001-1−ii−330000000000i−i0000
χ562-22-2-1221-1-22-2-22-210-12-1i3−i3-1-21111-22-1-22−2i2i-100i3−i300i3−i31-11i3i3−i3−i30000−i3i31-1−2i2i3−30000-22i−i002i−2i0000−33−330−i3i30001-1i−i3−30000000000−ii0000
χ5744444-2-244-2-2-2-2-2-244-21-244-21-2-2-2-211-200001-2-2-2-211-2-21111111004400000000-2-2-2-200000000000000000000-2-20000001111000000000000
χ5844444-2-244-2-2-2-2-2-244-21-244-21-2-2-2-211-200001-2-2-2-211-2-2111111100-4-40000000022220000000000000000000022000000-1-1-1-1000000000000
χ5944444-2-244-2-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2000012222-1-122111-1-1-1-1004-400000000-2-22200000000000000000000-2200000011-1-1000000000000
χ6044444-2-244-2-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2000012222-1-122111-1-1-1-100-440000000022-2-2000000000000000000002-2000000-1-111000000000000
χ614444-24-2-2-24-2-244-2-241-2-2-2-21-2-2-211-2-2-2004414-211-2-2-2-2111111104000000-2-2-2-2000000-2-2000000000000000-2000011110000000000000000
χ624444-24-2-2-24-2-244-2-241-2-2-2-21-2-2-211-2-2-200-4-414-211-2-2-2-211111110-400000022220000002200000000000000020000-1-1-1-10000000000000000
χ634444-24-2-2-24-2-244-2-2-41-2-2221-2-2-211-2-2-200441-42-1-12222111-1-1-1-10-4000000-2-222000000-2-20000000000000002000011-1-10000000000000000
χ644444-24-2-2-24-2-244-2-2-41-2-2221-2-2-211-2-2-200-4-41-42-1-12222111-1-1-1-10400000022-2-200000022000000000000000-20000-1-1110000000000000000
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χ864-44-4-2-242-224-42-2-420-2-212i3−2i3-22-1-1222-21-44001002i3−2i300−i3i3-11-1−i3−i3i3i30000−2i32i32-2000000002-2000000000000000i3−i3000-1100000000000000000000
χ874-4-44444-4-4-4-444-4-44044400-44-44-44-4-4-40000400000000-4-440000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-2-4-4-42-24-4240-2-24002-2-442-222-40000-20000000022-2000000000000000023−2300000000000000000000000000000023−2300000000000000
χ894-4-4444-2-4-4-42-24-4240-2-24002-2-442-222-40000-20000000022-20000000000000000−2323000000000000000000000000000000−232300000000000000
χ904-4-444-24-4-42-44-22-4404-2-200-4-22-2-442220000-20000000022-200000000000000000023−2300000000000000000000000000000023−23000000000000
χ914-4-444-24-4-42-44-22-4404-2-200-4-22-2-442220000-20000000022-2000000000000000000−2323000000000000000000000000000000−2323000000000000
χ924-4-444-2-2-4-422-2-22240-21-200212-22-2-1-120000100003-300-1-113-33-300000000000023−2323−230000000000000000000000000000−33−33000000000000
χ934-4-444-2-2-4-422-2-22240-21-200212-22-2-1-120000100003-300-1-113-33-3000000000000−2323−232300000000000000000000000000003−33−3000000000000
χ944-4-444-2-2-4-422-2-22240-21-200212-22-2-1-12000010000-3300-1-11-33-3300000000000023−23−23230000000000000000000000000000−333−3000000000000
χ954-4-444-2-2-4-422-2-22240-21-200212-22-2-1-12000010000-3300-1-11-33-33000000000000−232323−2300000000000000000000000000003−3−33000000000000
χ964-4-44-24422-4-444-4-4-20-24-200242-22-2-4-420000-20000000022-200000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ974-4-44-24422-4-444-4-4-20-24-200242-22-2-4-420000-20000000022-2000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
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
χ10088-8-88-4-48-8-44444-4-80-42-4004-2-44-442-2400002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-44844-8-8-4402-4-400-24-442-2-44400002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48-44-4-8-844840-4-4200442-2-44-44-200002000000002-2-20000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-44-44444-44022200-2-22-22-22-2-20000-100000000-111−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-44-44444-44022200-2-22-22-22-2-20000-100000000-1113i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-4-884-444-44-80-42-400-4-24444-22-40000200000000-22-20000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44-44-444-4440222−4i34i32-2-2-2-2-2-2220000-1002i3−2i3002i3−2i31-11−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-44-444-44402224i3−4i32-2-2-2-2-2-2220000-100−2i32i300−2i32i31-11i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-444-84-48-84-402-4-400-2-44-4-224440000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48444-88-44-8-40-4-42004-4-224-444-20000200000000-2-220000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44444-4-444-4022200-22-22-22-2-2-20000-100006-60011-1-33-33000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44444-4-444-4022200-22-22-22-2-2-20000-10000-660011-13-33-3000000000000000000000000000000000000000000000000000000000000

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