Finite Group Databasebeta

← Group #13171758

Character table — Group #13171758

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order122233366666666623336666666666644444436666666666666664444444121212121212121212121212121212122244121212121212121212121212121212121212121244466121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1111111111-1-1-1-11-1-111-1-1-1-1-1-1-11-1
χ3111111111111111111111111111111111-1-111111111111111111111111-111111-1-111111111-1-1-1-1-1-111111-11-11111-1-1-1-11111-11-1-1-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-11
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-111-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1111-1-1-1-111111111-1-11-1-111-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-111111111111111111111-11-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-11-11-1-1-1-11111-1-1-1-1-11-1-1-1-1-11111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-111-111
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-111-1-11111-1-111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-11111-1-111-1-1-1
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-111-11111-1-111-1-11-11
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11111-11-111-1-1-1-111-1-11111-1-1-1-1-1-11111-11-1111-1-1-1-11111-1-11-11-1-1-1-1-1-1-1-1111
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1111111-11-1
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1-111-1-111-1-1-1-11-1-1-1-1-11111-1-111-1-111-1-1-11111-1-1-111
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111111-11-1-11111-1-111-1-1-1-111-1-1-1-111111-11-1-1-11111-1-1-1-1111-11-1-1-1-1-1-11111-1
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-111-11-1-111-1-11111-1-1-11111-1-111111-1-1
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-11111-1-1-1-1-1-11
χ17222222-1-1-122222-1222-1-1222-1-122-1-1-1-1222200-12-122-1-1-1-1-1-1-1-1-1-1-10000022222222000000-1-1-1-122000000-1-102-1-1-1-1-1-1-1-10000200-1-10000000-10
χ18222222-1-1-122222-1222-1-1222-1-122-1-1-1-122-2-200-12-122-1-1-1-1-1-1-1-1-1-1-100000-222222-2-2000000-1-111-2-2000000-110-2-1-1-1-111110000-20011000000010
χ19222222-1-1-122222-1222-1-1222-1-122-1-1-1-1-2-22200-12-122-1-1-1-1-1-1-1-1-1-1-1000002-2-2-2-2-22200000011-1-1-2-20000001-1021111-1-1-1-10000-20011000000010
χ20222222-1-1-122222-1222-1-1222-1-122-1-1-1-1-2-2-2-200-12-122-1-1-1-1-1-1-1-1-1-1-100000-2-2-2-2-2-2-2-2000000111122000000110-2111111110000200-1-10000000-10
χ21222222-1-1-122222-12-22-1-1-2-22-1-122-1-1-1-1222200-1-21-2-21111-1-1-1111100000-2-222-2-222000000-1-1-1-122000000110-2-1-111-1-1110000-200-1-1000000010
χ22222222-1-1-122222-12-22-1-1-2-22-1-122-1-1-1-122-2-200-1-21-2-21111-1-1-11111000002-222-2-2-2-2000000-1-111-2-20000001-102-1-11111-1-10000200110000000-10
χ23222222-1-1-122222-12-22-1-1-2-22-1-122-1-1-1-1-2-22200-1-21-2-21111-1-1-1111100000-22-2-2222200000011-1-1-2-2000000-110-211-1-1-1-1110000200110000000-10
χ24222222-1-1-122222-12-22-1-1-2-22-1-122-1-1-1-1-2-2-2-200-1-21-2-21111-1-1-111110000022-2-222-2-2000000111122000000-1-10211-1-111-1-10000-200-1-1000000010
χ2522222-122222-1-1-1222-12-122-12-1-1-122-1-1002222-1-12-1-122-1-1-1-1-1-1-1-1-100002200000-1-12222-1-100220022000002-1-10000-1-1-1-1-1-1-1-100200-1-10000-100
χ2622222-122222-1-1-1222-12-122-12-1-1-122-1-10022-2-2-1-12-1-122-1-1-1-1-1-1-1-1-10000-2200000-1-1-2-2-2-211002200-2-20000021-10000-1-1-1-1111100-200110000100
χ2722222-122222-1-1-1222-12-122-12-1-1-122-1-100-2-222-1-12-1-122-1-1-1-1-1-1-1-1-100002-200000112222-1-100-2-200-2-200000-2-1100001111-1-1-1-100-200110000100
χ2822222-122222-1-1-1222-12-122-12-1-1-122-1-100-2-2-2-2-1-12-1-122-1-1-1-1-1-1-1-1-10000-2-20000011-2-2-2-21100-2-2002200000-21100001111111100200-1-10000-100
χ2922222-122222-1-1-122-2-12-1-2-2-12-1-1-122-1-1002222-11-211-2-211-1-1-111110000-2-200000-1-122-2-2-1-10022002200000-2110000-1-111-1-11100-200-1-10000100
χ3022222-122222-1-1-122-2-12-1-2-2-12-1-1-122-1-10022-2-2-11-211-2-211-1-1-1111100002-200000-1-1-2-22211002200-2-200000-2-110000-1-11111-1-100200110000-100
χ3122222-122222-1-1-122-2-12-1-2-2-12-1-1-122-1-100-2-222-11-211-2-211-1-1-111110000-22000001122-2-2-1-100-2-200-2-20000021-1000011-1-1-1-11100200110000-100
χ3222222-122222-1-1-122-2-12-1-2-2-12-1-1-122-1-100-2-2-2-2-11-211-2-211-1-1-111110000220000011-2-2221100-2-20022000002-1-1000011-1-111-1-100-200-1-10000100
χ332222-12222-1-12222-12-1-12-1-1-1-12-1-1-1-122220022-122-1-1-1-122-1-1-1-1-1-1-12222202-1-1-1-100-1-1-1-12222000000-1-1-1-12020-1-1-1-10000-1-1-1-10200000-1-100000
χ342222-12222-1-12222-12-1-12-1-1-1-12-1-1-1-1222200-2-2-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-2-202-1-1-1-1001111-2-222000000111120-20-1-1-1-1000011110-2000001100000
χ352222-12222-1-12222-12-1-12-1-1-1-12-1-1-1-122-2-20022-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-220-2111100-1-1-1-122-2-20000001111-202011110000-1-1-1-10-2000001100000
χ362222-12222-1-12222-12-1-12-1-1-1-12-1-1-1-122-2-200-2-2-122-1-1-1-122-1-1-1-1-1-1-12222-20-21111001111-2-2-2-2000000-1-1-1-1-20-201111000011110200000-1-100000
χ372222-12222-1-12222-1-2-1-1211-1-12-1-1-1-122220022-1-2-21111-2-2-1-1-111112222-20-2-1-11100-1-1112222000000-1-1-1-1-20-20-1-1110000-1-1110-2000001100000
χ382222-12222-1-12222-1-2-1-1211-1-12-1-1-1-1222200-2-2-1-2-21111-2-2-1-1-11111-2-2-2-220-2-1-1110011-1-1-2-2220000001111-2020-1-111000011-1-10200000-1-100000
χ392222-12222-1-12222-1-2-1-1211-1-12-1-1-1-122-2-20022-1-2-21111-2-2-1-1-11111-2-2-2-2-20211-1-100-1-11122-2-2000000111120-2011-1-10000-1-1110200000-1-100000
χ402222-12222-1-12222-1-2-1-1211-1-12-1-1-1-122-2-200-2-2-1-2-21111-2-2-1-1-11111222220211-1-10011-1-1-2-2-2-2000000-1-1-1-1202011-1-1000011-1-10-2000001100000
χ4122-2-2222-2-22-22-2-22-2022200-2-2-22-22-22-20000002000000002-2-200002i2i−2i−2i00000000000000000002-22i−2i2i2i−2i−2i00000000000000000002-22i−2i0000000
χ4222-2-2222-2-22-22-2-22-2022200-2-2-22-22-22-20000002000000002-2-200002i2i−2i−2i0000000000000000000-22−2i2i2i2i−2i−2i0000000000000000000-22−2i2i0000000
χ4322-2-2222-2-22-22-2-22-2022200-2-2-22-22-22-20000002000000002-2-20000−2i−2i2i2i00000000000000000002-2−2i2i−2i−2i2i2i00000000000000000002-2−2i2i0000000
χ4422-2-2222-2-22-22-2-22-2022200-2-2-22-22-22-20000002000000002-2-20000−2i−2i2i2i0000000000000000000-222i−2i−2i−2i2i2i0000000000000000000-222i−2i0000000
χ452-22-22222-2-2-2-22-2-2202220022-2-2-2-2-2-222i−2i002i−2i200000000-22-200002-22-20002i−2i00002i−2i002i−2i2i−2i0000002-22-200002i−2i0000002i−2i0000000000000000
χ462-22-22222-2-2-2-22-2-2202220022-2-2-2-2-2-222i−2i00−2i2i200000000-22-20000-22-220002i−2i0000−2i2i00−2i2i2i−2i000000-22-2200002i−2i000000−2i2i0000000000000000
χ472-22-22222-2-2-2-22-2-2202220022-2-2-2-2-2-22−2i2i002i−2i200000000-22-20000-22-22000−2i2i00002i−2i002i−2i−2i2i000000-22-220000−2i2i0000002i−2i0000000000000000
χ482-22-22222-2-2-2-22-2-2202220022-2-2-2-2-2-22−2i2i00−2i2i200000000-22-200002-22-2000−2i2i0000−2i2i00−2i2i−2i2i0000002-22-20000−2i2i000000−2i2i0000000000000000
χ492-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-21111-222i−2i002i−2i-100−i3i3−i3i3001-11−i3−i3i3i32-22-2000−ii3−300−ii3−32i−2i2i−2i000000-11-110000−ii3−30000−ii3−30000000−i3i300000
χ502-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-21111-222i−2i00−2i2i-100−i3i3−i3i3001-11−i3−i3i3i3-22-22000−ii3−300i−i−33−2i2i2i−2i0000001-11-10000−ii3−30000i−i−330000000i3−i300000
χ512-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-21111-22−2i2i002i−2i-100−i3i3−i3i3001-11−i3−i3i3i3-22-22000i−i−3300−ii3−32i−2i−2i2i0000001-11-10000i−i−330000−ii3−30000000i3−i300000
χ522-22-2-1222-211-22-2-2-10-1-12−i3i3-1-1-21111-22−2i2i00−2i2i-100−i3i3−i3i3001-11−i3−i3i3i32-22-2000i−i−3300i−i−33−2i2i−2i2i000000-11-110000i−i−330000i−i−330000000−i3i300000
χ532-22-2-1222-211-22-2-2-10-1-12i3−i3-1-1-21111-222i−2i002i−2i-100i3−i3i3−i3001-11i3i3−i3−i32-22-2000−ii−3300−ii−332i−2i2i−2i000000-11-110000−ii−330000−ii−330000000i3−i300000
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χ552-22-2-1222-211-22-2-2-10-1-12i3−i3-1-1-21111-22−2i2i002i−2i-100i3−i3i3−i3001-11i3i3−i3−i3-22-22000i−i3−300−ii−332i−2i−2i2i0000001-11-10000i−i3−30000−ii−330000000−i3i300000
χ562-22-2-1222-211-22-2-2-10-1-12i3−i3-1-1-21111-22−2i2i00−2i2i-100i3−i3i3−i3001-11i3i3−i3−i32-22-2000i−i3−300i−i3−3−2i2i−2i2i000000-11-110000i−i3−30000i−i3−30000000i3−i300000
χ572-2-22222-22-22-2-22-2-2022200-2-22-22-22-2-2002i−2i00200000000-2-2200002i−2i−2i2i00000002i−2i000000002i−2i00002i−2i−2i2i000000002i−2i0000000000000002-2000
χ582-2-22222-22-22-2-22-2-2022200-2-22-22-22-2-2002i−2i00200000000-2-220000−2i2i2i−2i00000002i−2i000000002i−2i0000−2i2i2i−2i000000002i−2i000000000000000-22000
χ592-2-22222-22-22-2-22-2-2022200-2-22-22-22-2-200−2i2i00200000000-2-2200002i−2i−2i2i0000000−2i2i00000000−2i2i00002i−2i−2i2i00000000−2i2i000000000000000-22000
χ602-2-22222-22-22-2-22-2-2022200-2-22-22-22-2-200−2i2i00200000000-2-220000−2i2i2i−2i0000000−2i2i00000000−2i2i0000−2i2i2i−2i00000000−2i2i0000000000000002-2000
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χ704444-2-2444-2-2-2-2-24-241-2-2-2-21-2-211-2-2-2-20000-4-41-2411-2-2-2-211111110000-400000000222222000000000000002000000000-1-1-1-100000000000000
χ714444-2-2444-2-2-2-2-24-2-41-2-2221-2-211-2-2-2-200004412-4-1-12222111-1-1-1-10000-400000000-2-222-2-200000000000000200000000011-1-100000000000000
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χ7344-4-444-2224-44-4-4-2-404-2-200-4224-4-22-22000000-200000000-2220000000000000000000000000004-40000000000000000000000000-22000000000
χ7444-4-444-2224-44-4-4-2-404-2-200-4224-4-22-22000000-200000000-222000000000000000000000000000-4400000000000000000000000002-2000000000
χ7544-4-44-24-4-44-4-2224-40-24-2002-42-224-4-22000000-200000000-222000000000000000000000000000004i−4i0000000000000000000000000−2i2i0000000
χ7644-4-44-24-4-44-4-2224-40-24-2002-42-224-4-22000000-200000000-22200000000000000000000000000000−4i4i00000000000000000000000002i−2i0000000
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χ7844-4-4-244-4-4-224-4-4420-2-240022-4-22-224-4000000-200000000-2220000−4i−4i4i4i000000000000000000000002i2i−2i−2i000000000000000000000000000000
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χ814-44-44-244-4-4-42-22-440-24-200-24222-4-42-200004i−4i-2000000002-22000000000000000004i−4i00−2i2i000000000000000000000000−2i2i0000000000000000
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χ844-44-4-24-2-2222-44-42-20-21-2−2i32i3-21222-1-12-2−4i4i0000100−2i32i3i3−i300-11-1i3i3−i3−i300000002i−2i−2323000000002i−2i00000000000000−ii3−30000000000000000000000
χ854-44-4-24-2-2222-44-42-20-21-22i3−2i3-21222-1-12-24i−4i00001002i3−2i3−i3i300-11-1−i3−i3i3i30000000−2i2i−232300000000−2i2i00000000000000i−i3−30000000000000000000000
χ864-44-4-24-2-2222-44-42-20-21-22i3−2i3-21222-1-12-2−4i4i00001002i3−2i3−i3i300-11-1−i3−i3i3i300000002i−2i23−23000000002i−2i00000000000000−ii−330000000000000000000000
χ874-44-4-2-244-4222-22-4-201-2-2−2i32i31-22-1-1222-200004i−4i100i3−i3−2i32i300-11-1i3i3−i3−i30000000000000−2i2i23−23−2i2i000000000000000000000000i−i−3300000000000000
χ884-44-4-2-244-4222-22-4-201-2-2−2i32i31-22-1-1222-20000−4i4i100i3−i3−2i32i300-11-1i3i3−i3−i300000000000002i−2i−23232i−2i000000000000000000000000−ii3−300000000000000
χ894-44-4-2-244-4222-22-4-201-2-22i3−2i31-22-1-1222-200004i−4i100−i3i32i3−2i300-11-1−i3−i3i3i30000000000000−2i2i−2323−2i2i000000000000000000000000i−i3−300000000000000
χ904-44-4-2-244-4222-22-4-201-2-22i3−2i31-22-1-1222-20000−4i4i100−i3i32i3−2i300-11-1−i3−i3i3i300000000000002i−2i23−232i−2i000000000000000000000000−ii−3300000000000000
χ914-4-4444-22-2-44-4-442-404-2-200-42-2-442-222004i−4i00-20000000022-20000000000000004i−4i00000000−2i2i0000000000000000−2i2i00000000000000000000
χ924-4-4444-22-2-44-4-442-404-2-200-42-2-442-22200−4i4i00-20000000022-2000000000000000−4i4i000000002i−2i00000000000000002i−2i00000000000000000000
χ934-4-444-24-44-4422-2-4-40-24-2002-4-22-2-4422004i−4i00-20000000022-2000000000000000−2i2i000000004i−4i0000000000000000−2i2i00000000000000000000
χ944-4-444-24-44-4422-2-4-40-24-2002-4-22-2-442200−4i4i00-20000000022-20000000000000002i−2i00000000−4i4i00000000000000002i−2i00000000000000000000
χ954-4-444-2-22-2-4422-22-40-2-21002212-22-2-1-1004i−4i0010000003-3-1-113-33-300000000000−2i2i00000000−2i2i0000000000000000i−i3i−3i000000000000000000
χ964-4-444-2-22-2-4422-22-40-2-21002212-22-2-1-1004i−4i001000000-33-1-11-33-3300000000000−2i2i00000000−2i2i0000000000000000i−i−3i3i000000000000000000
χ974-4-444-2-22-2-4422-22-40-2-21002212-22-2-1-100−4i4i0010000003-3-1-113-33-3000000000002i−2i000000002i−2i0000000000000000−ii−3i3i000000000000000000
χ984-4-444-2-22-2-4422-22-40-2-21002212-22-2-1-100−4i4i001000000-33-1-11-33-33000000000002i−2i000000002i−2i0000000000000000−ii3i−3i000000000000000000
χ994-4-44-244-442-2-4-44-420-2-24002242-22-2-4-4000000-20000000022-200004i−4i−4i4i00000000000000000000000−2i2i2i−2i000000000000000000000000000000
χ1004-4-44-244-442-2-4-44-420-2-24002242-22-2-4-4000000-20000000022-20000−4i4i4i−4i000000000000000000000002i−2i−2i2i000000000000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222000000-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222000000-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-4448-8-444-4-80-4-420044-2-44-442-20000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-444-448-8-8-440-42-4004-24-442-2-440000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-48-8-8-44-4448402-4-400-2442-2-44-440000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-444-44-444-44022200-2-2-22-22-22-2000000-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-44-444-44022200-2-2-22-22-22-2000000-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-44-8-84-44480-4-4200-4-4-24444-22000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4-44444-444-40222−4i34i322-2-2-2-2-2-22000000-1002i3−2i32i3−2i3001-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-44444-444-402224i3−4i322-2-2-2-2-2-22000000-100−2i32i3−2i32i3001-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-44-44-4-8-88440-42-4004-2-44-4-2244000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-884-444-4-8402-4-400-24-4-224-444000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44-44-444-444022200-2-22-22-22-2-2000000-10000006-611-1-33-330000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44-44-444-444022200-2-22-22-22-2-2000000-1000000-6611-13-33-30000000000000000000000000000000000000000000000000000000000000

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