Finite Group Databasebeta

← Group #13172119

Character table — Group #13172119

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order122233366666666623336666666666666666644366666666666624444121212121212121212121212121212121212121222666612121212121212121212224446644661212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-111-1111111-1-1111111111111-1-11111-1-11-111-1-1-1-11-1-11-1-1-1-1-1-111-1-1-1
χ31111111111111111111111111111111111111111111111111111-111-111111-1-111111111111111-1-1-1-1-1-111-11-1-11111-11-1-11-1-1-1-11-1-1-11-1
χ41111111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-11-11
χ51111111111111111111111111111111111111-1-1111111111111111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-1-111-1-1-1-1-11-1-1
χ61111111111111111111111111111111111111-1-111111111111111-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1-1-1-11-1-11-1-1111-1-1-111
χ71111111111111111111111111111111111111-1-11111111111111-11-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111-1-11-1-1-111-111-1-11
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111111-1-11-1-111-1-1-1-1-1111111-1-11-11-1
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-11-1-1-1111-1-1-1-11111-1-11111-1-1-1-1-1-11111-11-1-1-1-1-1-111-1111-1-1-1-1-11-111-11
χ111111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1111111-1-11-11-11-1-1-1-1-11-1111
χ121111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-111-1-1-1-1-111-111-1-11111-1-1-1111111-1-1-1-1
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111111-1-11-1-111-1-111-1-1-111-1-111-1-1-11
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-11-11-11-1-111-1-111-1-111-1-1-1-11111-1-11111-11-1-1-1-1-1-1111-11-11-1-111-11-111-1
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1111111-1-1-1111-1-1-1111-111-1-1
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1-1-1111-1-1111111-1-111-1-1-1-1111111-1-1-1-1-111-111-1-111-1-1-11111-1-1-1-11-111
χ17222222-12-1222-12-1222-1-1222222-12222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1220220000-1-1-1-1000000000000222-1-1-1222-1-1-1-1-1-1-100200-1-100000-100
χ18222222-12-1222-12-1222-1-1222222-12222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-12-202-20000-1-111000000000000-2-22-1-1-1-2-221-1-1111100-2001100000100
χ19222222-12-1222-12-1222-1-1222222-12222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-220-22000011-1-1000000000000-2-2-211122-2-111-1-1-1-100-2001100000100
χ20222222-12-1222-12-1222-1-1222222-12222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-20000111100000000000022-2111-2-2-2111111100200-1-100000-100
χ21222222-12-1222-12-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-111111-1-1-11111220-2-200001111000000000000222-1-1-12-2-2-111-1-11100-200-1-100000100
χ22222222-12-1222-12-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-111111-1-1-111112-20-22000011-1-1000000000000-2-22-1-1-1-22-211111-1-1002001100000-100
χ23222222-12-1222-12-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-111111-1-1-11111-2202-20000-1-111000000000000-2-2-21112-22-1-1-1-1-111002001100000-100
χ24222222-12-1222-12-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-111111-1-1-11111-2-20220000-1-1-1-100000000000022-2111-2221-1-111-1-100-200-1-100000100
χ2522222-12-1222-12-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-122-1222-1-1-1-1-1-1-1-1-120220-1-1-1-122002222-1-1-1-1-1-1-1-100-12-1-100-10-1-100002002000000-1-1000
χ2622222-12-1222-12-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-122-1222-1-1-1-1-1-1-1-1-1-202-20-1-1-1-1-2-2002222-1-1-1-1-1-1-1-1001-2110010110000-200-200000011000
χ2722222-12-1222-12-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-2-1222-1-1-1-1-1-1-1-1-120-22011112200-2-2-2-21111111100-12-1-100-10-1-10000-200-200000011000
χ2822222-12-1222-12-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-2-1222-1-1-1-1-1-1-1-1-1-20-2-201111-2-200-2-2-2-211111111001-21100101100002002000000-1-1000
χ2922222-12-1222-12-122-2-12-1-2-211-1-121111-1-122-1-122-1-2-2-211-1-1-1111120-2-20-1-111-2-20022-2-2-1-1-1-1111100-12-1-10010110000-20020000001-1000
χ3022222-12-1222-12-122-2-12-1-2-211-1-121111-1-122-1-122-1-2-2-211-1-1-11111-20-220-1-111220022-2-2-1-1-1-11111001-21100-10-1-10000200-2000000-11000
χ3122222-12-1222-12-122-2-12-1-2-211-1-121111-1-122-1-1-2-2-1-2-2-211-1-1-11111202-2011-1-1-2-200-2-2221111-1-1-1-100-12-1-10010110000200-2000000-11000
χ3222222-12-1222-12-122-2-12-1-2-211-1-121111-1-122-1-1-2-2-1-2-2-211-1-1-11111-2022011-1-12200-2-2221111-1-1-1-1001-21100-10-1-10000-20020000001-1000
χ332222-12222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-122-12-1-122-1-1-1-1-1-1-10220222220022-1-1-1-1-1-1-1-1-1-1-1-1000000-1-10200-1-1-1-1020020000-1000-10
χ342222-12222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-122-12-1-122-1-1-1-1-1-1-10-220-2222200-2-2-1-1-1-1-1-1-1-1-1-1-1-1000000110-20011110-200-20000100010
χ352222-12222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-12-1-122-1-1-1-1-1-1-102-202-2-2-2-20022111111111111000000-1-10200-1-1-1-10-200-20000100010
χ362222-12222-1-12222-12-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-12-1-122-1-1-1-1-1-1-10-2-20-2-2-2-2-200-2-2111111111111000000110-2001111020020000-1000-10
χ372222-12222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-122-1-211-2-2-1-1-1111102-20-222-2-200-2-2-1-111-1-1-1-11111000000-110200-1-1110-200200001000-10
χ382222-12222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-122-1-211-2-2-1-1-111110-2-20222-2-20022-1-111-1-1-1-111110000001-10-20011-1-10200-20000-100010
χ392222-12222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-1-211-2-2-1-1-111110220-2-2-22200-2-211-1-11111-1-1-1-1000000-110200-1-1110200-20000-100010
χ402222-12222-1-12222-1-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-1-211-2-2-1-1-111110-2202-2-222002211-1-11111-1-1-1-10000001-10-20011-1-10-200200001000-10
χ4122-2-22222-22-2-2-2-22-2022200002-2-200002-22-2-2-22i−2i2000002-2-20000000002i−2i0000002i−2i002i2i−2i−2i00002-200000000000000000002-22i−2i000000
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χ4544444-2-2-2-244-2-2-2-244-2-2144-2-2-2-2-2-2-2-2-211-2-21-2001-2-2-2111111111400400000-2-20000000000000000-2-21100-20110000000000000000000
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χ4844444-2-2-2-244-2-2-2-24-4-2-21-4-422-2-2-2222211-2-21-2001222-1-1111-1-1-1-1-400400000-2-2000000000000000022-1-100-20110000000000000000000
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χ534444-2-24-24-2-2-24-24-241-2-2-2-2-2-211-21111-2-2-2-2-214414-2-2-2-2111111100400-2-2-2-20000-2-2-2-2111111110000000000000000000000000000000
χ544444-2-24-24-2-2-24-24-241-2-2-2-2-2-211-21111-2-2-2-2-21-4-414-2-2-2-2111111100-400222200002222-1-1-1-1-1-1-1-10000000000000000000000000000000
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χ904-4-444-2-222-442-2-22-40-2-21002i3−2i32-222i3−2i3−2i32i3-1-12-212001000−i3i3-1-11−i3i3i3−i30000000002i3−2i30000000000000000003-30000−i3i30000000000000000000
χ914-4-44-244-4-42-2-444-420-2-2400002-220000-4-42-24200-20000022-2000000000000000000023−23000023−23−23230000000000000000000000000000000
χ924-4-44-244-4-42-2-444-420-2-2400002-220000-4-42-24200-20000022-20000000000000000000−23230000−232323−230000000000000000000000000000000
χ934-4-44-2-242-42-224-2-4201-2-200−2i32i3-112i3−i3−i3i3222-2-2-1001000−2i32i3-1-11i3−i3−i3i300000000000000023−233i−3i−3i3i−333−30000000000000000000000000000000
χ944-4-44-2-242-42-224-2-4201-2-200−2i32i3-112i3−i3−i3i3222-2-2-1001000−2i32i3-1-11i3−i3−i3i3000000000000000−2323−3i3i3i−3i3−3−330000000000000000000000000000000
χ954-4-44-2-242-42-224-2-4201-2-2002i3−2i3-112−i3i3i3−i3222-2-2-10010002i3−2i3-1-11−i3i3i3−i300000000000000023−23−3i3i3i−3i−333−30000000000000000000000000000000
χ964-4-44-2-242-42-224-2-4201-2-2002i3−2i3-112−i3i3i3−i3222-2-2-10010002i3−2i3-1-11−i3i3i3−i3000000000000000−23233i−3i−3i3i3−3−330000000000000000000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4-4-4222222222222200-1-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4-82224444222-2-2-2-222222200-14-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-448-8444-4-80-4-420000-44400002-2-44-24002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-484-44-84-8-440-42-40000-44-20000-442-244002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-44-44444-44022200002-2-266-6-62-22-2-2-200-100000-111-3-33300000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-44-44444-44022200002-2-2-6-6662-22-2-2-200-100000-11133-3-300000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-44-4-8-8-444480-4-42000044-40000-2244-2-400200000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-444-4444-40222−4i34i300-2-222i3−2i32i3−2i3-22-2-2-2200-102i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-444-4444-402224i3−4i300-2-22−2i32i3−2i32i3-22-2-2-2200-10−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-4-844-4-8-48440-42-400004-4-2000044-22-4400200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444-44-4-444022200−4i34i3-22-22i3−2i3−2i32i3-2-2-222-200-10002i3−2i311-1−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444-44-4-4440222004i3−4i3-22-2−2i32i32i3−2i3-2-2-222-200-1000−2i32i311-1i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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