Finite Group Databasebeta

← Group #13167976

Character table — Group #13167976

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order1222333666666666333466666666612124444443666121212121212121212121212222244412121212121212121212121212121212444466661212121212121212121212121212121222412121212121244664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-11-11111111-1-11111-1-1-1-111-1-1-1-1-1-11-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-11111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111111-1-111-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1111111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1-111111-1-111-1-1-1-1111-1111-1-111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-1-1-111-1-1-1-11-1-1-1-1-111-1-11111-1-11-1111-1-111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1111111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-11
χ17222222-122-12-1222-12-1-122-1-12-1-1-12-122002222-1-1-1-12-122-1-1-1-1-1-1-1-1000002222-1-100-1-100002222002200000-12-1-1-1-1-10000-1-1-1-10200000-1-1000-10
χ18222222-122-12-1222-12-1-122-1-12-1-1-12-1220022-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1000002-2-2-21100-1-10000222200-2-200000-1-2111110000-1-1-1-10-2000001100010
χ19222222-122-12-1222-12-1-122-1-12-1-1-12-12200-2-222-1-1-1-12-122-1-1-1-1-1-1-1-100000-2222-1-100110000-2-2-2-200-2-20000012-1-1-1-1-1000011110-2000001100010
χ20222222-122-12-1222-12-1-122-1-12-1-1-12-12200-2-2-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100000-2-2-2-21100110000-2-2-2-20022000001-211111000011110200000-1-1000-10
χ21222222-122-12-1222-12-1-1-22-1-12-1-1-12-1-2-2002222-1-1-1-1-21-2-21111111100000-2-222-1-100-1-1000022-2-20022000001-2111-1-10000-1-1110-200000-1-100010
χ22222222-122-12-1222-12-1-1-22-1-12-1-1-12-1-2-20022-2-2-1-1-1-1-21-2-21111111100000-22-2-21100-1-1000022-2-200-2-20000012-1-1-1110000-1-111020000011000-10
χ23222222-122-12-1222-12-1-1-22-1-12-1-1-12-1-2-200-2-222-1-1-1-1-21-2-211111111000002-222-1-100110000-2-22200-2-200000-1-2111-1-1000011-1-1020000011000-10
χ24222222-122-12-1222-12-1-1-22-1-12-1-1-12-1-2-200-2-2-2-2-1-1-1-1-21-2-2111111110000022-2-21100110000-2-222002200000-12-1-1-111000011-1-10-200000-1-100010
χ2522222-122-12-1222-12-12-12-12-1-12-1-1-1222220022-1-1-1-1-12-1-122-1-1-1-1-1-10000202-1-122-1-1002222000022000000-10-12-1-1-1-1-1-1-1-1000020000-1-10000-100
χ2622222-122-12-1222-12-12-12-12-1-12-1-1-12222200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1000020-211-2-2-1-10022220000-2-2000000-101-21111-1-1-1-10000-20000110000100
χ2722222-122-12-1222-12-12-12-12-1-12-1-1-1222-2-20022-1-1-1-1-12-1-122-1-1-1-1-1-10000-202-1-1221100-2-2-2-20000-2-200000010-12-1-1-1-111110000-20000110000100
χ2822222-122-12-1222-12-12-12-12-1-12-1-1-1222-2-200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10000-20-211-2-21100-2-2-2-2000022000000101-211111111000020000-1-10000-100
χ2922222-122-12-1222-12-12-1-2-12-1-12-1-1-12-2-2220022-1-1-1-11-211-2-21111110000-20-2-1-122-1-10022-2-2000022000000101-211-1-1-1-1110000-20000-1-10000100
χ3022222-122-12-1222-12-12-1-2-12-1-12-1-1-12-2-22200-2-2-1-1-1-11-211-2-21111110000-20211-2-2-1-10022-2-20000-2-200000010-12-1-111-1-111000020000110000-100
χ3122222-122-12-1222-12-12-1-2-12-1-12-1-1-12-2-2-2-20022-1-1-1-11-211-2-2111111000020-2-1-1221100-2-2220000-2-2000000-101-211-1-111-1-1000020000110000-100
χ3222222-122-12-1222-12-12-1-2-12-1-12-1-1-12-2-2-2-200-2-2-1-1-1-11-211-2-2111111000020211-2-21100-2-222000022000000-10-12-1-11111-1-10000-20000-1-10000100
χ332222-122-12222-1-122-1-122-1-12-1-122-1-1-1-1222200-1-1-1-122-1-1-1-122-1-1-1-1222222000002222-1-1-1-1-1-1-1-10000-1-1-1-122000000-1-1-1-1-1-1-1-1002-1-1000000000
χ342222-122-12222-1-122-1-122-1-12-1-122-1-1-1-122-2-200-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-22-20000022-2-2-1-1-1-11111000011112-2000000-1-1-1-1111100-211000000000
χ352222-122-12222-1-122-1-122-1-12-1-122-1-1-1-1-2-22200-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2200000-2-2221111-1-1-1-100001111-220000001111-1-1-1-100-211000000000
χ362222-122-12222-1-122-1-122-1-12-1-122-1-1-1-1-2-2-2-200-1-1-1-122-1-1-1-122-1-1-1-12222-2-200000-2-2-2-2111111110000-1-1-1-1-2-200000011111111002-1-1000000000
χ372222-122-12222-1-122-1-12-2-1-12-1-122-1-111222200-1-1-1-1-2-21111-2-211112222-2-2000002222-1-111-1-1110000-1-1-1-1-2-2000000-1-111-1-11100-211000000000
χ382222-122-12222-1-122-1-12-2-1-12-1-122-1-11122-2-200-1-1-1-1-2-21111-2-21111-2-2-2-2-220000022-2-2-1-11111-1-100001111-22000000-1-11111-1-1002-1-1000000000
χ392222-122-12222-1-122-1-12-2-1-12-1-122-1-111-2-22200-1-1-1-1-2-21111-2-21111-2-2-2-22-200000-2-22211-1-1-1-111000011112-200000011-1-1-1-111002-1-1000000000
χ402222-122-12222-1-122-1-12-2-1-12-1-122-1-111-2-2-2-200-1-1-1-1-2-21111-2-2111122222200000-2-2-2-211-1-111-1-10000-1-1-1-12200000011-1-111-1-100-211000000000
χ4122-2-2222-2-2-222-22-2-22220-2-22-2-2-2-2220000000022-2-200000000000022-2-200000000000000000002i−2i2i−2i22-2-20000000000000000000002i−2i2i−2i00000
χ4222-2-2222-2-2-222-22-2-22220-2-22-2-2-2-2220000000022-2-200000000000022-2-20000000000000000000−2i2i−2i2i22-2-2000000000000000000000−2i2i−2i2i00000
χ4322-2-2222-2-2-222-22-2-22220-2-22-2-2-2-2220000000022-2-2000000000000-2-22200000000000000000002i−2i−2i2i-2-2220000000000000000000002i−2i−2i2i00000
χ4422-2-2222-2-2-222-22-2-22220-2-22-2-2-2-2220000000022-2-2000000000000-2-2220000000000000000000−2i2i2i−2i-2-222000000000000000000000−2i2i2i−2i00000
χ452-22-2222-222-2-22-2-2-22220-2-2-222-22-2-2002i−2i2i−2i002-2-220000000000002-22-200000002i−2i2i−2i2i−2i002i−2i0000002-22-2000000002i−2i002i−2i0000000000000000
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χ472-22-2222-222-2-22-2-2-22220-2-2-222-22-2-200−2i2i2i−2i002-2-22000000000000-22-220000000−2i2i2i−2i−2i2i002i−2i000000-22-2200000000−2i2i002i−2i0000000000000000
χ482-22-2222-222-2-22-2-2-22220-2-2-222-22-2-200−2i2i−2i2i002-2-220000000000002-22-20000000−2i2i−2i2i−2i2i00−2i2i0000002-22-200000000−2i2i00−2i2i0000000000000000
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χ502-22-2-122122-2-2-11-2-2-1-12011-2-1-1-2211−i3i32i−2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i3-22-2200000002i−2i−2i2i−ii3−3i−i−3300001-11-100000000−ii3−3i−i−33000i3−i3000000000
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χ522-22-2-122122-2-2-11-2-2-1-12011-2-1-1-2211−i3i3−2i2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i32-22-20000000−2i2i−2i2ii−i−33i−i−330000-11-1100000000i−i−33i−i−33000−i3i3000000000
χ532-22-2-122122-2-2-11-2-2-1-12011-2-1-1-2211i3−i32i−2i2i−2i00-111-100i3−i3i3−i300i3i3−i3−i32-22-200000002i−2i2i−2i−ii−33−ii−330000-11-1100000000−ii−33−ii−33000i3−i3000000000
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χ844-44-4-24-224-2-42-22-42-21-202-12-212-22-1−2i32i300−4i4i001-1-1100−2i32i3i3−i300i3i3−i3−i300000000000002i−2i00002i−2i−232300000000000000000000−ii3−300000000000000
χ854-44-4-24-224-2-42-22-42-21-202-12-212-22-12i3−2i3004i−4i001-1-11002i3−2i3−i3i300−i3−i3i3i30000000000000−2i2i0000−2i2i−232300000000000000000000i−i3−300000000000000
χ864-44-4-24-224-2-42-22-42-21-202-12-212-22-12i3−2i300−4i4i001-1-11002i3−2i3−i3i300−i3−i3i3i300000000000002i−2i00002i−2i23−2300000000000000000000−ii−3300000000000000
χ874-44-4-2-242-242-4-222-41-2-20-1221-22-2-12−2i32i34i−4i00001-1-1100i3−i3−2i32i300i3i3−i3−i300000000000−2i2i00−2i2i23−2300000000000000000000i−i−33000000000000000000
χ884-44-4-2-242-242-4-222-41-2-20-1221-22-2-12−2i32i3−4i4i00001-1-1100i3−i3−2i32i300i3i3−i3−i3000000000002i−2i002i−2i−232300000000000000000000−ii3−3000000000000000000
χ894-44-4-2-242-242-4-222-41-2-20-1221-22-2-122i3−2i34i−4i00001-1-1100−i3i32i3−2i300−i3−i3i3i300000000000−2i2i00−2i2i−232300000000000000000000i−i3−3000000000000000000
χ904-44-4-2-242-242-4-222-41-2-20-1221-22-2-122i3−2i3−4i4i00001-1-1100−i3i32i3−2i300−i3−i3i3i3000000000002i−2i002i−2i23−2300000000000000000000−ii−33000000000000000000
χ914-4-4444-24-42-42-4-44-24-2-204-22-42-22-420000004i−4i-22-2200000000000000000004i−4i−2i2i00000000000000000000000000−2i2i0000000000000000000000
χ924-4-4444-24-42-42-4-44-24-2-204-22-42-22-42000000−4i4i-22-220000000000000000000−4i4i2i−2i000000000000000000000000002i−2i0000000000000000000000
χ934-4-444-2442-42-4-4-4-24-24-20-2422-4-222-40000004i−4i-22-220000000000000000000−2i2i4i−4i00000000000000000000000000−2i2i0000000000000000000000
χ944-4-444-2442-42-4-4-4-24-24-20-2422-4-222-4000000−4i4i-22-2200000000000000000002i−2i−4i4i000000000000000000000000002i−2i0000000000000000000000
χ954-4-444-2-242222-4-4-2-2-2-210-2-2-1221-1220000004i−4i1-11-10000003i−3i3i−3i3i−3i0000000−2i2i−2i2i0000000000000000000000003-3i−i0000000000000000000000
χ964-4-444-2-242222-4-4-2-2-2-210-2-2-1221-1220000004i−4i1-11-1000000−3i3i−3i3i−3i3i0000000−2i2i−2i2i000000000000000000000000-33i−i0000000000000000000000
χ974-4-444-2-242222-4-4-2-2-2-210-2-2-1221-122000000−4i4i1-11-10000003i−3i3i−3i3i−3i00000002i−2i2i−2i000000000000000000000000-33−ii0000000000000000000000
χ984-4-444-2-242222-4-4-2-2-2-210-2-2-1221-122000000−4i4i1-11-1000000−3i3i−3i3i−3i3i00000002i−2i2i−2i0000000000000000000000003-3−ii0000000000000000000000
χ994-4-44-244-2-4-4-4-42244-2-240-2-2-4224-42200000000-22-220000000000004-4-4400000000000000000000000-222-2000000000000000000000000000000
χ1004-4-44-244-2-4-4-4-42244-2-240-2-2-4224-42200000000-22-22000000000000-444-4000000000000000000000002-2-22000000000000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-4-844-4-4-8844-4-42044244-2-2-4-40000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-44-848-44-4-84-42-404-2-44-244-420000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4844-8-484-44-82-4-40-24-4-24442-40000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4444-4-44-4442220-2-22-2-2-2-22200000000-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4444-4-44-4442220-2-22-2-2-2-22200000000-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-8-4-4448-844-4-42044-2-4-4-2244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-44-4-444-44442220-2-2-222-22-2-2−4i34i3000000-111-1002i3−2i32i3−2i300−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-4-444-44442220-2-2-222-22-2-24i3−4i3000000-111-100−2i32i3−2i32i300i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4-4-84-84448-4-42-40-4244-2-444-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-44-84-844-482-4-402-44-24-44-24000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-4444444-4-4222022-2-2-22-2-2-200000000-11-110000006i−6i−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-4444444-4-4222022-2-2-22-2-2-200000000-11-11000000−6i6i3i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000

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