Finite Group Databasebeta

← Group #13168557

Character table — Group #13168557

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order122233366666666633346666666661212444444366612121212121212121212121244412121212121212121212121212121212224412121212121212121212121212121212121212122444666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-1-1-1111111111111-1-111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-11111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111-111111111-1-1-1-1-11-11-1-1-1-111-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-11-11-1-1-111-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-111111-1-1-1-111111-11-1-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-11-11-1-1-1-111111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-1-11111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-111-111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-111-1-1111111-1-1-1111-1-111-1-1-1-111-1-111-1-1-1-11111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1111111-1-11-111-1-1-1-11111-1-111-1-1-1-111-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-111-1-1-1-1111111111-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-111-111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1111-1-1111111111-1-1-1
χ17222222-1222-1-1-12222-1-122-1-1-1-122-1-1-1-1222200-1-1-1-122-1-1-1-122-1-1-1-122000-1-1-1-1-1-1-1-12222002222-1-1-1-100220000-1-1-1-1-1-1-1-10000-1-1000000000
χ18222222-1222-1-1-12222-1-122-1-1-1-122-1-1-1-122-2-200-1-1-1-122-1-1-1-122-1-1-1-12-2000-1-1-1-1111122-2-200-2-2-2-21111002-20000-1-1-1-11111000011000000000
χ19222222-1222-1-1-12222-1-122-1-1-1-122-1-1-1-1-2-22200-1-1-1-122-1-1-1-122-1-1-1-1-220001111-1-1-1-1-2-22200-2-2-2-2111100-2200001111-1-1-1-1000011000000000
χ20222222-1222-1-1-12222-1-122-1-1-1-122-1-1-1-1-2-2-2-200-1-1-1-122-1-1-1-122-1-1-1-1-2-200011111111-2-2-2-2002222-1-1-1-100-2-20000111111110000-1-1000000000
χ21222222-1222-1-1-12222-1-1-22-1-1-1-122-1-111222200-1-1-1-1-2-21111-2-21111-2-2000-1-111-1-11122220022-2-2111100-2-20000-1-111-1-1110000-1-1000000000
χ22222222-1222-1-1-12222-1-1-22-1-1-1-122-1-11122-2-200-1-1-1-1-2-21111-2-21111-22000-1-11111-1-122-2-200-2-222-1-1-1-100-220000-1-11111-1-1000011000000000
χ23222222-1222-1-1-12222-1-1-22-1-1-1-122-1-111-2-22200-1-1-1-1-2-21111-2-211112-200011-1-1-1-111-2-22200-2-222-1-1-1-1002-2000011-1-1-1-111000011000000000
χ24222222-1222-1-1-12222-1-1-22-1-1-1-122-1-111-2-2-2-200-1-1-1-1-2-21111-2-211112200011-1-111-1-1-2-2-2-20022-2-211110022000011-1-111-1-10000-1-1000000000
χ2522222-12-12-122222-1-12-12-12-12-1-1-12-122002222-1-1-1-1-1222-1-1-1-1-1-1-1-1022220000222200-1-1-1-100000000-120-1-1-1-1-10000-1-1-1-1202000-1-100000-10
χ2622222-12-12-122222-1-12-12-12-12-1-1-12-1220022-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-102-2-2-20000222200-1-111000000001-20-111110000-1-1-1-1-20-2000110000010
χ2722222-12-12-122222-1-12-12-12-12-1-1-12-12200-2-222-1-1-1-1-1222-1-1-1-1-1-1-1-10-22220000-2-2-2-20011-1-100000000-1201-1-1-1-100001111-20-2000110000010
χ2822222-12-12-122222-1-12-12-12-12-1-1-12-12200-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-2-2-20000-2-2-2-2001111000000001-201111100001111202000-1-100000-10
χ2922222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-2002222-1-1-1-11-2-2-2111111110-2-222000022-2-200-1-1-1-1000000001-201-1-1110000-1-11120-2000-1-10000010
χ3022222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-20022-2-2-1-1-1-11-2-2-2111111110-22-2-2000022-2-200-1-11100000000-120111-1-10000-1-111-2020001100000-10
χ3122222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-200-2-222-1-1-1-11-2-2-21111111102-2220000-2-2220011-1-1000000001-20-1-1-111000011-1-1-2020001100000-10
χ3222222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-200-2-2-2-2-1-1-1-11-2-2-211111111022-2-20000-2-22200111100000000-120-111-1-1000011-1-120-2000-1-10000010
χ332222-1222-12222-1-12-1-122-1-12-12-1-1-1222220022-1-1-1-12-1-1-122-1-1-1-1-1-1202-1-122220000-1-10022000000002-1-10-1-1-1-1-1-1-1-1000002020000-1-100-100
χ342222-1222-12222-1-12-1-122-1-12-12-1-1-12222200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-120-21122220000-1-100-2-200000000-21-101111-1-1-1-100000-20-200001100100
χ352222-1222-12222-1-12-1-122-1-12-12-1-1-1222-2-20022-1-1-1-12-1-1-122-1-1-1-1-1-1-202-1-1-2-2-2-20000110022000000002-110-1-1-1-1111100000-20-200001100100
χ362222-1222-12222-1-12-1-122-1-12-12-1-1-1222-2-200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-211-2-2-2-200001100-2-200000000-211011111111000002020000-1-100-100
χ372222-1222-12222-1-12-1-12-2-1-12-12-1-1-12-2-2220022-1-1-1-1-2111-2-2111111-20-2-1-122-2-20000-1-1002200000000-2110-1-111-1-11100000-2020000-1-100100
χ382222-1222-12222-1-12-1-12-2-1-12-12-1-1-12-2-22200-2-2-1-1-1-1-2111-2-2111111-2021122-2-20000-1-100-2-2000000002-11011-1-1-1-1110000020-200001100-100
χ392222-1222-12222-1-12-1-12-2-1-12-12-1-1-12-2-2-2-20022-1-1-1-1-2111-2-211111120-2-1-1-2-222000011002200000000-21-10-1-11111-1-10000020-200001100-100
χ402222-1222-12222-1-12-1-12-2-1-12-12-1-1-12-2-2-2-200-2-2-1-1-1-1-2111-2-211111120211-2-22200001100-2-2000000002-1-1011-1-111-1-100000-2020000-1-100100
χ412-22-2222-22-22-2-2-2-222220-22-2-2-22-2-220000002-222-2-20000000000000002-20000000000002-2002i−2i2i2i−2i−2i00002-2000000000000000000002i−2i000
χ422-22-2222-22-22-2-2-2-222220-22-2-2-22-2-220000002-222-2-20000000000000002-20000000000002-200−2i2i−2i−2i2i2i00002-200000000000000000000−2i2i000
χ432-22-2222-22-22-2-2-2-222220-22-2-2-22-2-22000000-2222-2-2000000000000000-22000000000000-22002i−2i2i2i−2i−2i0000-2200000000000000000000−2i2i000
χ442-22-2222-22-22-2-2-2-222220-22-2-2-22-2-22000000-2222-2-2000000000000000-22000000000000-2200−2i2i−2i−2i2i2i0000-22000000000000000000002i−2i000
χ452-2-22222-2-22-2-222-2-22220-2-2-222-22-2-2002i−2i2i−2i002-2-22000000000000000002i−2i002i−2i002i−2i2i−2i002-2000000000000002i−2i002i−2i0000002-2000000000
χ462-2-22222-2-22-2-222-2-22220-2-2-222-22-2-2002i−2i−2i2i002-2-22000000000000000002i−2i00−2i2i002i−2i−2i2i00-22000000000000002i−2i00−2i2i000000-22000000000
χ472-2-22222-2-22-2-222-2-22220-2-2-222-22-2-200−2i2i2i−2i002-2-2200000000000000000−2i2i002i−2i00−2i2i2i−2i00-2200000000000000−2i2i002i−2i000000-22000000000
χ482-2-22222-2-22-2-222-2-22220-2-2-222-22-2-200−2i2i−2i2i002-2-2200000000000000000−2i2i00−2i2i00−2i2i−2i2i002-200000000000000−2i2i00−2i2i0000002-2000000000
χ492-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211−i3i32i−2i2i−2i00-111-100−i3i3−i3i300−i3−i3i3i300000−ii3−3−ii3−32i−2i2i−2i002-200−i3i3−i3i300000000−ii3−3−ii3−30000-11000000000
χ502-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211−i3i32i−2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i300000−ii3−3i−i−332i−2i−2i2i00-2200i3−i3i3−i300000000−ii3−3i−i−3300001-1000000000
χ512-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211−i3i3−2i2i2i−2i00-111-100−i3i3−i3i300−i3−i3i3i300000i−i−33−ii3−3−2i2i2i−2i00-2200i3−i3i3−i300000000i−i−33−ii3−300001-1000000000
χ522-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211−i3i3−2i2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i300000i−i−33i−i−33−2i2i−2i2i002-200−i3i3−i3i300000000i−i−33i−i−330000-11000000000
χ532-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211i3−i32i−2i2i−2i00-111-100i3−i3i3−i300i3i3−i3−i300000−ii−33−ii−332i−2i2i−2i002-200i3−i3i3−i300000000−ii−33−ii−330000-11000000000
χ542-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211i3−i32i−2i−2i2i00-111-100i3−i3i3−i300i3i3−i3−i300000−ii−33i−i3−32i−2i−2i2i00-2200−i3i3−i3i300000000−ii−33i−i3−300001-1000000000
χ552-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211i3−i3−2i2i2i−2i00-111-100i3−i3i3−i300i3i3−i3−i300000i−i3−3−ii−33−2i2i2i−2i00-2200−i3i3−i3i300000000i−i3−3−ii−3300001-1000000000
χ562-2-2222-1-2-2211-12-2-22-1-10-211-1-1-2211i3−i3−2i2i−2i2i00-111-100i3−i3i3−i300i3i3−i3−i300000i−i3−3i−i3−3−2i2i−2i2i002-200i3−i3i3−i300000000i−i3−3i−i3−30000-11000000000
χ5744444-2-2-24-2-2-2-244-2-2-214-2-21-21-2-2-21-2-20044001111-24-2-211-2-21111040000000-2-2-2-200-2-20000000000000-2000000001111000000000000000
χ5844444-2-2-24-2-2-2-244-2-2-214-2-21-21-2-2-21-2-200-4-4001111-24-2-211-2-211110-40000000222200220000000000000200000000-1-1-1-1000000000000000
χ5944444-2-2-24-2-2-2-244-2-2-21-4-2-21-21-2-2-212200440011112-422-1-122-1-1-1-10-40000000-2-22200-2-2000000000000020000000011-1-1000000000000000
χ6044444-2-2-24-2-2-2-244-2-2-21-4-2-21-21-2-2-212200-4-40011112-422-1-122-1-1-1-104000000022-2-200220000000000000-200000000-1-111000000000000000
χ614444-24-24-24-2-2-2-2-24-21-24-21-21-2-2-21-2-2-244000011114-211-2-2-2-2111140000-2-2-2-20000-2-200000000000000-20000011110000000000000000000
χ624444-24-24-24-2-2-2-2-24-21-24-21-21-2-2-21-2-2-2-4-4000011114-211-2-2-2-21111-40000222200002200000000000000200000-1-1-1-10000000000000000000
χ634444-24-24-24-2-2-2-2-24-21-2-4-21-21-2-2-21-2224400001111-42-1-12222-1-1-1-1-40000-2-2220000-2-20000000000000020000011-1-10000000000000000000
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χ814-44-4-244-4-2-44-4-4224-2-2402-2-42-4-2224000000-44-2-2220000000000000002-2000000000000-440000000000002-20000000000000000000000000
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χ864-4-444-242-4-2-4-444-42-24-202-424-22-2-4200004i−4i00-222-20000000000000000000004i−4i0000−2i2i0000000000000000000000−2i2i00000000000000000
χ874-4-444-242-4-2-4-444-42-24-202-424-22-2-420000−4i4i00-222-2000000000000000000000−4i4i00002i−2i00000000000000000000002i−2i00000000000000000
χ884-4-444-2-22-4-222-24-42-2-21022-1-212-22-1−2i32i3004i−4i001-1-1100−2i32i3i3−i300i3i3−i3−i3000000000−2i2i23−2300−2i2i0000000000000000000000i−i−33000000000000000
χ894-4-444-2-22-4-222-24-42-2-21022-1-212-22-1−2i32i300−4i4i001-1-1100−2i32i3i3−i300i3i3−i3−i30000000002i−2i−2323002i−2i0000000000000000000000−ii3−3000000000000000
χ904-4-444-2-22-4-222-24-42-2-21022-1-212-22-12i3−2i3004i−4i001-1-11002i3−2i3−i3i300−i3−i3i3i3000000000−2i2i−232300−2i2i0000000000000000000000i−i3−3000000000000000
χ914-4-444-2-22-4-222-24-42-2-21022-1-212-22-12i3−2i300−4i4i001-1-11002i3−2i3−i3i300−i3−i3i3i30000000002i−2i23−23002i−2i0000000000000000000000−ii−33000000000000000
χ924-4-44-244-424-4-44-22-4-2-24022-4-242-22-4004i−4i0000-222-2000000000000000004i−4i000000−2i2i00000000000000000000−2i2i000000000000000000000
χ934-4-44-244-424-4-44-22-4-2-24022-4-242-22-400−4i4i0000-222-200000000000000000−4i4i0000002i−2i000000000000000000002i−2i000000000000000000000
χ944-4-44-24-2-42422-2-22-4-21-202-121-22-2-12−2i32i34i−4i00001-1-1100i3−i3−2i32i300i3i3−i3−i300000−2i2i23−230000−2i2i00000000000000000000i−i−330000000000000000000
χ954-4-44-24-2-42422-2-22-4-21-202-121-22-2-12−2i32i3−4i4i00001-1-1100i3−i3−2i32i300i3i3−i3−i3000002i−2i−232300002i−2i00000000000000000000−ii3−30000000000000000000
χ964-4-44-24-2-42422-2-22-4-21-202-121-22-2-122i3−2i34i−4i00001-1-1100−i3i32i3−2i300−i3−i3i3i300000−2i2i−23230000−2i2i00000000000000000000i−i3−30000000000000000000
χ974-4-44-24-2-42422-2-22-4-21-202-121-22-2-122i3−2i3−4i4i00001-1-1100−i3i32i3−2i300−i3−i3i3i3000002i−2i23−2300002i−2i00000000000000000000−ii−330000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-4-844-44-884-4-420-4424-244-4-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-484-84-444-4-8-42-40-4-2-4-244424000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48-444-88-84-442-4-4024-444-2-2-44000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4444-444-4422202-22-2-2-2-22-200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-4444-444-4422202-22-2-2-2-22-200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-4484-444-8-8-4-4-4204-4-24-2-44420000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4-8-4-8-444448-42-40424-24-44-2-40000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-44-44444-42220-22-2-2-22-2-2200000000-1-1110000006i−6i−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-44-44-44444-42220-22-2-2-22-2-2200000000-1-111000000−6i6i3i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4844-4-8-88-4442-4-40-244-4-4-2244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-444-4-4442220-2-2-222-22-2-2−4i34i3000000-111-1002i3−2i32i3−2i300−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-444-4-4442220-2-2-222-22-2-24i3−4i3000000-111-100−2i32i3−2i32i300i3i3−i3−i30000000000000000000000000000000000000000000000000000000000

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