Finite Group Databasebeta

← Group #13168370

Character table — Group #13168370

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212244466666612121212121212121212444444441212121266666121212121212121212121244121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111-1-1-1-1111111111-1-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-11111-1-1-1-11-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-111-1-11-1-111-1-111-1-11-111-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-11-1-1-11111-1-1-111111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-11-1111-1-1-1-11111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-111-1-1-1-11111-1-111111111-111-1-1-111-1-111-1-111-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-11111-1-111-1-1111111111-1-1111-1-111-1-111-1-1-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111111-1-111-11-1-1-11111-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-1111-1111-1-1-1-111-111111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-11-1-111-111-1-111-1-1111-111-1-1111-11-1
χ17222222-122-12-12-1222-1-122-1-1-12-1-1-12222200-1-1-1-12-122-1-1-1-1-1-1-1-1202222-1-12222-1-1000000000022000000-1-1-1-1-1-120-1-1-1-100002000-1-100-1000
χ18222222-122-12-12-1222-1-122-1-1-12-1-1-12222200-1-1-1-12-122-1-1-1-1-1-1-1-120-2-222-1-122-2-2110000000000-2-2000000-1-1-1-1-11-2011110000-200011001000
χ19222222-122-12-12-1222-1-122-1-1-12-1-1-1222-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2022-2-211-2-222-1-10000000000-2-200000011111-120-1-1-1-10000-200011001000
χ20222222-122-12-12-1222-1-122-1-1-12-1-1-1222-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-2-2-211-2-2-2-211000000000022000000111111-20111100002000-1-100-1000
χ21222222-122-12-12-1222-1-1-22-1-1-12-1-1-12-2-22200-1-1-1-1-21-2-211111111-202-222-1-1-2-222110000000000-2-20000001-1-111-1-20-1-111000020001100-1000
χ22222222-122-12-12-1222-1-1-22-1-1-12-1-1-12-2-22200-1-1-1-1-21-2-211111111-20-2222-1-1-2-2-2-2-1-10000000000220000001-1-11112011-1-10000-2000-1-1001000
χ23222222-122-12-12-1222-1-1-22-1-1-12-1-1-12-2-2-2-200-1-1-1-1-21-2-211111111202-2-2-211222211000000000022000000-111-1-1-1-20-1-1110000-2000-1-1001000
χ24222222-122-12-12-1222-1-1-22-1-1-12-1-1-12-2-2-2-200-1-1-1-1-21-2-21111111120-22-2-21122-2-2-1-10000000000-2-2000000-111-1-112011-1-1000020001100-1000
χ2522222-12-122-12222-1-12-12-12-1-1-1-122-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-12200-1-122-1-1000022-1-1-1-122220000-1-1-1-12-1-1-1-10020000-1-1-1-100-1-100000000
χ2622222-12-122-12222-1-12-12-12-1-1-1-122-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-12-200-1-122-1-10000-2-21111-2-2-2-2000011112-1-1-1-100-200001111001100000000
χ2722222-12-122-12222-1-12-12-12-1-1-1-122-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-220011-2-211000022-1-1-1-1-2-2-2-200001111-211110020000-1-1-1-1001100000000
χ2822222-12-122-12222-1-12-12-12-1-1-1-122-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-2-20011-2-2110000-2-2111122220000-1-1-1-1-2111100-20000111100-1-100000000
χ2922222-12-122-12222-1-12-1-2-12-1-1-1-122-1112222-1-1-1-1-2-21111-2-21111-2-200-1-12211000022-1-111-2-22200001111-2-1-11100-20000-1-11100-1-100000000
χ3022222-12-122-12222-1-12-1-2-12-1-1-1-122-11122-2-2-1-1-1-1-2-21111-2-21111-2200-1-122110000-2-211-1-122-2-20000-1-1-1-1-2-1-111002000011-1-1001100000000
χ3122222-12-122-12222-1-12-1-2-12-1-1-1-122-111-2-222-1-1-1-1-2-21111-2-211112-20011-2-2-1-1000022-1-11122-2-20000-1-1-1-1211-1-100-20000-1-111001100000000
χ3222222-12-122-12222-1-12-1-2-12-1-1-1-122-111-2-2-2-2-1-1-1-1-2-21111-2-21111220011-2-2-1-10000-2-211-1-1-2-22200001111211-1-1002000011-1-100-1-100000000
χ332222-1222-1222-12-12-1-122-1-122-12-1-1-1220022-1-1-1-1-12-1-122-1-1-1-1-1-10222000000-1-122-1-12222000000220000000002-1-1-1-1-1-1-1-1-1-1020000-1-10-100
χ342222-1222-1222-12-12-1-122-1-122-12-1-1-1220022-1-1-1-1-12-1-122-1-1-1-1-1-102-2-200000011-2-2-1-12222000000-2-2000000000-21-11111-1-1-1-10-20000110100
χ352222-1222-1222-12-12-1-122-1-122-12-1-1-12200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10-222000000-1-12211-2-2-2-2000000-2-20000000002-11-1-1-1-111110-20000110100
χ362222-1222-1222-12-12-1-122-1-122-12-1-1-12200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10-2-2-200000011-2-211-2-2-2-200000022000000000-21111111111020000-1-10-100
χ372222-1222-1222-12-12-1-12-2-1-122-12-1-1-1-2-20022-1-1-1-11-211-2-21111110-22-2000000-1-1-2-2-1-122-2-200000022000000000211-1-111-1-1110-20000-1-10100
χ382222-1222-1222-12-12-1-12-2-1-122-12-1-1-1-2-20022-1-1-1-11-211-2-21111110-2-220000001122-1-122-2-2000000-2-2000000000-2-1111-1-1-1-111020000110-100
χ392222-1222-1222-12-12-1-12-2-1-122-12-1-1-1-2-200-2-2-1-1-1-11-211-2-2111111022-2000000-1-1-2-211-2-222000000-2-200000000021-1-1-11111-1-1020000110-100
χ402222-1222-1222-12-12-1-12-2-1-122-12-1-1-1-2-200-2-2-1-1-1-11-211-2-211111102-22000000112211-2-22200000022000000000-2-1-111-1-111-1-10-20000-1-10100
χ4122-2-2222-2-2-2-22-2-2222220-222-2-2-2-2-2200000022-2-2000000000000000000000000000000002-2002i−2i2i−2i22-2-2000000000000000000002i−2i2i−2i0000
χ4222-2-2222-2-2-2-22-2-2222220-222-2-2-2-2-2200000022-2-2000000000000000000000000000000002-200−2i2i−2i2i22-2-200000000000000000000−2i2i−2i2i0000
χ4322-2-2222-2-2-2-22-2-2222220-222-2-2-2-2-2200000022-2-200000000000000000000000000000000-22002i−2i−2i2i-2-222000000000000000000002i−2i−2i2i0000
χ4422-2-2222-2-2-2-22-2-2222220-222-2-2-2-2-2200000022-2-200000000000000000000000000000000-2200−2i2i2i−2i-2-22200000000000000000000−2i2i2i−2i0000
χ452-2-222222-2-2-2-222-2-22220-2-2-2-222-22-2002-22i−2i2-2-2200000000000000002-22-20000002i−2i2i−2i00002i−2i0000000002-20000000002i−2i00002i−2i00000000
χ462-2-222222-2-2-2-222-2-22220-2-2-2-222-22-2002-2−2i2i2-2-2200000000000000002-22-2000000−2i2i−2i2i0000−2i2i0000000002-2000000000−2i2i0000−2i2i00000000
χ472-2-222222-2-2-2-222-2-22220-2-2-2-222-22-200-222i−2i2-2-220000000000000000-22-220000002i−2i2i−2i0000−2i2i000000000-220000000002i−2i0000−2i2i00000000
χ482-2-222222-2-2-2-222-2-22220-2-2-2-222-22-200-22−2i2i2-2-220000000000000000-22-22000000−2i2i−2i2i00002i−2i000000000-22000000000−2i2i00002i−2i00000000
χ492-2-222-12-1-2-21-222-21-12-101-211-1-1-221−i3i32-22i−2i-111-100−i3i3−i3i300−i3−i3i3i30000-112-2−i3i300002i−2i−ii3−3002i−2i00003−33−30-11−i3i30000000−ii3−300−ii00000000
χ502-2-222-12-1-2-21-222-21-12-101-211-1-1-221−i3i32-2−2i2i-111-100−i3i3−i3i300−i3−i3i3i30000-112-2−i3i30000−2i2ii−i−3300−2i2i0000−33−330-11−i3i30000000i−i−3300i−i00000000
χ512-2-222-12-1-2-21-222-21-12-101-211-1-1-221−i3i3-222i−2i-111-100−i3i3−i3i300−i3−i3i3i300001-1-22i3−i300002i−2i−ii3−300−2i2i0000−33−3301-1i3−i30000000−ii3−300i−i00000000
χ522-2-222-12-1-2-21-222-21-12-101-211-1-1-221−i3i3-22−2i2i-111-100−i3i3−i3i300−i3−i3i3i300001-1-22i3−i30000−2i2ii−i−33002i−2i00003−33−301-1i3−i30000000i−i−3300−ii00000000
χ532-2-222-12-1-2-21-222-21-12-101-211-1-1-221i3−i32-22i−2i-111-100i3−i3i3−i300i3i3−i3−i30000-112-2i3−i300002i−2i−ii−33002i−2i0000−33−330-11i3−i30000000−ii−3300−ii00000000
χ542-2-222-12-1-2-21-222-21-12-101-211-1-1-221i3−i32-2−2i2i-111-100i3−i3i3−i300i3i3−i3−i30000-112-2i3−i30000−2i2ii−i3−300−2i2i00003−33−30-11i3−i30000000i−i3−300i−i00000000
χ552-2-222-12-1-2-21-222-21-12-101-211-1-1-221i3−i3-222i−2i-111-100i3−i3i3−i300i3i3−i3−i300001-1-22−i3i300002i−2i−ii−3300−2i2i00003−33−301-1−i3i30000000−ii−3300i−i00000000
χ562-2-222-12-1-2-21-222-21-12-101-211-1-1-221i3−i3-22−2i2i-111-100i3−i3i3−i300i3i3−i3−i300001-1-22−i3i30000−2i2ii−i3−3002i−2i0000−33−3301-1−i3i30000000i−i3−300−ii00000000
χ5744444-2-2-24-2-2-24-24-2-2-214-2-211-21-2-2-2-2-2440011114-2-2-211-2-211114000-2-2-2-2-2-20000000000000000000000-2111100000000000000000000000
χ5844444-2-2-24-2-2-24-24-2-2-214-2-211-21-2-2-2-2-2-4-40011114-2-2-211-2-21111-400022222200000000000000000000002-1-1-1-100000000000000000000000
χ5944444-2-2-24-2-2-24-24-2-2-21-4-2-211-21-2-2-22244001111-4222-1-122-1-1-1-1-4000-2-2-2-2220000000000000000000000211-1-100000000000000000000000
χ6044444-2-2-24-2-2-24-24-2-2-21-4-2-211-21-2-2-222-4-4001111-4222-1-122-1-1-1-140002222-2-20000000000000000000000-2-1-11100000000000000000000000
χ614444-24-24-2-24-2-2-2-24-21-24-21-2-2-2-211-24400001111-2-2-2-2-2-21111110044000000-2-2-2-200000000000000000000000-2-2011110000000000000000
χ624444-24-24-2-24-2-2-2-24-21-24-21-2-2-2-211-24400001111-2-2-2-2-2-211111100-4-4000000222200000000000000000000000220-1-1-1-10000000000000000
χ634444-24-24-2-24-2-2-2-24-21-2-4-21-2-2-2-211-2-4-400001111222222-1-1-1-1-1-1004-4000000-2-22200000000000000000000000-22011-1-10000000000000000
χ644444-24-24-2-24-2-2-2-24-21-2-4-21-2-2-2-211-2-4-400001111222222-1-1-1-1-1-100-4400000022-2-2000000000000000000000002-20-1-1110000000000000000
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χ894-4-444-2-2-2-42224-2-42-2-21022-1-1-212-22−2i32i3-44001-1-1100−2i32i3i3−i300i3i3−i3−i300002-22-22i3−2i300000000000000000000000-11−i3i300000000000000000000000
χ904-4-444-2-2-2-42224-2-42-2-21022-1-1-212-222i3−2i34-4001-1-11002i3−2i3−i3i300−i3−i3i3i30000-22-222i3−2i3000000000000000000000001-1−i3i300000000000000000000000
χ914-4-444-2-2-2-42224-2-42-2-21022-1-1-212-222i3−2i3-44001-1-11002i3−2i3−i3i300−i3−i3i3i300002-22-2−2i32i300000000000000000000000-11i3−i300000000000000000000000
χ924-4-44-24442-4-4-4-242-4-2-24022-4-4-242-2200004i−4i-222-200000000000000000000000000−2i2i4i−4i00000000000000000000000000−2i2i00000000000000
χ934-4-44-24442-4-4-4-242-4-2-24022-4-4-242-220000−4i4i-222-2000000000000000000000000002i−2i−4i4i000000000000000000000000002i−2i00000000000000
χ944-4-44-2-24-22-42-4-24221-2-20-12221-22-2-1−2i32i3004i−4i1-1-1100i3−i3−2i32i300i3i3−i3−i300000000000000−2i2i−2i2i23−23000000000000000000000000i−i−33000000000000
χ954-4-44-2-24-22-42-4-24221-2-20-12221-22-2-1−2i32i300−4i4i1-1-1100i3−i3−2i32i300i3i3−i3−i3000000000000002i−2i2i−2i−2323000000000000000000000000−ii3−3000000000000
χ964-4-44-2-24-22-42-4-24221-2-20-12221-22-2-12i3−2i3004i−4i1-1-1100−i3i32i3−2i300−i3−i3i3i300000000000000−2i2i−2i2i−2323000000000000000000000000i−i3−3000000000000
χ974-4-44-2-24-22-42-4-24221-2-20-12221-22-2-12i3−2i300−4i4i1-1-1100−i3i32i3−2i300−i3−i3i3i3000000000000002i−2i2i−2i23−23000000000000000000000000−ii−33000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-44-844-4-848-4-4-4204-42-24-244-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-844-8-444-48-42-4042-4444-2-2-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4844-8484-8-4-42-4-40-2-4-44-2444200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44444-444-4-42220-222-2-2-2-2-22000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44444-444-4-42220-222-2-2-2-2-22000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-448-4-44-84-84-4-420-44-224-2-4440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-484-48-4-84-8442-4-40244-4-24-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-4-4-44444422202-2-22-2-22-2-2000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-44-4-4-44444422202-2-22-2-22-2-2000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4844-84-4-44-8-42-404-244-4-4-2240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-44444-4-4442220-2-2-2-222-22-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-44444-4-4442220-2-2-2-222-22-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000

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