Finite Group Databasebeta

← Group #13178263

Character table — Group #13178263

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order12223334466666666623333346666666666666666612121212121212126666666666661212121212121212121212121212121212121212121222444444441212121222444446666121212121212121212126121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-11111-1-1-11-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-11-1-11111-1-111-1-1-1-111-1-111
χ6111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-11-1-1-11111-1-1-1-1-1-111111111-1-1
χ7111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-11-11-1-1-11111111111-1-1-1-1-1-1
χ8111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11111-11-1-1-1-111-1-1-1-1-1-1-1-11111
χ91111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-11-111-1-11111-1-111-1-11-11-1
χ101111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-1-111-11111111-1-111-1-1-1-1-11-11
χ111111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-1-11-1-1-1-1-1-1-1-11111-1-1111-1-11
χ121111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-11-1-111-1-111-1-1-1-1-1-11111-111-1
χ131111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-111111111-1-11-1-1-1111-1-1-1-11111-1-1-1-1-111-1
χ141111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1111111-1-111-11111-1-1-1-1-1-111-1-11-1-11
χ151111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-11-11
χ161111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-11111-1-111-1-1111-11-1
χ17222222-122-12222-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100220000000000220000200-1-100-1-1000000-1-100
χ18222222-122-12222-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-20000000000-2-20000-2001100110000001100
χ19222222-122-12222-1-122-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-21-2-211111111-2122-1-1-1-1-1-1-1-1-2-211111111002200000000002-20000-200-1-100-1-10000001100
χ20222222-122-12222-1-122-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-21-2-211111111-2122-1-1-1-1-1-1-1-1-2-21111111100-2-20000000000-220000200110011000000-1-100
χ21222222-1-2-2-12222-1-12222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-1-21-2-211111111-2-21111111100220000000000-220000-2001100-1-1000000-1100
χ22222222-1-2-2-12222-1-12222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-1-21-2-211111111-2-21111111100-2-200000000002-20000200-1-100110000001-100
χ23222222-1-2-2-12222-1-122-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-21-2-2111111112-1-2-21111111122-1-1-1-1-1-1-1-100220000000000-2-200002001100-1-10000001-100
χ24222222-1-2-2-12222-1-122-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-21-2-2111111112-1-2-21111111122-1-1-1-1-1-1-1-100-2-20000000000220000-200-1-10011000000-1100
χ2522222-12222-1-122222-12-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12200222200-1-1-1-10002000-1-100-1-1000000-1-10000
χ2622222-12222-1-122222-12-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-2-2001111000-2000110011000000110000
χ2722222-12222-1-122222-1-2-12-1-1-1-211-12-1-1-1-1-122-1-1-1-1-1-1-1-1222211-2-211-2-2111111-2-2-1-122-1-1-1-1-1-111-2-2111111220022-2-2001111000-2000-1-10011000000-1-10000
χ2822222-12222-1-122222-1-2-12-1-1-1-211-12-1-1-1-1-122-1-1-1-1-1-1-1-1222211-2-211-2-2111111-2-2-1-122-1-1-1-1-1-111-2-2111111-2-200-2-22200-1-1-1-100020001100-1-1000000110000
χ2922222-12-2-22-1-122222-12-12-1-1-1-2-1-1-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-21122-1-122-1-1-1-1-1-1-2-211-2-211111111-2-21111112200-2-2-2-20011110002000-1-100-1-1000000110000
χ3022222-12-2-22-1-122222-12-12-1-1-1-2-1-1-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-21122-1-122-1-1-1-1-1-1-2-211-2-211111111-2-2111111-2-200222200-1-1-1-1000-2000110011000000-1-10000
χ3122222-12-2-22-1-122222-1-2-12-1-1-1211-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2-1-1-2-211-2-21111112211-2-2111111-1-122-1-1-1-1-1-12200-2-22200-1-1-1-1000-2000-1-10011000000110000
χ3222222-12-2-22-1-122222-1-2-12-1-1-1211-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2-1-1-2-211-2-21111112211-2-2111111-1-122-1-1-1-1-1-1-2-20022-2-200111100020001100-1-1000000-1-10000
χ332222-12222222-1-122-122-1-12-1-1222-1-12-1-1-1-1-1-122-1-1-1-122-1-12222-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000220000002022000000000-1-1-1-10000-1-1
χ342222-12222222-1-122-122-1-12-1-1222-1-12-1-1-1-1-1-122-1-1-1-122-1-12222-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2000000-20-2-20000000001111000011
χ352222-12222222-1-122-12-2-1-12-1-1-2-2-2-1-12-1-1-1-1-1-122-1-1-1-122-1-122-2-21-21111-2-211111-2-1-1-1-122-1-1-1-11111-2-211110000000022000000-20-22000000000-1-1-1-1000011
χ362222-12222222-1-122-12-2-1-12-1-1-2-2-2-1-12-1-1-1-1-1-122-1-1-1-122-1-122-2-21-21111-2-211111-2-1-1-1-122-1-1-1-11111-2-2111100000000-2-2000000202-200000000011110000-1-1
χ372222-122-2-2222-1-122-122-1-12-1-1-222-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-2-2-12-1-1-1-122-1-1-1-11-21111-2-211111111-2-211110000000022000000-202-2000000000-1-11100001-1
χ382222-122-2-2222-1-122-122-1-12-1-1-222-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-2-2-12-1-1-1-122-1-1-1-11-21111-2-211111111-2-2111100000000-2-200000020-2200000000011-1-10000-11
χ392222-122-2-2222-1-122-12-2-1-12-1-12-2-2-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2221-21111-2-21111-121111-2-21111-1-1-1-122-1-1-1-1000000002200000020-2-2000000000-1-1110000-11
χ402222-122-2-2222-1-122-12-2-1-12-1-12-2-2-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2221-21111-2-21111-121111-2-21111-1-1-1-122-1-1-1-100000000-2-2000000-202200000000011-1-100001-1
χ4122-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000002-2002i−2i2i−2i2i2i−2i−2i00000000000002-22i−2i00000000
χ4222-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000002-200−2i2i−2i2i−2i−2i2i2i00000000000002-2−2i2i00000000
χ4322-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000-22002i−2i−2i2i2i2i−2i−2i0000000000000-22−2i2i00000000
χ4422-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000-2200−2i2i2i−2i−2i−2i2i2i0000000000000-222i−2i00000000
χ452-22-22222i−2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-2002i−2i0000000000000002-200000000002i−2i0000
χ462-22-22222i−2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-2200−2i2i000000000000000-220000000000−2i2i0000
χ472-22-2222−2i2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-200−2i2i0000000000000002-20000000000−2i2i0000
χ482-22-2222−2i2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-22002i−2i000000000000000-2200000000002i−2i0000
χ492-22-22-122i−2i21-1-2-2-2-2210-12-1-1-10−i3i3-12-1-1-111-2-2111111−ii2i−2i2i−2i3−300−i3i300−i3i3−i3−i3i3i300−ii2i−2i−ii−i−iii3−3003−333−3−32-2002i−2i00003−33−30000000-1100−i3i3000000−ii0000
χ502-22-22-122i−2i21-1-2-2-2-2210-12-1-1-10−i3i3-12-1-1-111-2-2111111−ii2i−2i2i−2i3−300−i3i300−i3i3−i3−i3i3i300−ii2i−2i−ii−i−iii3−3003−333−3−3-2200−2i2i0000−33−3300000001-100i3−i3000000i−i0000
χ512-22-22-122i−2i21-1-2-2-2-2210-12-1-1-10i3−i3-12-1-1-111-2-2111111−ii2i−2i2i−2i−3300i3−i300i3−i3i3i3−i3−i300−ii2i−2i−ii−i−iii−3300−33−3−3332-2002i−2i0000−33−330000000-1100i3−i3000000−ii0000
χ522-22-22-122i−2i21-1-2-2-2-2210-12-1-1-10i3−i3-12-1-1-111-2-2111111−ii2i−2i2i−2i−3300i3−i300i3−i3i3i3−i3−i300−ii2i−2i−ii−i−iii−3300−33−3−333-2200−2i2i00003−33−300000001-100−i3i3000000i−i0000
χ532-22-22-12−2i2i21-1-2-2-2-2210-12-1-1-10−i3i3-12-1-1-111-2-2111111i−i−2i2i−2i2i−3300−i3i300−i3i3−i3−i3i3i300i−i−2i2ii−iii−i−i−3300−33−3−3332-200−2i2i0000−33−330000000-1100−i3i3000000i−i0000
χ542-22-22-12−2i2i21-1-2-2-2-2210-12-1-1-10−i3i3-12-1-1-111-2-2111111i−i−2i2i−2i2i−3300−i3i300−i3i3−i3−i3i3i300i−i−2i2ii−iii−i−i−3300−33−3−333-22002i−2i00003−33−300000001-100i3−i3000000−ii0000
χ552-22-22-12−2i2i21-1-2-2-2-2210-12-1-1-10i3−i3-12-1-1-111-2-2111111i−i−2i2i−2i2i3−300i3−i300i3−i3i3i3−i3−i300i−i−2i2ii−iii−i−i3−3003−333−3−32-200−2i2i00003−33−30000000-1100i3−i3000000i−i0000
χ562-22-22-12−2i2i21-1-2-2-2-2210-12-1-1-10i3−i3-12-1-1-111-2-2111111i−i−2i2i−2i2i3−300i3−i300i3−i3i3i3−i3−i300i−i−2i2ii−iii−i−i3−3003−333−3−3-22002i−2i0000−33−3300000001-100−i3i3000000−ii0000
χ5744444-2-244-2-2-244-2-24-24-2-21114-2-2-2-2111-2-2-2-2111111-2-244-2-2-2-24-2-2-2-2-21111114-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-244-2-2-244-2-24-2-4-2-2111-422-2-2111-2-2-2-2111111-2-244-2-222-422222-1-1-1-1-1-1-42-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-4-2-2-244-2-24-24-2-2111-4-2-2-2-2111-2-2-2-211111122-4-422224-2-2-2-2-2111111-422222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ6044444-2-2-4-4-2-2-244-2-24-2-4-2-2111422-2-2111-2-2-2-211111122-4-422-2-2-422222-1-1-1-1-1-14-22222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ614444-24-244-244-2-2-2-2-244-21-211444-21-211-2-211-2-2111144-2-2-2-244-2-2-2-211-2-21111-2-2-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-244-244-2-2-2-2-24-4-21-211-4-4-4-21-211-2-211-2-2111144-2-2-2-2-4-42222-1-122-1-1-1-122-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-4-244-2-2-2-2-244-21-211-444-21-211-2-211-2-21111-4-42222-4-4-2-2-2-211-2-211112222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ644444-24-2-4-4-244-2-2-2-2-24-4-21-2114-4-4-21-211-2-211-2-21111-4-42222442222-1-122-1-1-1-1-2-222-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ654444-2-24444-2-2-2-244-2-241-2-2114-2-21-2-21111-2-2-2-21111-2-2-2-244-2-2-2411-2-2-2-21111-2411-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-24444-2-2-2-244-2-2-41-2-211-4221-2-21111-2-2-2-21111-2-2-2-244222-4-1-12222-1-1-1-12-411-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-44-2-2-2-244-2-241-2-211-4-2-21-2-21111-2-2-2-211112222-4-422-2411-2-2-2-211112-4-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000000
χ684444-2-24-4-44-2-2-2-244-2-2-41-2-2114221-2-21111-2-2-2-211112222-4-4-2-22-4-1-12222-1-1-1-1-24-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
χ694444-2-2-244-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i324-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000000
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χ1014-44-4-2-2-24i−4i-22-22222-220111−1+3i32−1−3i320−2i32i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32−2i2i−2i2i−2i2i23−2300i3−i3-33i3−i33−i32−3−i32−3+i323+i3200i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ11−33−3i3i−33−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000000000000000000
χ1024-44-4-2-2-24i−4i-22-22222-220111−1+3i32−1−3i3202i3−2i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32−2i2i−2i2i−2i2i−232300−i3i33-3−i3i3−3+i323+i323−i32−3−i3200i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ113−33i−3i3−32ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000000000000000000
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χ1054-44-4-2-2-2−4i4i-22-22222-220111−1+3i32−1−3i320−2i32i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i322i−2i2i−2i2i−2i−232300i3−i3-33i3−i33−i32−3−i32−3+i323+i3200−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ113−33i−3i3−32ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000000000000000000
χ1064-44-4-2-2-2−4i4i-22-22222-220111−1+3i32−1−3i3202i3−2i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i322i−2i2i−2i2i−2i23−2300−i3i33-3−i3i3−3+i323+i323−i32−3−i3200−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11−33−3i3i−33−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000000000000000000
χ1074-4-4444400-4-4-4-44-44-44044444000-4-4-4-4-4-44-44-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ11888-8-8-4-4-4004-44-44-44440222−1+3i3−1−3i3000-2-2-21−3i31+3i32-22-22-2−1+3i3−1−3i31−3i31+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1228-8-88-4-4-4004444-44-44-40222−1−3i3−1+3i3000-2-2-21+3i31−3i3-22-22-221+3i31−3i3−1−3i3−1+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1238-8-88-4-4-4004444-44-44-40222−1+3i3−1−3i3000-2-2-21−3i31+3i3-22-22-221−3i31+3i3−1+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.