Finite Group Databasebeta

← Group #13178268

Character table — Group #13178268

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order12223334466666666623333346666666666666666612121212121212126666666666661212121212121212121212121212121212121212121244444444441212121222222446666661212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11-1-1-111-1-1-1-111-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-11-1-1-1-111-1-1-1-111-1-1-11-11
χ5111111111111111111-111111-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-11-11-1-11-1-111-1-11111-1-111-11-11
χ6111111111111111111-111111-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1-11111-1-111111-11-1
χ7111111111111111111-111111-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-1111111-1-11111-1-1-1-1-1-1
χ8111111111111111111-111111-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ91111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11-11-11-1111-1-1111111-1-1-1-11-1-11
χ101111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-11-11-11111-1-111-1-111-1-1-111-1
χ111111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ121111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-11111-1-1-1-1-1-111-1-111
χ131111111-1-1111111111-1111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111
χ141111111-1-1111111111-1111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-11111-1-1-1-1111111-1-1-1-1-1-111-1-1
χ151111111-1-1111111111-1111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11-1-1111-111-1-111-1-111-1-111-111-1
χ161111111-1-1111111111-1111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1111-1-1-111111-1-1-1-1-1-111111-1-11
χ17222222-1222-12222-1-1222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000022000000022020000-1-10000-1-1000-10-1
χ18222222-1222-12222-1-1222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-20000000-2-20-2000011000011000101
χ19222222-1222-12222-1-12-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-222-1-122-21-2-211111111-2122-1-1-1-1-1-1-1-1-2-21111111100000000220000000-220-20000-1-10000-1-1000101
χ20222222-1222-12222-1-12-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-222-1-122-21-2-211111111-2122-1-1-1-1-1-1-1-1-2-21111111100000000-2-200000002-202000011000011000-10-1
χ21222222-1-2-22-12222-1-1222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-1-21-2-211111111-2-211111111000000002200000002-20-20000110000-1-1000-101
χ22222222-1-2-22-12222-1-1222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-1-21-2-211111111-2-21111111100000000-2-20000000-22020000-1-100001100010-1
χ23222222-1-2-22-12222-1-12-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-122-2-211-2-2-21-2-2111111112-1-2-21111111122-1-1-1-1-1-1-1-100000000220000000-2-2020000110000-1-100010-1
χ24222222-1-2-22-12222-1-12-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-122-2-211-2-2-21-2-2111111112-1-2-21111111122-1-1-1-1-1-1-1-100000000-2-20000000220-20000-1-1000011000-101
χ2522222-1222-1222-1-12222-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-1-12222-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000022000000022002000-1-10000-1-10000-10-10
χ2622222-1222-1222-1-12222-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-1-12222-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000-2-20000000-2-200-20001100001100001010
χ2722222-1222-1222-1-1222-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-1-122221-211-2-21111111-2-1-122-1-1-1-1-1-111-2-21111110000002200000002-200-2000-1-10000-1-100001010
χ2822222-1222-1222-1-1222-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-1-122221-211-2-21111111-2-1-122-1-1-1-1-1-111-2-2111111000000-2-20000000-22002000110000110000-10-10
χ2922222-12-2-2-1222-1-12222-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2-2-2-12-1-122-1-1-1-1-1-11-211-2-211111111-2-2111111000000220000000-2200-2000110000-1-10000-1010
χ3022222-12-2-2-1222-1-12222-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2-2-2-12-1-122-1-1-1-1-1-11-211-2-211111111-2-2111111000000-2-200000002-2002000-1-1000011000010-10
χ3122222-12-2-2-1222-1-1222-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-12211-2-2-2-21-211-2-2111111-1211-2-2111111-1-122-1-1-1-1-1-1000000220000000-2-2002000110000-1-1000010-10
χ3222222-12-2-2-1222-1-1222-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-12211-2-2-2-21-211-2-2111111-1211-2-2111111-1-122-1-1-1-1-1-1000000-2-200000002200-2000-1-10000110000-1010
χ332222-1222222-1-12222-12-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222220000-1-1-1-12000000-1-10000-1-10000-1-10000
χ342222-1222222-1-12222-12-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-200001111-2000000110000110000110000
χ352222-1222222-1-12222-1-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-1112222-1-1-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-211112222-2-200001111-2000000110000-1-10000-1-10000
χ362222-1222222-1-12222-1-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-1112222-1-1-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-21111-2-2-2-2220000-1-1-1-12000000-1-10000110000110000
χ372222-122-2-222-1-12222-12-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-2111122-2-2-2-2000011112000000-1-10000-1-10000110000
χ382222-122-2-222-1-12222-12-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-21111-2-222220000-1-1-1-1-2000000110000110000-1-10000
χ392222-122-2-222-1-12222-1-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-122-2-2220000-1-1-1-1-2000000110000-1-10000110000
χ402222-122-2-222-1-12222-1-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-1-2-222-2-2000011112000000-1-10000110000-1-10000
χ4122-2-22222i−2i22-22-2-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2002i−2i2i−2i2i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-22i−2i000000000000000000000002-200002i−2i0000
χ4222-2-22222i−2i22-22-2-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2002i−2i2i−2i2i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-22−2i2i00000000000000000000000-220000−2i2i0000
χ4322-2-2222−2i2i22-22-2-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-200−2i2i−2i2i−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-2−2i2i000000000000000000000002-20000−2i2i0000
χ4422-2-2222−2i2i22-22-2-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-200−2i2i−2i2i−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-222i−2i00000000000000000000000-2200002i−2i0000
χ4522-2-2-1222i−2i221-1-2-2-2-210-1-12-1-10−i3i3-1-12-1-11111-2-211113−32i−2i2i−2i−ii00−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−32-22i−2i00000033−3−30000000−i3i30000-110000−ii0000
χ4622-2-2-1222i−2i221-1-2-2-2-210-1-12-1-10−i3i3-1-12-1-11111-2-211113−32i−2i2i−2i−ii00−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−3-22−2i2i000000−3−3330000000i3−i300001-10000i−i0000
χ4722-2-2-1222i−2i221-1-2-2-2-210-1-12-1-10i3−i3-1-12-1-11111-2-21111−332i−2i2i−2i−ii00i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−3332-22i−2i000000−3−3330000000i3−i30000-110000−ii0000
χ4822-2-2-1222i−2i221-1-2-2-2-210-1-12-1-10i3−i3-1-12-1-11111-2-21111−332i−2i2i−2i−ii00i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−333-22−2i2i00000033−3−30000000−i3i300001-10000i−i0000
χ4922-2-2-122−2i2i221-1-2-2-2-210-1-12-1-10−i3i3-1-12-1-11111-2-21111−33−2i2i−2i2ii−i00−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−3332-2−2i2i000000−3−3330000000−i3i30000-110000i−i0000
χ5022-2-2-122−2i2i221-1-2-2-2-210-1-12-1-10−i3i3-1-12-1-11111-2-21111−33−2i2i−2i2ii−i00−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−333-222i−2i00000033−3−30000000i3−i300001-10000−ii0000
χ5122-2-2-122−2i2i221-1-2-2-2-210-1-12-1-10i3−i3-1-12-1-11111-2-211113−3−2i2i−2i2ii−i00i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−32-2−2i2i00000033−3−30000000i3−i30000-110000i−i0000
χ5222-2-2-122−2i2i221-1-2-2-2-210-1-12-1-10i3−i3-1-12-1-11111-2-211113−3−2i2i−2i2ii−i00i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−3-222i−2i000000−3−3330000000−i3i300001-10000−ii0000
χ532-2-2222200-2-2-2-22-22-22022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000002-22-22-22-22-20000000000000002-22-2000000
χ542-2-2222200-2-2-2-22-22-22022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000002-2-22-222-22-2000000000000000-22-22000000
χ552-2-2222200-2-2-2-22-22-22022222000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000000000-222-2-22-22-220000000000000002-2-22000000
χ562-2-2222200-2-2-2-22-22-22022222000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000000000-22-222-2-22-22000000000000000-222-2000000
χ5744444-2-244-2-244-2-2-2-244-2-2111444-2-2111-2-2-2-211111144-2-2-2-244-2-2-2-2-2-2111111-2-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-244-2-244-2-2-2-24-4-2-2111-4-4-4-2-2111-2-2-2-2111111-4-4-2-2-2-244222222-1-1-1-1-1-122-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-4-2-244-2-2-2-244-2-2111-444-2-2111-2-2-2-2111111-4-42222-4-4-2-2-2-2-2-2111111222222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ6044444-2-2-4-4-2-244-2-2-2-24-4-2-21114-4-4-2-2111-2-2-2-2111111442222-4-4222222-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ614444-24-2444-2-2-244-2-2-24-21-2114-2-2-21-211-2-211-2-21111-2-244-2-2-2-24-2-2-211-2-211114-2-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-2444-2-2-244-2-2-2-4-21-211-422-21-211-2-211-2-211112244-2-2-2-2-4222-1-122-1-1-1-1-42-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-44-2-2-244-2-2-24-21-211-4-2-2-21-211-2-211-2-2111122-4-422224-2-2-211-2-21111-4222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ644444-24-2-4-44-2-2-244-2-2-2-4-21-211422-21-211-2-211-2-21111-2-2-4-42222-4222-1-122-1-1-1-14-222-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ654444-2-2444-24-2-2-2-244-241-2-2114-2-21-2-21111-2-2-2-21111-2-2-2-244-2-2-2411-2-2-2-21111-2411-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-2444-24-2-2-2-244-2-41-2-211-4221-2-21111-2-2-2-2111122-2-244-2-22-4-1-12222-1-1-1-12-411-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-4-24-2-2-2-244-241-2-211-4-2-21-2-21111-2-2-2-211112222-4-422-2411-2-2-2-211112-4-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000000
χ684444-2-24-4-4-24-2-2-2-244-2-41-2-2114221-2-21111-2-2-2-21111-2-222-4-4222-4-1-12222-1-1-1-1-24-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
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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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.