Finite Group Databasebeta

← Group #13178269

Character table — Group #13178269

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order122233344666666666233333466666666666666666121212121212121266666666666612121212121212121212121212121212121212121212224444444412121212224444466121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11-1-11-11-1-1-1-1-111-1-1-1-111-1-11-11-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-11-11-1-1-1-1-1-111-1-1-1-111-11-11
χ5111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-11-11-1-1111-1-111-1-11111-1-1-11-11
χ6111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-111-111-1-1-1-11111-1-1111-11-1
χ7111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1-1111111-1-11111-1-1-1-1
χ8111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ91111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11-11-11-111111-1-111-1-111-1-11-1-11
χ101111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1111-11-1111111-1-1-1-1-1-111-111-1
χ111111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ121111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-1111111-1-1-1-1-1-111
χ131111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ141111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111111-111-1-111-1-11111-1-1-1-1-1-111-1-1
χ151111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-111-111-1-1-111-1-1111111-1-1-111-1
χ161111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11-111-1-11-1-11111-1-111-1-1111-1-11
χ17222222-12222-122-122-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000002200000200202000000-1-10000-1-10-10-1
χ18222222-12222-122-122-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-200000-200-20-2000000110000110101
χ19222222-12222-122-122-1-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-21-2-211111111-2122-1-1-1-1-1-1-1-1-2-211111111000000002200000-20020-2000000-1-10000-1-10101
χ20222222-12222-122-122-1-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-21-2-211111111-2122-1-1-1-1-1-1-1-1-2-21111111100000000-2-200000200-202000000110000110-10-1
χ21222222-1-2-222-122-122-122-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-1-21-2-211111111-2-211111111000000002200000200-20-2000000110000-1-10-101
χ22222222-1-2-222-122-122-122-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-1-21-2-211111111-2-21111111100000000-2-200000-200202000000-1-1000011010-1
χ23222222-1-2-222-122-122-1-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-21-2-2111111112-1-2-21111111122-1-1-1-1-1-1-1-1000000002200000-200-202000000110000-1-1010-1
χ24222222-1-2-222-122-122-1-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-21-2-2111111112-1-2-21111111122-1-1-1-1-1-1-1-100000000-2-20000020020-2000000-1-10000110-101
χ2522222-12222-122-122-122-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-1-12222-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000002200000020020200000-1-10000-1-100-10-10
χ2622222-12222-122-122-122-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-122-1-12222-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000-2-2000000-200-20-20000011000011001010
χ2722222-12222-122-122-12-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-122-1-122-2-21-211-2-21111111-2-1-122-1-1-1-1-1-111-2-211111100000022000000-20020-200000-1-10000-1-1001010
χ2822222-12222-122-122-12-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-122-1-122-2-21-211-2-21111111-2-1-122-1-1-1-1-1-111-2-2111111000000-2-2000000200-202000001100001100-10-10
χ2922222-12-2-22-122-122-122-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2-2-2-12-1-122-1-1-1-1-1-11-211-2-211111111-2-211111100000022000000200-20-200000110000-1-100-1010
χ3022222-12-2-22-122-122-122-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2-2-2-12-1-122-1-1-1-1-1-11-211-2-211111111-2-2111111000000-2-2000000-20020200000-1-10000110010-10
χ3122222-12-2-22-122-122-12-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2221-211-2-2111111-1211-2-2111111-1-122-1-1-1-1-1-100000022000000-200-20200000110000-1-10010-10
χ3222222-12-2-22-122-122-12-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2221-211-2-2111111-1211-2-2111111-1-122-1-1-1-1-1-1000000-2-200000020020-200000-1-100001100-1010
χ332222-12222-122-122-1222-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222220000-1-1-1-10020000-1-1-1-10000-1-100000000
χ342222-12222-122-122-1222-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-20000111100-20000111100001100000000
χ352222-12222-122-122-122-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-1-1-1222211-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-211112222-2-20000111100-20000-1-1110000-1-100000000
χ362222-12222-122-122-122-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-1-1-1222211-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-21111-2-2-2-2220000-1-1-1-1002000011-1-100001100000000
χ372222-122-2-2-122-122-1222-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-2111122-2-2-2-2000011110020000-1-1-1-100001100000000
χ382222-122-2-2-122-122-1222-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-21111-2-222220000-1-1-1-100-2000011110000-1-100000000
χ392222-122-2-2-122-122-122-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-2-1-1-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-122-2-2220000-1-1-1-100-20000-1-11100001100000000
χ402222-122-2-2-122-122-122-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-2-1-1-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-1-2-222-2-200001111002000011-1-10000-1-100000000
χ412-22-22222i−2i-2-2-2222-2-2-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-22i−2i000000000000000002-20000002i−2i00000000
χ422-22-22222i−2i-2-2-2222-2-2-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-22−2i2i00000000000000000-22000000−2i2i00000000
χ432-22-2222−2i2i-2-2-2222-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-2−2i2i000000000000000002-2000000−2i2i00000000
χ442-22-2222−2i2i-2-2-2222-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-222i−2i00000000000000000-220000002i−2i00000000
χ452-22-2-1222i−2i1-2-2-1221-2-20-1-12-1-10−i3i3-1-12-1-11111-2-21111−ii2i−2i2i−2i3−300−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−32-22i−2i00000033−3−30000000-11−i3i30000−ii00000000
χ462-22-2-1222i−2i1-2-2-1221-2-20-1-12-1-10−i3i3-1-12-1-11111-2-21111−ii2i−2i2i−2i3−300−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−3-22−2i2i000000−3−33300000001-1i3−i30000i−i00000000
χ472-22-2-1222i−2i1-2-2-1221-2-20-1-12-1-10i3−i3-1-12-1-11111-2-21111−ii2i−2i2i−2i−3300i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−3332-22i−2i000000−3−3330000000-11i3−i30000−ii00000000
χ482-22-2-1222i−2i1-2-2-1221-2-20-1-12-1-10i3−i3-1-12-1-11111-2-21111−ii2i−2i2i−2i−3300i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−333-22−2i2i00000033−3−300000001-1−i3i30000i−i00000000
χ492-22-2-122−2i2i1-2-2-1221-2-20-1-12-1-10−i3i3-1-12-1-11111-2-21111i−i−2i2i−2i2i−3300−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−3332-2−2i2i000000−3−3330000000-11−i3i30000i−i00000000
χ502-22-2-122−2i2i1-2-2-1221-2-20-1-12-1-10−i3i3-1-12-1-11111-2-21111i−i−2i2i−2i2i−3300−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−333-222i−2i00000033−3−300000001-1i3−i30000−ii00000000
χ512-22-2-122−2i2i1-2-2-1221-2-20-1-12-1-10i3−i3-1-12-1-11111-2-21111i−i−2i2i−2i2i3−300i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−32-2−2i2i00000033−3−30000000-11i3−i30000i−i00000000
χ522-22-2-122−2i2i1-2-2-1221-2-20-1-12-1-10i3−i3-1-12-1-11111-2-21111i−i−2i2i−2i2i3−300i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−3-222i−2i000000−3−33300000001-1−i3i30000−ii00000000
χ532-2-2222200-2-2-2-2-2-2222022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000002-22-22-22-22-2000000000000000002-22-20000
χ542-2-2222200-2-2-2-2-2-2222022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000002-2-22-222-22-200000000000000000-22-220000
χ552-2-2222200-2-2-2-2-2-2222022222000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000000000-222-2-22-22-22000000000000000002-2-220000
χ562-2-2222200-2-2-2-2-2-2222022222000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000000000-22-222-2-22-2200000000000000000-222-20000
χ5744444-2-2444-2-24-2-24-2-24-2-2111444-2-2111-2-2-2-211111144-2-2-2-244-2-2-2-2-2-2111111-2-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-2444-2-24-2-24-2-2-4-2-2111-4-4-4-2-2111-2-2-2-211111144-2-2-2-2-4-4222222-1-1-1-1-1-122-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-44-2-24-2-24-2-24-2-2111-444-2-2111-2-2-2-2111111-4-42222-4-4-2-2-2-2-2-2111111222222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ6044444-2-2-4-44-2-24-2-24-2-2-4-2-21114-4-4-2-2111-2-2-2-2111111-4-4222244222222-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ614444-24-244-24-2-24-2-24-24-21-2114-2-2-21-211-2-211-2-21111-2-244-2-2-2-24-2-2-211-2-211114-2-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-244-24-2-24-2-24-2-4-21-211-422-21-211-2-211-2-21111-2-244-2-222-4222-1-122-1-1-1-1-42-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-4-24-2-24-2-24-24-21-211-4-2-2-21-211-2-211-2-2111122-4-422224-2-2-211-2-21111-4222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ644444-24-2-4-4-24-2-24-2-24-2-4-21-211422-21-211-2-211-2-2111122-4-422-2-2-4222-1-122-1-1-1-14-222-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ654444-2-2444-2-24-2-24-2-2441-2-2114-2-21-2-21111-2-2-2-21111-2-2-2-244-2-2-2411-2-2-2-21111-2411-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-2444-2-24-2-24-2-24-41-2-211-4221-2-21111-2-2-2-21111-2-2-2-244222-4-1-12222-1-1-1-12-411-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-4-2-24-2-24-2-2441-2-211-4-2-21-2-21111-2-2-2-211112222-4-422-2411-2-2-2-211112-4-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000000
χ684444-2-24-4-4-2-24-2-24-2-24-41-2-2114221-2-21111-2-2-2-211112222-4-4-2-22-4-1-12222-1-1-1-1-24-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
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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χ1034-44-4-2-2-24i−4i222-2-2-22220111−1+3i32−1−3i3202i3−2i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32−2i2i−2i2i−2i2i−232300−i3i3−i3i33-3−3+i323+i323−i32−3−i3200i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ113−33−33i−3i2ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000000000000000000
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χ1074-44-4-2-2-2−4i4i222-2-2-22220111−1+3i32−1−3i3202i3−2i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i322i−2i2i−2i2i−2i23−2300−i3i3−i3i33-3−3+i323+i323−i32−3−i3200−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11−33−33−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000000000000000000
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χ11888-8-8-4-4-400-4-4-44444440222−1+3i3−1−3i3000-2-2-21−3i31+3i3-22-22-221−3i31+3i3−1+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1238-8-88-4-4-400444444-4-4-40222−1+3i3−1−3i3000-2-2-21−3i31+3i32-22-22-2−1+3i3−1−3i31−3i31+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000

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