Finite Group Databasebeta

← Group #13178323

Character table — Group #13178323

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11112222222222222244444444444444444444444444444444888888888888888888888888888888888899991818181818181818181818181818363636363636363636363636363636363636363672727272
order12223334466666666633333446666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212444422444444441212121222444466121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-11-111-1-1-1-111-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-11-1-111-1-1-1-111-1-1-1-11-1-11
χ511111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1
χ611111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1111-1-11111-1-1-1-1111-1-11
χ811111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1111-1-1-11111-1-111-1-111-111-1
χ91111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111111-1-11-1111-1-1-1-1-1-111-1-111-11-11
χ101111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-11111-11-111-1-1-111-1-111-1-1-1-1111-11-1
χ111111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-1-1111111-1-1-1-111-1-111-1-1
χ121111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-111-1-1-1-111111111-1-1-1-111
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-111-11-111-1-111-1-111-1-1-1-11-11-1
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111111-11-1-11-1-1111111-1-1-1-1-1-1-11-11
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-111
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-11-1-1-1-1-1-1-1-11111111111-1-1
χ17222222-122-122-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-12222-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022220000000000200020-1-10000-1-10000000-1-10
χ18222222-122-122-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-12222-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000000000-2000-20110000110000000110
χ19222222-122-122-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-2-2-2-21-2-21-2-21111111122-1-1-1-1-1-1-1-1-2-211111111000022220000000000-2000-20-1-10000-1-10000000110
χ20222222-122-122-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-2-2-2-21-2-21-2-21111111122-1-1-1-1-1-1-1-1-2-2111111110000-2-2-2-20000000000200020110000110000000-1-10
χ21222222-1-2-2-122-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-21122-2-212-2-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-1000022-2-200000000002000-20-1-10000110000000-110
χ22222222-1-2-2-122-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-21122-2-212-2-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-10000-2-2220000000000-200020110000-1-100000001-10
χ23222222-1-2-2-122-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-2-222-1-22122-1-1-1-1-1-1-1-1-2-211111111-2-211111111000022-2-20000000000-200020-1-100001100000001-10
χ24222222-1-2-2-122-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-2-222-1-22122-1-1-1-1-1-1-1-1-2-211111111-2-2111111110000-2-22200000000002000-20110000-1-10000000-110
χ2522222-12222-122-122-12-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-1222222222-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000002222000002000200-1-10000-1-10000-100-1
χ2622222-12222-122-122-12-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-1222222222-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000-2-2-2-200000-2000-2001100001100001001
χ2722222-12222-122-122-12-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-12222-2-2-2-2-211-211-2-2111111-1-122-1-1-1-1-1-111-2-21111110000000000222200000-2000-200-1-10000-1-100001001
χ2822222-12222-122-122-12-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-12222-2-2-2-2-211-211-2-2111111-1-122-1-1-1-1-1-111-2-21111110000000000-2-2-2-2000002000200110000110000-100-1
χ2922222-12-2-22-122-122-12-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-222-2-2-2-11211-2-211111111-2-2111111-1-122-1-1-1-1-1-1000000000022-2-2000002000-200-1-10000110000-1001
χ3022222-12-2-22-122-122-12-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-222-2-2-2-11211-2-211111111-2-2111111-1-122-1-1-1-1-1-10000000000-2-22200000-2000200110000-1-10000100-1
χ3122222-12-2-22-122-122-12-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-2-2-22221-1-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111000000000022-2-200000-2000200-1-10000110000100-1
χ3222222-12-2-22-122-122-12-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-2-2-22221-1-2-1-122-1-1-1-1-1-111-2-211111111-2-21111110000000000-2-222000002000-200110000-1-10000-1001
χ332222-1222222-122-122-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122220000220000-1-1-1-10022000000-1-10000-1-1-1-10000
χ342222-1222222-122-122-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-20000-2-20000111100-2-200000011000011110000
χ352222-1222222-122-122-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-122-1-1221111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111122220000220000-1-1-1-100-2-2000000110000-1-1110000
χ362222-1222222-122-122-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-122-1-1221111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111-2-2-2-20000-2-2000011110022000000-1-1000011-1-10000
χ372222-122-2-222-122-122-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-2-1-111-22-221111-2-211111111-2-21111-1-1-1-122-1-1-1-122220000-2-20000-1-1-1-100-2200000011000011-1-10000
χ382222-122-2-222-122-122-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-2-1-111-22-221111-2-211111111-2-21111-1-1-1-122-1-1-1-1-2-2-2-200002200001111002-2000000-1-10000-1-1110000
χ392222-122-2-222-122-122-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-211-1-12-22-2-1-1-1-122-1-1-1-11111-2-211111111-2-2111122220000-2-20000-1-1-1-1002-2000000-1-1000011110000
χ402222-122-2-222-122-122-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-211-1-12-22-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-2-2-2-20000220000111100-22000000110000-1-1-1-10000
χ4122-2-222200-22-2-2-222-2-22222200-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000002i2i−2i−2i2-20000002i−2i2i2i−2i−2i0000002-20000002i−2i00000000
χ4222-2-222200-22-2-2-222-2-22222200-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000002i2i−2i−2i-22000000−2i2i2i2i−2i−2i000000-22000000−2i2i00000000
χ4322-2-222200-22-2-2-222-2-22222200-2-2-2-2-2-2-2-2-2-22222200000000000000000000000000000000000000000000−2i−2i2i2i2-2000000−2i2i−2i−2i2i2i0000002-2000000−2i2i00000000
χ4422-2-222200-22-2-2-222-2-22222200-2-2-2-2-2-2-2-2-2-22222200000000000000000000000000000000000000000000−2i−2i2i2i-220000002i−2i−2i−2i2i2i000000-220000002i−2i00000000
χ452-22-22222i−2i2-2-2-22-2-2-222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002i−2i2i−2i00002-200002i−2i2i−2i00000000000000002-2000000
χ462-22-22222i−2i2-2-2-22-2-2-222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000−2i2i−2i2i0000-220000−2i2i−2i2i0000000000000000-22000000
χ472-22-2222−2i2i2-2-2-22-2-2-222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002i−2i2i−2i0000-2200002i−2i2i−2i0000000000000000-22000000
χ482-22-2222−2i2i2-2-2-22-2-2-222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000−2i2i−2i2i00002-20000−2i2i−2i2i00000000000000002-2000000
χ492-22-2-1222i−2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i−ii2i−2i3−3−i3i30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−32i−2i2i−2i00002-20000−ii−ii00000000003−30000-11−i3i30000
χ502-22-2-1222i−2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i−ii2i−2i3−3−i3i30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−3−2i2i−2i2i0000-220000i−ii−i0000000000−3300001-1i3−i30000
χ512-22-2-1222i−2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i−ii2i−2i−33i3−i30000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−3332i−2i2i−2i00002-20000−ii−ii0000000000−330000-11i3−i30000
χ522-22-2-1222i−2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i−ii2i−2i−33i3−i30000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−333−2i2i−2i2i0000-220000i−ii−i00000000003−300001-1−i3i30000
χ532-22-2-122−2i2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2ii−i−2i2i3−3i3−i30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−32i−2i2i−2i0000-220000−ii−ii0000000000−3300001-1−i3i30000
χ542-22-2-122−2i2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2ii−i−2i2i3−3i3−i30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−3−2i2i−2i2i00002-20000i−ii−i00000000003−30000-11i3−i30000
χ552-22-2-122−2i2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2ii−i−2i2i−33−i3i30000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−3332i−2i2i−2i0000-220000−ii−ii00000000003−300001-1i3−i30000
χ562-22-2-122−2i2i2-21-221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2ii−i−2i2i−33−i3i30000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−333−2i2i−2i2i00002-20000i−ii−i0000000000−330000-11−i3i30000
χ572-2-2222200-2-222-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002-2-22002i−2i002i−2i002-2-22000000002i−2i002i−2i0000000000
χ582-2-2222200-2-222-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002-2-2200−2i2i00−2i2i002-2-2200000000−2i2i00−2i2i0000000000
χ592-2-2222200-2-222-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-222-2002i−2i00−2i2i00-222-200000000−2i2i002i−2i0000000000
χ602-2-2222200-2-222-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-222-200−2i2i002i−2i00-222-2000000002i−2i00−2i2i0000000000
χ6144444-2-244-2-24-2-24-2-24-2-211144-2-2111-2-2111-2-2111-2-244-2-24444-2-2-2-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000000
χ6244444-2-244-2-24-2-24-2-24-2-2111-4-4-2-2111-2-2111-2-2111-2-244-2-2-4-4-4-422222222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000000
χ6344444-2-2-4-4-2-24-2-24-2-24-2-21114-4-2-2111-2-2111-2-211122-4-42244-4-42-22-22222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000000
χ6444444-2-2-4-4-2-24-2-24-2-24-2-2111-44-2-2111-2-2111-2-211122-4-422-4-444-22-22-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000000
χ654444-24-244-24-2-24-2-24-2-21-21144-21-211-21-211-21-21144-2-2-2-2-2-2-2-2-244-2-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000000
χ664444-24-244-24-2-24-2-24-2-21-211-4-4-21-211-21-211-21-21144-2-2-2-222222-4-4222-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000000
χ674444-24-2-4-4-24-2-24-2-24-2-21-2114-4-21-211-21-211-21-211-4-42222-2-22224-4-222-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.