Finite Group Databasebeta

← Group #13178329

Character table — Group #13178329

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order1222333446666666663333344666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222444444446666222444466121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-111-1-1-1-11-1-11
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11-111-1-1-1-111-1-1-1-1-1-1-111-1
χ511111111111111111111111-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-11-11-1-1111-1-111111111-1-1-1-1-1-1
χ611111111111111111111111-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11-1111-1-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111111-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11-1-1-11111-1-111-1-111-111-1
χ811111111111111111111111-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11-1-11111-1-111-1-1-1-1111-1-11
χ91111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-11-11-1-1-1-1111111-1-1-1-1-1-1-11-11
χ101111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-11-11111-1-1-1-111-1-1-1-11-11-1
χ111111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-11111-1-111
χ121111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11-1-1-1-1-1-11111111111-1-1
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111111111-1-1-1-11-1-1-1-1-11111-1-1-1-1111-11-1
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-11111-1-111-1-1-1-1-1-111-1-111-11-11
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-11111111-1-1-1-111-1-111-1-1
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-111
χ17222222-1222-12-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-12222-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000002200000220020-1-10000-1-10000000-1-10
χ18222222-1222-12-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-12222-122-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-200000-2-200-20110000110000000110
χ19222222-1222-12-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-2-2-1-122-2-21-2-21-2-21111111122-1-1-1-1-1-1-1-1-2-2111111110000000022000002-200-20-1-10000-1-10000000110
χ20222222-1222-12-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-2-2-1-122-2-21-2-21-2-21111111122-1-1-1-1-1-1-1-1-2-21111111100000000-2-200000-220020110000110000000-1-10
χ21222222-1-2-22-12-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-22211-2-2-2-2-1-22122-1-1-1-1-1-1-1-1-2-211111111-2-211111111000000002200000-2200-20110000-1-10000000-110
χ22222222-1-2-22-12-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-22211-2-2-2-2-1-22122-1-1-1-1-1-1-1-1-2-211111111-2-21111111100000000-2-2000002-20020-1-100001100000001-10
χ23222222-1-2-22-12-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-2-22212-2-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-1000000002200000-2-20020110000-1-100000001-10
χ24222222-1-2-22-12-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-2-22212-2-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-100000000-2-2000002200-20-1-10000110000000-110
χ2522222-122222-122-12-12-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-1222222222-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000220000000020022000000-1-100-1-10000-100-1
χ2622222-122222-122-12-12-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-1222222222-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-200000000-200-2-200000011001100001001
χ2722222-122222-122-12-12-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-1-2-22222-2-2-211-211-2-2111111-1-122-1-1-1-1-1-111-2-211111100002200000000-2002-2000000-1-100-1-100001001
χ2822222-122222-122-12-12-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-1-2-22222-2-2-211-211-2-2111111-1-122-1-1-1-1-1-111-2-21111110000-2-200000000200-220000001100110000-100-1
χ2922222-12-2-222-122-12-12-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-11122-2-2-2-2-2-221-1-2-1-122-1-1-1-1-1-111-2-211111111-2-211111100002200000000-200-22000000-1-100110000100-1
χ3022222-12-2-222-122-12-12-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-11122-2-2-2-2-2-221-1-2-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-2000000002002-20000001100-1-10000-1001
χ3122222-12-2-222-122-12-12-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-2-2-222-2-11211-2-211111111-2-2111111-1-122-1-1-1-1-1-100002200000000200-2-2000000-1-100110000-1001
χ3222222-12-2-222-122-12-12-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-2-2-222-2-11211-2-211111111-2-2111111-1-122-1-1-1-1-1-10000-2-200000000-200220000001100-1-10000100-1
χ332222-12222-1222-1222-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222002200-1-1-1-1000000200-1-1000000-1-1-1-10000
χ342222-12222-1222-1222-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-200-2-2001111000000-2001100000011110000
χ352222-12222-1222-1222-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1221122-1-111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111122-2-200-2-200-1-1-1-100000020011000000-1-1110000
χ362222-12222-1222-1222-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1221122-1-111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111-2-2220022001111000000-200-1-100000011-1-10000
χ372222-122-2-2-1222-1222-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-1-1-2-211112-22-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111222200-2-200-1-1-1-1000000-200-1-100000011110000
χ382222-122-2-2-1222-1222-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-1-1-2-211112-22-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111-2-2-2-2002200111100000020011000000-1-1-1-10000
χ392222-122-2-2-1222-1222-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-211-1-1-22-221111-2-211111111-2-21111-1-1-1-122-1-1-1-122-2-2002200-1-1-1-1000000-2001100000011-1-10000
χ402222-122-2-2-1222-1222-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-211-1-1-22-221111-2-211111111-2-21111-1-1-1-122-1-1-1-1-2-22200-2-2001111000000200-1-1000000-1-1110000
χ4122-2-22222i−2i-22-2-222-2-2-22222200-2-2-2-2-222222-2-2-2-2-22i−2i002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000002-2002i−2i0000000000000002-2000000002i−2i0000
χ4222-2-22222i−2i-22-2-222-2-2-22222200-2-2-2-2-222222-2-2-2-2-22i−2i002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i000000000000-2200−2i2i000000000000000-2200000000−2i2i0000
χ4322-2-2222−2i2i-22-2-222-2-2-22222200-2-2-2-2-222222-2-2-2-2-2−2i2i00−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000002-200−2i2i0000000000000002-200000000−2i2i0000
χ4422-2-2222−2i2i-22-2-222-2-2-22222200-2-2-2-2-222222-2-2-2-2-2−2i2i00−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i000000000000-22002i−2i000000000000000-22000000002i−2i0000
χ4522-2-2-1222i−2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-2112i−2i−i3i32i−2i−ii3−30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−3002-2002i−2i00−i3−i3i3i3000000000-110000003−3−ii0000
χ4622-2-2-1222i−2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-2112i−2i−i3i32i−2i−ii3−30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−300-2200−2i2i00i3i3−i3−i30000000001-1000000−33i−i0000
χ4722-2-2-1222i−2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-2112i−2ii3−i32i−2i−ii−330000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−333002-2002i−2i00i3i3−i3−i3000000000-11000000−33−ii0000
χ4822-2-2-1222i−2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-2112i−2ii3−i32i−2i−ii−330000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−33300-2200−2i2i00−i3−i3i3i30000000001-10000003−3i−i0000
χ4922-2-2-122−2i2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-211−2i2i−i3i3−2i2ii−i−330000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−333002-200−2i2i00−i3−i3i3i3000000000-11000000−33i−i0000
χ5022-2-2-122−2i2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-211−2i2i−i3i3−2i2ii−i−330000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−33300-22002i−2i00i3i3−i3−i30000000001-10000003−3−ii0000
χ5122-2-2-122−2i2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-211−2i2ii3−i3−2i2ii−i3−30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−3002-200−2i2i00i3i3−i3−i3000000000-110000003−3i−i0000
χ5222-2-2-122−2i2i12-2-2-12-2-21-1-12-1-10011-211-1-12-1-111-211−2i2ii3−i3−2i2ii−i3−30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−300-22002i−2i00−i3−i3i3i30000000001-1000000−33−ii0000
χ532-22-2222002-2-22-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002-2002i−2i002i−2i2-22-2000000000002i−2i2i−2i0000000000
χ542-22-2222002-2-22-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002-200−2i2i00−2i2i2-22-200000000000−2i2i−2i2i0000000000
χ552-22-2222002-2-22-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-22002i−2i00−2i2i-22-22000000000002i−2i−2i2i0000000000
χ562-22-2222002-2-22-2-2-22-2222220022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-2200−2i2i002i−2i-22-2200000000000−2i2i2i−2i0000000000
χ5744444-2-2444-2-2-24-2-2-24-2-211144-2-2111-2-2111-2-2111-2-244-2-24444-2-2-2-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-2444-2-2-24-2-2-24-2-2111-4-4-2-2111-2-2111-2-2111-2-2-4-4-2-244-4-422222222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-44-2-2-24-2-2-24-2-21114-4-2-2111-2-2111-2-2111224422-4-4-4-4-22-22-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ6044444-2-2-4-44-2-2-24-2-2-24-2-2111-44-2-2111-2-2111-2-211122-4-422-4-4442-22-22222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ614444-24-244-2-24-2-24-24-2-21-21144-21-211-21-211-21-21144-2-2-2-2-2-2-2-2-244-2-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-244-2-24-2-24-24-2-21-211-4-4-21-211-21-211-21-2114422-2-2-2-2222-4-4222-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-4-2-24-2-24-24-2-21-2114-4-21-211-21-211-21-211-4-4-2-2222222-2-442-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ644444-24-2-4-4-2-24-2-24-24-2-21-211-44-21-211-21-211-21-211-4-4222222-2-224-4-222-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ654444-2-2444-24-24-2-24-2-21-2-211441-2-2111-2-2111-2-211-2-2-2-244-2-2-2-24-2-2411-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-2444-24-24-2-24-2-21-2-211-4-41-2-2111-2-2111-2-211-2-22244-2-222-422-4-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-4-24-24-2-24-2-21-2-2114-41-2-2111-2-2111-2-21122-2-2-4-4222242-2-411-2-2-2-21111-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000000
χ684444-2-24-4-4-24-24-2-24-2-21-2-211-441-2-2111-2-2111-2-2112222-4-422-2-2-4-224-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
χ694444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i3244111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+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.