Finite Group Databasebeta

← Group #13137352

Character table — Group #13137352

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222222222222222226666666666666666121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order122244443444466612121212121212121212121233666666121212121212121236661212121212121212121212121212121212121212888888882424242424242424242424242424242424446688881212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ5111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1
χ6111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ7111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-111i−ii−i-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-1-1−ii−ii11-1-111−i−iii−i−iii
χ111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-111−ii−ii-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11-1-1i−ii−i11-1-111ii−i−iii−i−i
χ131111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-1111i−i−ii-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1-1-1−iii−i1111-1-1−i−iiiii−i−i
χ151111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1111−iii−i-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-1i−i−ii1111-1-1ii−i−i−i−iii
χ1722222222222222222222222222222-1222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002222-1-10000-1-1-1-1-1-100000000
χ1822222222222222222222222222222-1222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-211000011111100000000
χ192222222222222222222222222222-12-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000002222000000-1-1-1-1-1-1-1-1
χ202222222222222222222222222222-12-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000-2-2-2-200000011111111
χ21222222222-2-2-2-2222-2-2-2-2-2-2-2-222222-1222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-11111111100000000000000000000000022-2-2-1-10000-1-1111100000000
χ22222222222-2-2-2-2222-2-2-2-2-2-2-2-222222-1222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-111111111000000000000000000000000-2-22211000011-1-1-1-100000000
χ23222222222-2-2-2-2222-2-2-2-2-2-2-2-22222-12-1-1-12222222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-11111111100000000000000000000000000000022-2-2000000-1-1-1-11111
χ24222222222-2-2-2-2222-2-2-2-2-2-2-2-22222-12-1-1-12222222-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-111111111000000000000000000000000000000-2-2220000001111-1-1-1-1
χ252222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-11111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-111110000000000000000000000002-22-2-1-1000011-1-11100000000
χ262222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-11111-2-2-2-2-1-1-1-122-2-2-1-1111111-1-1-1-11111000000000000000000000000-22-22110000-1-111-1-100000000
χ272222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-111110000000000000000000000000000002i−2i2i−2i000000−i−iii−i−iii
χ282222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-1-1-1-11122-2-21111-1-1-1-11111000000000000000000000000000000−2i2i−2i2i000000ii−i−iii−i−i
χ292222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-22-1222-1-1-11111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000000000000000000000002-2-22-1-100001111-1-100000000
χ302222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-22-1222-1-1-11111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-1000000000000000000000000-222-2110000-1-1-1-11100000000
χ312222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-10000000000000000000000000000002i−2i−2i2i000000−i−iiiii−i−i
χ322222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1000000000000000000000000000000−2i2i2i−2i000000ii−i−i−i−iii
χ3322-2-222-2-222i−2i2i−2i2-2-22i2i−2i−2i2i2i−2i−2i22-2-2222-2-22-2-222-2-222-2-222-2-22i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ3422-2-222-2-222i−2i2i−2i2-2-22i2i−2i−2i2i2i−2i−2i22-2-22-12-2-2-111-1-11122-2-2-1-1112i−2i2i−2i−ii−ii-1-111−i−iii−i−iii0000000000000000000000000000−i3i30000−i3i33−33−300000000
χ3522-2-222-2-222i−2i2i−2i2-2-22i2i−2i−2i2i2i−2i−2i22-2-22-12-2-2-111-1-11122-2-2-1-1112i−2i2i−2i−ii−ii-1-111−i−iii−i−iii0000000000000000000000000000i3−i30000i3−i3−33−3300000000
χ3622-2-222-2-222i−2i2i−2i2-2-22i2i−2i−2i2i2i−2i−2i22-2-2-12-1112-2-222-2-2-1-111-1-111−ii−ii2i−2i2i−2i-1-111−i−iii−i−iii00000000000000000000000000000000000000003−33−3−i3i3−i3i3
χ3722-2-222-2-222i−2i2i−2i2-2-22i2i−2i−2i2i2i−2i−2i22-2-2-12-1112-2-222-2-2-1-111-1-111−ii−ii2i−2i2i−2i-1-111−i−iii−i−iii0000000000000000000000000000000000000000−33−33i3−i3i3−i3
χ3822-2-222-2-22−2i2i−2i2i2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2222-2-22-2-222-2-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3922-2-222-2-22−2i2i−2i2i2-2-2−2i−2i2i2i−2i−2i2i2i22-2-22-12-2-2-111-1-11122-2-2-1-111−2i2i−2i2ii−ii−i-1-111ii−i−iii−i−i0000000000000000000000000000−i3i30000−i3i3−33−3300000000
χ4022-2-222-2-22−2i2i−2i2i2-2-2−2i−2i2i2i−2i−2i2i2i22-2-22-12-2-2-111-1-11122-2-2-1-111−2i2i−2i2ii−ii−i-1-111ii−i−iii−i−i0000000000000000000000000000i3−i30000i3−i33−33−300000000
χ4122-2-222-2-22−2i2i−2i2i2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2-12-1112-2-222-2-2-1-111-1-111i−ii−i−2i2i−2i2i-1-111ii−i−iii−i−i00000000000000000000000000000000000000003−33−3i3−i3i3−i3
χ4222-2-222-2-22−2i2i−2i2i2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2-12-1112-2-222-2-2-1-111-1-111i−ii−i−2i2i−2i2i-1-111ii−i−iii−i−i0000000000000000000000000000000000000000−33−33−i3i3−i3i3
χ4322-2-2-2-22222i−2i−2i2i2-2-22i2i−2i−2i−2i−2i2i2i-2-222222-2-22-2-2-2-222-2-22222-2-22i−2i−2i2i2i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4422-2-2-2-22222i−2i−2i2i2-2-22i2i−2i−2i−2i−2i2i2i-2-2222-12-2-2-11111-1-1-2-222-1-1112i−2i−2i2i−iii−i11-1-1−i−iiiii−i−i0000000000000000000000000000−i3i30000i3−i33−3−3300000000
χ4522-2-2-2-22222i−2i−2i2i2-2-22i2i−2i−2i−2i−2i2i2i-2-2222-12-2-2-11111-1-1-2-222-1-1112i−2i−2i2i−iii−i11-1-1−i−iiiii−i−i0000000000000000000000000000i3−i30000−i3i3−333−300000000
χ4622-2-2-2-22222i−2i−2i2i2-2-22i2i−2i−2i−2i−2i2i2i-2-222-12-1112-2-2-2-22211-1-1-1-111−iii−i2i−2i−2i2i11-1-1−i−iiiii−i−i0000000000000000000000000000000000000000−i3i3i3−i3−333−3
χ4722-2-2-2-22222i−2i−2i2i2-2-22i2i−2i−2i−2i−2i2i2i-2-222-12-1112-2-2-2-22211-1-1-1-111−iii−i2i−2i−2i2i11-1-1−i−iiiii−i−i0000000000000000000000000000000000000000i3−i3−i3i33−3−33
χ4822-2-2-2-2222−2i2i2i−2i2-2-2−2i−2i2i2i2i2i−2i−2i-2-222222-2-22-2-2-2-222-2-22222-2-2−2i2i2i−2i−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4922-2-2-2-2222−2i2i2i−2i2-2-2−2i−2i2i2i2i2i−2i−2i-2-2222-12-2-2-11111-1-1-2-222-1-111−2i2i2i−2ii−i−ii11-1-1ii−i−i−i−iii0000000000000000000000000000−i3i30000i3−i3−333−300000000
χ5022-2-2-2-2222−2i2i2i−2i2-2-2−2i−2i2i2i2i2i−2i−2i-2-2222-12-2-2-11111-1-1-2-222-1-111−2i2i2i−2ii−i−ii11-1-1ii−i−i−i−iii0000000000000000000000000000i3−i30000−i3i33−3−3300000000
χ5122-2-2-2-2222−2i2i2i−2i2-2-2−2i−2i2i2i2i2i−2i−2i-2-222-12-1112-2-2-2-22211-1-1-1-111i−i−ii−2i2i2i−2i11-1-1ii−i−i−i−iii0000000000000000000000000000000000000000−i3i3i3−i33−3−33
χ5222-2-2-2-2222−2i2i2i−2i2-2-2−2i−2i2i2i2i2i−2i−2i-2-222-12-1112-2-2-2-22211-1-1-1-111i−i−ii−2i2i2i−2i11-1-1ii−i−i−i−iii0000000000000000000000000000000000000000i3−i3−i3i3−333−3
χ532-22-22i−2i2i−2i20000-22-2000000002i−2i2i−2i22-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000
χ542-22-22i−2i2i−2i20000-22-2000000002i−2i2i−2i22-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22-2000000002i−2i2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000
χ552-22-2−2i2i−2i2i20000-22-200000000−2i2i−2i2i22-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000
χ562-22-2−2i2i−2i2i20000-22-200000000−2i2i−2i2i22-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000000−2i2i−2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
χ572-2-222i−2i−2i2i20000-2-22000000002i−2i−2i2i22-2-22-2-222i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000000000000000000000
χ582-2-222i−2i−2i2i20000-2-22000000002i−2i−2i2i22-2-22-2-222i−2i−2i2i2i−2i−2i2i2-2-22000000002i−2i−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ592-2-22−2i2i2i−2i20000-2-2200000000−2i2i2i−2i22-2-22-2-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ602-2-22−2i2i2i−2i20000-2-2200000000−2i2i2i−2i22-2-22-2-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000−2i2i2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000
χ614444444444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000000000
χ62444444444-4-4-4-4444-4-4-4-4-4-4-4-44444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000
χ634444-4-4-4-4444-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2222222221111-2-222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000000000000000
χ644444-4-4-4-44-4-444444-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-222222222111122-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000000000000000
χ6544-4-444-4-444i−4i4i−4i4-4-44i4i−4i−4i4i4i−4i−4i44-4-4-2-2-222-222-2-222-2-22211-1-1−2i2i−2i2i−2i2i−2i2i11-1-1ii−i−iii−i−i000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.