Finite Group Databasebeta

← Group #72342881

Character table — Group #72342881

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222233334466666666668888888888881212161616161616161616161616242424242424242424242424242424242424242432323232323232324848484848484848
order12442444448888224488244444888836121216161616242424248861212121212242424242424888888888888888816161616484848484848484824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i-1-1-1-1111-1-1-1-11-1-11111iiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1
χ6111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i-1-1-1-1111-1-1-1-11-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-1-1-1-11111
χ7111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iii-1-1-1-1111-1-1-1-11-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-1-1-1-11111
χ8111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iii-1-1-1-1111-1-1-1-11-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii1111-1-1-1-1
χ911-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−iii−i−i11-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ii−i−i1-1-1ii−i−i1i−i11-1-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-11-1i−ii−i
χ1011-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−iii−i−i11-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ii−i−i1-1-1ii−i−i1i−i11-1-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-11-11−ii−ii
χ1111-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−iii−i−i11-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ii−i−i1-1-1ii−i−i1i−i11-1-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-11-11−ii−ii
χ1211-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−iii−i−i11-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ii−i−i1-1-1ii−i−i1i−i11-1-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-11-1i−ii−i
χ1311-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−i−iii11-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−i−iii1-1-1−i−iii1−ii11-1-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-11-1−ii−ii
χ1411-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−i−iii11-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−i−iii1-1-1−i−iii1−ii11-1-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-11-11i−ii−i
χ1511-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−i−iii11-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−i−iii1-1-1−i−iii1−ii11-1-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-11-11i−ii−i
χ1611-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−i−iii11-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−i−iii1-1-1−i−iii1−ii11-1-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-11-1−ii−ii
χ17222222222222222222222222222222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ18222222222222222222222222222222-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ192222222222-2-2-2-22222-2-2222222-2-2-2-222220000-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000
χ202222222222-2-2-2-22222-2-2222222-2-2-2-2-1-1-1-100001111-2-2-1-1-1-1-1-1111111000000000000000000003−33−33−33−300000000
χ212222222222-2-2-2-22222-2-2222222-2-2-2-2-1-1-1-100001111-2-2-1-1-1-1-1-111111100000000000000000000−33−33−33−3300000000
χ22222222-2-2-2-222222222-2-222-2-2-2-22222222200002222-2-22-2-2-2-2222-2-2-2-2000000000000000000000000000000000000
χ23222222-2-2-2-222222222-2-222-2-2-2-22222-1-1-1-10000-1-1-1-1-2-2-11111-1-1-1111100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ24222222-2-2-2-222222222-2-222-2-2-2-22222-1-1-1-10000-1-1-1-1-2-2-11111-1-1-1111100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ25222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-1-1-1-12i2i−2i−2i111122-11111-111-1-1-1-100000000000000002i2i−2i−2i−i−i−i−iiiii00000000
χ26222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-1-1-1-1−2i−2i2i2i111122-11111-111-1-1-1-10000000000000000−2i−2i2i2iiiii−i−i−i−i00000000
χ272222-2-2000022-2-2222200-2-200002-22-222220000-2-2-2-200-20000-2220000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000000000
χ282222-2-2000022-2-2222200-2-200002-22-222220000-2-2-2-200-20000-2220000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000000
χ292222-2-20000-2-222222200-2-20000-22-2222220000222200-20000-2-2-200002−22−2−22−222−22−2−22−2200000000000000000000
χ302222-2-20000-2-222222200-2-20000-22-2222220000222200-20000-2-2-20000−22−222−22−2−22−222−22−200000000000000000000
χ3122-2-22-200002i−2i−2i2i22-2-2002-200002i−2i−2i2i22-2-20000−2i−2i2i2i0020000-22i−2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000000000
χ3222-2-22-200002i−2i−2i2i22-2-2002-200002i−2i−2i2i22-2-20000−2i−2i2i2i0020000-22i−2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000000000
χ3322-2-22-20000−2i2i2i−2i22-2-2002-20000−2i2i2i−2i22-2-200002i2i−2i−2i0020000-2−2i2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000000000
χ3422-2-22-20000−2i2i2i−2i22-2-2002-20000−2i2i2i−2i22-2-200002i2i−2i−2i0020000-2−2i2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000000000
χ3522-2-2-222i2i−2i−2i2i−2i2i−2i22-2-22-2-222i2i−2i−2i2i2i−2i−2i-1-1112ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−i−iii2-21−i−iii-1−ii-1-11100000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000
χ3622-2-2-222i2i−2i−2i2i−2i2i−2i22-2-22-2-222i2i−2i−2i2i2i−2i−2i-1-111−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−i−iii2-21−i−iii-1−ii-1-1110000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000
χ3722-2-2-222i2i−2i−2i−2i2i−2i2i22-2-2-22-222i2i−2i−2i−2i−2i2i2i22-2-20000−2i−2i2i2i-22-22i2i−2i−2i2−2i2i-2-222000000000000000000000000000000000000
χ3822-2-2-222i2i−2i−2i−2i2i−2i2i22-2-2-22-222i2i−2i−2i−2i−2i2i2i-1-1110000ii−i−i-221−i−iii-1i−i11-1-100000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ3922-2-2-222i2i−2i−2i−2i2i−2i2i22-2-2-22-222i2i−2i−2i−2i−2i2i2i-1-1110000ii−i−i-221−i−iii-1i−i11-1-100000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ4022-2-2-22−2i−2i2i2i2i−2i2i−2i22-2-2-22-22−2i−2i2i2i2i2i−2i−2i22-2-200002i2i−2i−2i-22-2−2i−2i2i2i22i−2i-2-222000000000000000000000000000000000000
χ4122-2-2-22−2i−2i2i2i2i−2i2i−2i22-2-2-22-22−2i−2i2i2i2i2i−2i−2i-1-1110000−i−iii-221ii−i−i-1−ii11-1-100000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ4222-2-2-22−2i−2i2i2i2i−2i2i−2i22-2-2-22-22−2i−2i2i2i2i2i−2i−2i-1-1110000−i−iii-221ii−i−i-1−ii11-1-100000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ4322-2-2-22−2i−2i2i2i−2i2i−2i2i22-2-22-2-22−2i−2i2i2i−2i−2i2i2i-1-111−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ii−i−i2-21ii−i−i-1i−i-1-1110000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000
χ4422-2-2-22−2i−2i2i2i−2i2i−2i2i22-2-22-2-22−2i−2i2i2i−2i−2i2i2i-1-1112ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23ii−i−i2-21ii−i−i-1i−i-1-11100000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000
χ4533333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1000033330000-1-100000000000011111111-1-1-1-1-1-1-1-1-1-1-1-10000000011-1-111-1-1
χ4633333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1000033330000-1-1000000000000-1-1-1-1-1-1-1-111111111-1-1-1-100000000-1-111-1-111
χ4733333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-10000-3-3-3-30000-1-100000000000011111111-1-1-1-1-1-1-1-1111100000000-1-111-1-111
χ4833333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-10000-3-3-3-30000-1-1000000000000-1-1-1-1-1-1-1-11111111111110000000011-1-111-1-1
χ49333333-3-3-3-3-3-3-3-3-1-1-1-133-1-11111111100003i3i−3i−3i0000-1-1000000000000iiii−i−i−i−i−i−i−i−iiiii−i−iii0000000011-1-1-1-111
χ50333333-3-3-3-3-3-3-3-3-1-1-1-133-1-11111111100003i3i−3i−3i0000-1-1000000000000−i−i−i−iiiiiiiii−i−i−i−i−i−iii00000000-1-11111-1-1
χ51333333-3-3-3-3-3-3-3-3-1-1-1-133-1-1111111110000−3i−3i3i3i0000-1-1000000000000iiii−i−i−i−i−i−i−i−iiiiiii−i−i00000000-1-11111-1-1
χ52333333-3-3-3-3-3-3-3-3-1-1-1-133-1-1111111110000−3i−3i3i3i0000-1-1000000000000−i−i−i−iiiiiiiii−i−i−i−iii−i−i0000000011-1-1-1-111
χ5333-3-3-333i3i−3i−3i3i−3i3i−3i-1-1113-31-1−i−iii−i−iii00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ130000-11000000000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13000000001-1-11i−i−ii
χ5433-3-3-333i3i−3i−3i3i−3i3i−3i-1-1113-31-1−i−iii−i−iii00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ130000-11000000000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000-111-1−iii−i
χ5533-3-3-333i3i−3i−3i3i−3i3i−3i-1-1113-31-1−i−iii−i−iii0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ130000-11000000000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000-111-1−iii−i
χ5633-3-3-333i3i−3i−3i3i−3i3i−3i-1-1113-31-1−i−iii−i−iii0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ130000-11000000000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000001-1-11i−i−ii
χ5733-3-3-33−3i−3i3i3i−3i3i−3i3i-1-1113-31-1ii−i−iii−i−i0000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ230000-11000000000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23000000001-1-11−iii−i
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.