Finite Group Databasebeta

← Group #68103

Character table — Group #68103

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111222222222244444444446666888888888888888812121212121224242424
order12222234444666224466121212124444668888121224242424242424242244448888
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-111
χ811111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1
χ91111111-1-1-1-111111-1-111-1-1-1-1111111i−ii−i-1-1ii−i−iii−i−i-1-1-1-111i−ii−i
χ101111111-1-1-1-111111-1-111-1-1-1-1111111−ii−ii-1-1−i−iii−i−iii-1-1-1-111−ii−ii
χ111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-111i−ii−i-1-1ii−i−iii−i−i1111-1-1−ii−ii
χ121111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-111−ii−ii-1-1−i−iii−i−iii1111-1-1i−ii−i
χ131111111-1-1-1-1111-1-11111-1-1-1-11111-1-1i−i−ii11ii−i−i−i−iii11-1-1-1-1i−i−ii
χ141111111-1-1-1-1111-1-11111-1-1-1-11111-1-1−iii−i11−i−iiiii−i−i11-1-1-1-1−iii−i
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1i−i−ii11ii−i−i−i−iii-1-11111−iii−i
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1−iii−i11−i−iiiii−i−i-1-11111i−i−ii
χ17222222-12222-1-1-12222-1-1-1-1-1-10000-1-12222-1-1-1-1-1-1-1-1-1-10000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-10000-1-1-2-2-2-2-1-1111111110000000000
χ19222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-100001122-2-211-1-1-1-111110000000000
χ20222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1000011-2-222111111-1-1-1-10000000000
χ21222222-1-2-2-2-2-1-1-122-2-2-1-111110000-1-12i−2i2i−2i11−i−iii−i−iii0000000000
χ22222222-1-2-2-2-2-1-1-122-2-2-1-111110000-1-1−2i2i−2i2i11ii−i−iii−i−i0000000000
χ23222222-1-2-2-2-2-1-1-1-2-222-1-111110000112i−2i−2i2i-1-1−i−iiiii−i−i0000000000
χ24222222-1-2-2-2-2-1-1-1-2-222-1-11111000011−2i2i2i−2i-1-1ii−i−i−i−iii0000000000
χ252222-2-2222-2-22220000-2-222-2-222-2-20000000000000000002-2000000
χ262222-2-2222-2-22220000-2-222-2-2-2-222000000000000000000-22000000
χ272222-2-22-2-2222220000-2-2-2-22222-2-2000000000000000000-22000000
χ282222-2-22-2-2222220000-2-2-2-222-2-2220000000000000000002-2000000
χ292-22-22-222i−2i2i−2i2-2-200002-22i−2i2i−2i000000000000000000002-2002i−2i0000
χ302-22-22-222i−2i2i−2i2-2-200002-22i−2i2i−2i00000000000000000000-2200−2i2i0000
χ312-22-22-22−2i2i−2i2i2-2-200002-2−2i2i−2i2i000000000000000000002-200−2i2i0000
χ322-22-22-22−2i2i−2i2i2-2-200002-2−2i2i−2i2i00000000000000000000-22002i−2i0000
χ332-22-2-2222i−2i−2i2i2-2-22-22i−2i-222i−2i−2i2i00002-200002i−2i000000000000000000
χ342-22-2-2222i−2i−2i2i2-2-2-22−2i2i-222i−2i−2i2i0000-220000−2i2i000000000000000000
χ352-22-2-222−2i2i2i−2i2-2-22-2−2i2i-22−2i2i2i−2i00002-20000−2i2i000000000000000000
χ362-22-2-222−2i2i2i−2i2-2-2-222i−2i-22−2i2i2i−2i0000-2200002i−2i000000000000000000
χ372-22-2-22-12i−2i−2i2i-1112-22i−2i1-1−iii−i0000-110000−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ382-22-2-22-12i−2i−2i2i-1112-22i−2i1-1−iii−i0000-110000−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ392-22-2-22-12i−2i−2i2i-111-22−2i2i1-1−iii−i00001-10000i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ402-22-2-22-12i−2i−2i2i-111-22−2i2i1-1−iii−i00001-10000i−iζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ412-22-2-22-1−2i2i2i−2i-1112-2−2i2i1-1i−i−ii0000-110000i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ422-22-2-22-1−2i2i2i−2i-1112-2−2i2i1-1i−i−ii0000-110000i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ432-22-2-22-1−2i2i2i−2i-111-222i−2i1-1i−i−ii00001-10000−iiζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ442-22-2-22-1−2i2i2i−2i-111-222i−2i1-1i−i−ii00001-10000−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ454444-4-4-244-4-4-2-2-2000022-2-222000000000000000000000000000000
χ464444-4-4-2-4-444-2-2-200002222-2-2000000000000000000000000000000
χ4744-4-40040000-44-40000000000004i−4i00000000000000000000000000
χ4844-4-40040000-44-4000000000000−4i4i00000000000000000000000000
χ494-44-44-4-24i−4i4i−4i-2220000-22−2i2i−2i2i000000000000000000000000000000
χ504-44-44-4-2−4i4i−4i4i-2220000-222i−2i2i−2i000000000000000000000000000000
χ514-4-440040000-4-4400000000004-40000000000000000000000000000
χ524-4-440040000-4-440000000000-440000000000000000000000000000
χ5388-8-800-400004-440000000000000000000000000000000000000000
χ548-8-8800-4000044-40000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.