Finite Group Databasebeta

← Group #8972

Character table — Group #8972

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222244444444444444444488888888888888881616
order1222444444444444244444444444448888248888888888888844
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-1-1-111-1-111-1-1-1111-1-1iiii−i−i−i−iii−i−i1-1i−iii−i−iii−i−i11-1-11-1
χ101111-1-1-1-111-1-111-1-1-1111-1-1iiii−i−i−i−i−i−iii1-1−ii−i−iiiii−i−i-1-111-11
χ111111-1-1-1-111-1-111-1-1-1111-1-1−i−i−i−iiiiiii−i−i1-1i−iii−i−i−i−iii-1-111-11
χ121111-1-1-1-111-1-111-1-1-1111-1-1−i−i−i−iiiii−i−iii1-1−ii−i−iii−i−iii11-1-11-1
χ131111-1-1-1-111-1-111-1-1-11-1-111iiii−i−i−i−iii−i−i-11i−i−i−iii−i−iii11-1-1-11
χ141111-1-1-1-111-1-111-1-1-11-1-111iiii−i−i−i−i−i−iii-11−iiii−i−i−i−iii-1-1111-1
χ151111-1-1-1-111-1-111-1-1-11-1-111−i−i−i−iiiiiii−i−i-11i−i−i−iiiii−i−i-1-1111-1
χ161111-1-1-1-111-1-111-1-1-11-1-111−i−i−i−iiiii−i−iii-11−iiii−i−iii−i−i11-1-1-11
χ172222222222-2-2-2-222-2-2000000000000222200-2-200000000000000
χ182222222222-2-2-2-222-2-2000000000000-2-2-2-2002200000000000000
χ1922222222-2-22222-2-2-2-22222000000000000-2-20000000000000000
χ2022222222-2-22222-2-2-2-2-2-2-2-2000000000000220000000000000000
χ2122222222-2-2-2-2-2-2-2-222000000000000000000002-22-20000000000
χ2222222222-2-2-2-2-2-2-2-22200000000000000000000-22-220000000000
χ232222-2-2-2-22222-2-2-2-22-20000000000002i2i−2i−2i00−2i2i00000000000000
χ242222-2-2-2-22222-2-2-2-22-2000000000000−2i−2i2i2i002i−2i00000000000000
χ252222-2-2-2-2-2-222-2-222-22000000000000000000002i−2i−2i2i0000000000
χ262222-2-2-2-2-2-222-2-222-2200000000000000000000−2i2i2i−2i0000000000
χ272222-2-2-2-2-2-2-2-222222-222-2-2000000000000-220000000000000000
χ282222-2-2-2-2-2-2-2-222222-2-2-2220000000000002-20000000000000000
χ292-22-22i−2i2i−2i002i−2i2-200002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000001−i−1+i1+i−1−i000000
χ302-22-22i−2i2i−2i002i−2i2-200002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000−1+i1−i−1−i1+i000000
χ312-22-22i−2i2i−2i002i−2i2-20000−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000−1+i1−i−1−i1+i000000
χ322-22-22i−2i2i−2i002i−2i2-20000−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000001−i−1+i1+i−1−i000000
χ332-22-2−2i2i−2i2i00−2i2i2-200002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000−1−i1+i−1+i1−i000000
χ342-22-2−2i2i−2i2i00−2i2i2-200002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000001+i−1−i1−i−1+i000000
χ352-22-2−2i2i−2i2i00−2i2i2-20000−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000001+i−1−i1−i−1+i000000
χ362-22-2−2i2i−2i2i00−2i2i2-20000−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000−1−i1+i−1+i1−i000000
χ372-2-222i−2i−2i2i2-200002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ−2ζ2ζ3−2ζ30000000000002−2i2−i200
χ382-2-222i−2i−2i2i2-200002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ2ζ−2ζ32ζ3000000000000−22−i2i200
χ392-2-222i−2i−2i2i2-200002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ−2ζ2ζ3−2ζ3000000000000−22−i2i200
χ402-2-222i−2i−2i2i2-200002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ2ζ−2ζ32ζ30000000000002−2i2−i200
χ412-2-22−2i2i2i−2i2-20000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ3−2ζ32ζ−2ζ000000000000−22i2−i200
χ422-2-22−2i2i2i−2i2-20000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ32ζ3−2ζ2ζ0000000000002−2−i2i200
χ432-2-22−2i2i2i−2i2-20000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ3−2ζ32ζ−2ζ0000000000002−2−i2i200
χ442-2-22−2i2i2i−2i2-20000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ32ζ3−2ζ2ζ000000000000−22i2−i200
χ4544-4-444-4-4000000000000002-2-222-2-220000000000000000000000
χ4644-4-444-4-400000000000000-222-2-222-20000000000000000000000
χ4744-4-4-4-444000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ4844-4-4-4-44400000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ494-44-44i−4i4i−4i00−4i4i-4400000000000000000000000000000000000000
χ504-44-4−4i4i−4i4i004i−4i-4400000000000000000000000000000000000000
χ514-4-444i−4i−4i4i-440000−4i4i000000000000000000000000000000000000
χ524-4-44−4i4i4i−4i-4400004i−4i000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.