Finite Group Databasebeta

← Group #8415

Character table — Group #8415

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43
size111122222222444444488888888888888888888881616
order1222444444442224444244444444444448888888888
χ11111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-11-11-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111-1-1111-1-11-11-111-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111-1-1111-1-11-11-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ9111111-1-1-1-1-1-111-111-1-111-1-11-111-1-1ii−i−iii−i−iii−i−ii−i
χ10111111-1-1-1-1-1-111-111-1-111-1-11-111-1-1−i−iii−i−iii−i−iii−ii
χ11111111-1-1-1-1-1-111-111-1-1-111-1-11-1-111ii−i−iii−i−i−i−iii−ii
χ12111111-1-1-1-1-1-111-111-1-1-111-1-11-1-111−i−iii−i−iiiii−i−ii−i
χ13111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-111ii−i−i−i−iiiii−i−i−ii
χ14111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-111−i−iiiii−i−i−i−iiii−i
χ15111111-1-1-1-1-1-1-1-1-11111-1-111-1111-1-1ii−i−i−i−iii−i−iiii−i
χ16111111-1-1-1-1-1-1-1-1-11111-1-111-1111-1-1−i−iiiii−i−iii−i−i−ii
χ172222222222-2-222-2-2-2220-20-200000000000000000000
χ182222222222-2-2-2-2-2-2-2-2-2020200000000000000000000
χ19222222-2-2-2-222222-2-2-2-20-20200000000000000000000
χ20222222-2-2-2-222-2-22-2-222020-200000000000000000000
χ212222-2-222-2-22200-2-22000000002-22-200000000000000
χ222222-2-222-2-22200-2-2200000000-22-2200000000000000
χ232222-2-222-2-2-2-20022-20020-20-22000000000000000000
χ242222-2-222-2-2-2-20022-200-20202-2000000000000000000
χ252222-2-2-2-2222200-22-2002020-2-2000000000000000000
χ262222-2-2-2-2222200-22-200-20-2022000000000000000000
χ272222-2-2-2-222-2-2002-22000000002-2-2200000000000000
χ282222-2-2-2-222-2-2002-2200000000-222-200000000000000
χ292-22-22-22i−2i2i−2i002-20002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000
χ302-22-22-22i−2i2i−2i002-20002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000
χ312-22-22-22i−2i2i−2i00-22000−2i2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000
χ322-22-22-22i−2i2i−2i00-22000−2i2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000
χ332-22-22-2−2i2i−2i2i002-2000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000
χ342-22-22-2−2i2i−2i2i002-2000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000
χ352-22-22-2−2i2i−2i2i00-220002i−2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000
χ362-22-22-2−2i2i−2i2i00-220002i−2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000
χ374-44-4-444i−4i−4i4i000000000000000000000000000000000
χ384-44-4-44−4i4i4i−4i000000000000000000000000000000000
χ394-4-440000004i−4i00000000000000000000000002ζ3−2ζ32ζ−2ζ00
χ404-4-440000004i−4i0000000000000000000000000−2ζ32ζ3−2ζ2ζ00
χ414-4-44000000−4i4i00000000000000000000000002ζ−2ζ2ζ3−2ζ300
χ424-4-44000000−4i4i0000000000000000000000000−2ζ2ζ−2ζ32ζ300
χ4388-8-8000000000000000000000000000000000000000

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