Finite Group Databasebeta

← Group #7671

Character table — Group #7671

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222222244444444444444442244448888888888888888888888884444
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1-11-1
χ6111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-11-11
χ7111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-11-11
χ8111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1-11-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ1922222222-2-2-2-22222-2-2-2-2222222-2-2-2-20000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000
χ2122-22-2-22-200002i2i−2i−2i00002i2i−2i−2i2-200001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000
χ2222-22-2-22-200002i2i−2i−2i00002i2i−2i−2i2-20000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000
χ2322-22-2-22-200002i2i−2i−2i0000−2i−2i2i2i-2200001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000
χ2422-22-2-22-200002i2i−2i−2i0000−2i−2i2i2i-220000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000
χ2522-22-2-22-20000−2i−2i2i2i00002i2i−2i−2i-2200001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000
χ2622-22-2-22-20000−2i−2i2i2i00002i2i−2i−2i-220000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000
χ2722-22-2-22-20000−2i−2i2i2i0000−2i−2i2i2i2-200001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000
χ2822-22-2-22-20000−2i−2i2i2i0000−2i−2i2i2i2-20000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000
χ292-222-2-2-222i2i−2i−2i000000002-22-200002i−2ii2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000000
χ302-222-2-2-222i2i−2i−2i000000002-22-200002i−2i−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000000
χ312-222-2-2-222i2i−2i−2i00000000-22-220000−2i2i2−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ322-222-2-2-222i2i−2i−2i00000000-22-220000−2i2i−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ332-222-2-2-22−2i−2i2i2i000000002-22-20000−2i2ii2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000000
χ342-222-2-2-22−2i−2i2i2i000000002-22-20000−2i2i−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000000
χ352-222-2-2-22−2i−2i2i2i00000000-22-2200002i−2i2−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ362-222-2-2-22−2i−2i2i2i00000000-22-2200002i−2i−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ372-22-22-22-22i−2i2i−2i2i−2i2i−2i22-2-200000000000000000000000000i2−i22−22−2i2−i20000
χ382-22-22-22-22i−2i2i−2i2i−2i2i−2i22-2-200000000000000000000000000−i2i2−22−22−i2i20000
χ392-22-22-22-22i−2i2i−2i−2i2i−2i2i-2-222000000000000000000000000002−2−i2i2i2−i2−220000
χ402-22-22-22-22i−2i2i−2i−2i2i−2i2i-2-22200000000000000000000000000−22i2−i2−i2i22−20000
χ412-22-22-22-2−2i2i−2i2i2i−2i2i−2i-2-222000000000000000000000000002−2i2−i2−i2i2−220000
χ422-22-22-22-2−2i2i−2i2i2i−2i2i−2i-2-22200000000000000000000000000−22−i2i2i2−i22−20000
χ432-22-22-22-2−2i2i−2i2i−2i2i−2i2i22-2-200000000000000000000000000i2−i2−22−22i2−i20000
χ442-22-22-22-2−2i2i−2i2i−2i2i−2i2i22-2-200000000000000000000000000−i2i22−22−2−i2i20000
χ452-2-2222-2-2000000002i−2i2i−2i2i−2i−2i2i002-20000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ462-2-2222-2-2000000002i−2i2i−2i2i−2i−2i2i002-2000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ472-2-2222-2-2000000002i−2i2i−2i−2i2i2i−2i00-22002ζ−2ζ−2ζ2ζ000000002ζ3−2ζ3−2ζ32ζ3000000000000
χ482-2-2222-2-2000000002i−2i2i−2i−2i2i2i−2i00-2200−2ζ2ζ2ζ−2ζ00000000−2ζ32ζ32ζ3−2ζ3000000000000
χ492-2-2222-2-200000000−2i2i−2i2i2i−2i−2i2i00-22002ζ3−2ζ3−2ζ32ζ3000000002ζ−2ζ−2ζ2ζ000000000000
χ502-2-2222-2-200000000−2i2i−2i2i2i−2i−2i2i00-2200−2ζ32ζ32ζ3−2ζ300000000−2ζ2ζ2ζ−2ζ000000000000
χ512-2-2222-2-200000000−2i2i−2i2i−2i2i2i−2i002-20000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ522-2-2222-2-200000000−2i2i−2i2i−2i2i2i−2i002-2000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ53444-4-44-4-44-4-440000000000000000000000000000000000000000000000
χ54444-4-44-4-4-444-40000000000000000000000000000000000000000000000
χ5544-4-44-4-44000000004i−4i−4i4i00000000000000000000000000000000000000
χ5644-4-44-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000
χ574-4-4-4-444400004-4-44000000000000000000000000000000000000000000
χ584-4-4-4-44440000-444-4000000000000000000000000000000000000000000

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