Finite Group Databasebeta

← Group #7679

Character table — Group #7679

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222222244444444444444444444448888888888888888888888882244
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
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000000000000000
χ1922222222-2-2-2-2222222-2-2-2-222-2-222-2-20000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ212222-2-2-2-2000000002i−2i2i2i−2i−2i2i−2i2-2000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ222222-2-2-2-2000000002i−2i2i2i−2i−2i2i−2i2-200000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ232222-2-2-2-2000000002i−2i−2i−2i2i2i2i−2i-2200002ζ32ζ3−2ζ3−2ζ3000000002ζ2ζ−2ζ−2ζ000000000000
χ242222-2-2-2-2000000002i−2i−2i−2i2i2i2i−2i-220000−2ζ3−2ζ32ζ32ζ300000000−2ζ−2ζ2ζ2ζ000000000000
χ252222-2-2-2-200000000−2i2i2i2i−2i−2i−2i2i-2200002ζ2ζ−2ζ−2ζ000000002ζ32ζ3−2ζ3−2ζ3000000000000
χ262222-2-2-2-200000000−2i2i2i2i−2i−2i−2i2i-220000−2ζ−2ζ2ζ2ζ00000000−2ζ3−2ζ32ζ32ζ3000000000000
χ272222-2-2-2-200000000−2i2i−2i−2i2i2i−2i2i2-2000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ282222-2-2-2-200000000−2i2i−2i−2i2i2i−2i2i2-200000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ2922-2-222-2-2000022-2-22i−2i0000−2i2i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3022-2-222-2-2000022-2-22i−2i0000−2i2i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3122-2-222-2-2000022-2-2−2i2i00002i−2i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3222-2-222-2-2000022-2-2−2i2i00002i−2i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3322-2-222-2-20000-2-2222i−2i0000−2i2i00−2i2i001+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i000000000000
χ3422-2-222-2-20000-2-2222i−2i0000−2i2i00−2i2i00−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i000000000000
χ3522-2-222-2-20000-2-222−2i2i00002i−2i002i−2i001−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i000000000000
χ3622-2-222-2-20000-2-222−2i2i00002i−2i002i−2i00−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i000000000000
χ3722-2-2-2-22222-2-20000220000-2-200002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ3822-2-2-2-22222-2-20000220000-2-200002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ3922-2-2-2-22222-2-20000-2-20000220000-222−2−222−2−22−222−2−222−2000000000000
χ4022-2-2-2-22222-2-20000-2-20000220000-22−222−2−222−22−2−222−2−22000000000000
χ4122-2-2-2-222-2-2220000220000-2-20000-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ4222-2-2-2-222-2-2220000220000-2-20000-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ4322-2-2-2-222-2-2220000-2-200002200002-22−2−22−222−22−2−22−222−2000000000000
χ4422-2-2-2-222-2-2220000-2-200002200002-2−222−22−2−22−222−22−2−22000000000000
χ452-22-22-22-22i−2i2i−2i2-22-2002i−2i2i−2i0000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ462-22-22-22-22i−2i2i−2i2-22-2002i−2i2i−2i000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ472-22-22-22-22i−2i2i−2i-22-2200−2i2i−2i2i0000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ482-22-22-22-22i−2i2i−2i-22-2200−2i2i−2i2i000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ492-22-22-22-2−2i2i−2i2i2-22-200−2i2i−2i2i0000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ502-22-22-22-2−2i2i−2i2i2-22-200−2i2i−2i2i000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ512-22-22-22-2−2i2i−2i2i-22-22002i−2i2i−2i0000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ522-22-22-22-2−2i2i−2i2i-22-22002i−2i2i−2i000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ534-44-4-44-4400000000004-4-44000000000000000000000000000000000000
χ544-44-4-44-440000000000-444-4000000000000000000000000000000000000
χ554-4-444-4-4400004-4-44000000000000000000000000000000000000000000
χ564-4-444-4-440000-444-4000000000000000000000000000000000000000000
χ574-4-44-444-44i−4i−4i4i0000000000000000000000000000000000000000000000
χ584-4-44-444-4−4i4i4i−4i0000000000000000000000000000000000000000000000

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