Finite Group Databasebeta

← Group #7658

Character table — Group #7658

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222222244444444444444442244448888888888888888888888882444
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−i1-1-11
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-111-1
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-111-1
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−iiiii1-1-11
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
χ1311111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-1
χ1411111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-11
χ1511111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11-11
χ1611111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-11-1
χ172222222222222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000000000000000
χ1922222222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000
χ2122-222-2-2-2000000002i−2i2i2i−2i−2i2i−2i002-20000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ2222-222-2-2-2000000002i−2i2i2i−2i−2i2i−2i002-2000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ2322-222-2-2-2000000002i−2i−2i−2i2i2i2i−2i00-22002ζ32ζ3−2ζ3−2ζ3000000002ζ2ζ−2ζ−2ζ000000000000
χ2422-222-2-2-2000000002i−2i−2i−2i2i2i2i−2i00-2200−2ζ3−2ζ32ζ32ζ300000000−2ζ−2ζ2ζ2ζ000000000000
χ2522-222-2-2-200000000−2i2i2i2i−2i−2i−2i2i00-22002ζ2ζ−2ζ−2ζ000000002ζ32ζ3−2ζ3−2ζ3000000000000
χ2622-222-2-2-200000000−2i2i2i2i−2i−2i−2i2i00-2200−2ζ−2ζ2ζ2ζ00000000−2ζ3−2ζ32ζ32ζ3000000000000
χ2722-222-2-2-200000000−2i2i−2i−2i2i2i−2i2i002-20000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ2822-222-2-2-200000000−2i2i−2i−2i2i2i−2i2i002-2000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ2922-2-2-222-22i2i−2i−2i2i2i−2i−2i002-22-20000000000000000000000002−2i2−i2i2−i22−20000
χ3022-2-2-222-22i2i−2i−2i2i2i−2i−2i002-22-2000000000000000000000000−22−i2i2−i2i2−220000
χ3122-2-2-222-22i2i−2i−2i−2i−2i2i2i00-22-22000000000000000000000000i2−i2−222−2−i2i20000
χ3222-2-2-222-22i2i−2i−2i−2i−2i2i2i00-22-22000000000000000000000000−i2i22−2−22i2−i20000
χ3322-2-2-222-2−2i−2i2i2i2i2i−2i−2i00-22-22000000000000000000000000i2−i22−2−22−i2i20000
χ3422-2-2-222-2−2i−2i2i2i2i2i−2i−2i00-22-22000000000000000000000000−i2i2−222−2i2−i20000
χ3522-2-2-222-2−2i−2i2i2i−2i−2i2i2i002-22-20000000000000000000000002−2−i2i2−i2i22−20000
χ3622-2-2-222-2−2i−2i2i2i−2i−2i2i2i002-22-2000000000000000000000000−22i2−i2i2−i2−220000
χ372-222-22-2-22i−2i2i−2i00002i−2i0000−2i2i00002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-222-22-2-22i−2i2i−2i00002i−2i0000−2i2i00002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-222-22-2-22i−2i2i−2i0000−2i2i00002i−2i0000-221−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i000000000000
χ402-222-22-2-22i−2i2i−2i0000−2i2i00002i−2i0000-22−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i000000000000
χ412-222-22-2-2−2i2i−2i2i00002i−2i0000−2i2i0000-221+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i000000000000
χ422-222-22-2-2−2i2i−2i2i00002i−2i0000−2i2i0000-22−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i000000000000
χ432-222-22-2-2−2i2i−2i2i0000−2i2i00002i−2i00002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ442-222-22-2-2−2i2i−2i2i0000−2i2i00002i−2i00002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ452-2-22-2-22200002-22-2220000-2-22-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ462-2-22-2-22200002-22-2220000-2-22-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ472-2-22-2-22200002-22-2-2-2000022-2200002−2−22−222−22−2−22−222−2000000000000
χ482-2-22-2-22200002-22-2-2-2000022-220000−222−22−2−22−222−22−2−22000000000000
χ492-2-22-2-2220000-22-22220000-2-2-220000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ502-2-22-2-2220000-22-22220000-2-2-220000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ512-2-22-2-2220000-22-22-2-20000222-200002−2−222−2−22−222−2−222−2000000000000
χ522-2-22-2-2220000-22-22-2-20000222-20000−222−2−222−22−2−222−2−22000000000000
χ53444-4-4-4-4400000000004i−4i−4i4i000000000000000000000000000000000000
χ54444-4-4-4-440000000000−4i4i4i−4i000000000000000000000000000000000000
χ554-44-44-44-400004i−4i−4i4i000000000000000000000000000000000000000000
χ564-44-44-44-40000−4i4i4i−4i000000000000000000000000000000000000000000
χ574-4-4-444-444-4-440000000000000000000000000000000000000000000000
χ584-4-4-444-44-444-40000000000000000000000000000000000000000000000

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