Finite Group Databasebeta

← Group #7670

Character table — Group #7670

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
χ5111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1-1-11
χ6111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-111-1
χ7111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-111-1
χ8111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1-1-11
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−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
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-1
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-11
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11-11
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-11-11-1
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000000000000000
χ1922222222-2-2-2-22222-2-2-2-22222-2-222-2-20000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ21222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i00002-200002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ22222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i00002-20000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ23222-2-2-2-22000000002i2i−2i−2i−2i−2i2i2i0000-222ζ2ζ−2ζ−2ζ000000002ζ32ζ3−2ζ3−2ζ3000000000000
χ24222-2-2-2-22000000002i2i−2i−2i−2i−2i2i2i0000-22−2ζ−2ζ2ζ2ζ00000000−2ζ3−2ζ32ζ32ζ3000000000000
χ25222-2-2-2-2200000000−2i−2i2i2i2i2i−2i−2i0000-222ζ32ζ3−2ζ3−2ζ3000000002ζ2ζ−2ζ−2ζ000000000000
χ26222-2-2-2-2200000000−2i−2i2i2i2i2i−2i−2i0000-22−2ζ3−2ζ32ζ32ζ300000000−2ζ−2ζ2ζ2ζ000000000000
χ27222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i00002-200002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ28222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i00002-20000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ2922-222-2-2-200002i2i−2i−2i00002-22-2002i−2i00i2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000000
χ3022-222-2-2-200002i2i−2i−2i00002-22-2002i−2i00−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000000
χ3122-222-2-2-200002i2i−2i−2i0000-22-2200−2i2i002−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ3222-222-2-2-200002i2i−2i−2i0000-22-2200−2i2i00−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ3322-222-2-2-20000−2i−2i2i2i00002-22-200−2i2i00i2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000000
χ3422-222-2-2-20000−2i−2i2i2i00002-22-200−2i2i00−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000000
χ3522-222-2-2-20000−2i−2i2i2i0000-22-22002i−2i002−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ3622-222-2-2-20000−2i−2i2i2i0000-22-22002i−2i00−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ3722-2-2-222-22i2i−2i−2i000000002i−2i−2i2i2-200001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ3822-2-2-222-22i2i−2i−2i000000002i−2i−2i2i2-20000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ3922-2-2-222-22i2i−2i−2i00000000−2i2i2i−2i-2200001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ4022-2-2-222-22i2i−2i−2i00000000−2i2i2i−2i-220000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ4122-2-2-222-2−2i−2i2i2i000000002i−2i−2i2i-2200001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ4222-2-2-222-2−2i−2i2i2i000000002i−2i−2i2i-220000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ4322-2-2-222-2−2i−2i2i2i00000000−2i2i2i−2i2-200001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ4422-2-2-222-2−2i−2i2i2i00000000−2i2i2i−2i2-20000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ452-222-22-2-22i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000002−2i2−i2i2−i22−20000
χ462-222-22-2-22i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000−22−i2i2−i2i2−220000
χ472-222-22-2-22i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000000000i2−i2−222−2−i2i20000
χ482-222-22-2-22i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000000000−i2i22−2−22i2−i20000
χ492-222-22-2-2−2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000000000i2−i22−2−22−i2i20000
χ502-222-22-2-2−2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000000000−i2i2−222−2i2−i20000
χ512-222-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-2000000000000000000000000002−2−i2i2−i2i22−20000
χ522-222-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000−22i2−i2i2−i2−220000
χ534-44-44-44-4000000004i−4i−4i4i00000000000000000000000000000000000000
χ544-44-44-44-400000000−4i4i4i−4i00000000000000000000000000000000000000
χ554-4-44-4-44400004-4-44000000000000000000000000000000000000000000
χ564-4-44-4-4440000-444-4000000000000000000000000000000000000000000
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.