Finite Group Databasebeta

← Group #9604

Character table — Group #9604

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111111111111111222222224444444444444444444444448888888888888888
order1222222244444444444444444444444488888888888888888888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ1922222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ212222-2-2-2-22222-2-2-2-200000000002-2002-222−2−222−2−222−2−222−2−20000000000000000
χ222222-2-2-2-22222-2-2-2-200000000002-2002-2−2−222−2−222−2−222−2−2220000000000000000
χ232222-2-2-2-22222-2-2-2-20000000000-2200-2222−2−222−2−2−2−222−2−2220000000000000000
χ242222-2-2-2-22222-2-2-2-20000000000-2200-22−2−222−2−22222−2−222−2−20000000000000000
χ252222-2-2-2-2-2-2-2-2222200000000002-200-2222−2−2−2−22222−2−2−2−2220000000000000000
χ262222-2-2-2-2-2-2-2-2222200000000002-200-22−2−22222−2−2−2−22222−2−20000000000000000
χ272222-2-2-2-2-2-2-2-222220000000000-22002-222−2−2−2−222−2−22222−2−20000000000000000
χ282222-2-2-2-2-2-2-2-222220000000000-22002-2−2−22222−2−222−2−2−2−2220000000000000000
χ2922-2-222-2-222-2-222-2-22222-2-2-2-20000000000000000000000002-22-2000000000000
χ3022-2-222-2-222-2-222-2-22222-2-2-2-2000000000000000000000000-22-22000000000000
χ3122-2-222-2-222-2-222-2-2-2-2-2-2222200000000000000000000000000002i−2i2i−2i00000000
χ3222-2-222-2-222-2-222-2-2-2-2-2-222220000000000000000000000000000−2i2i−2i2i00000000
χ3322-2-222-2-2-2-222-2-22222-2-222-2-20000000000000000000000002i−2i−2i2i000000000000
χ3422-2-222-2-2-2-222-2-22222-2-222-2-2000000000000000000000000−2i2i2i−2i000000000000
χ3522-2-222-2-2-2-222-2-222-2-222-2-22200000000000000000000000000002-2-2200000000
χ3622-2-222-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000-222-200000000
χ372-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002i−2i00i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ382-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002i−2i00−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ392-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200−2i2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ402-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200−2i2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ412-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-200−2i2i00i2−i2i2−i2−22−22i2−i2i2−i2−22−220000000000000000
χ422-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-200−2i2i00−i2i2−i2i22−22−2−i2i2−i2i22−22−20000000000000000
χ432-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-22002i−2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ442-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-22002i−2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ452-22-2-22-222i−2i2i−2i−2i2i−2i2i2-22i−2i2i−2i2-200000000000000002i−2i−2i2i2-2-220000000000000000
χ462-22-2-22-222i−2i2i−2i−2i2i−2i2i2-22i−2i2i−2i2-20000000000000000−2i2i2i−2i-222-20000000000000000
χ472-22-2-22-222i−2i2i−2i−2i2i−2i2i-22−2i2i−2i2i-22000000002i−2i−2i2i2-2-22000000000000000000000000
χ482-22-2-22-222i−2i2i−2i−2i2i−2i2i-22−2i2i−2i2i-2200000000−2i2i2i−2i-222-2000000000000000000000000
χ492-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-2−2i2i−2i2i2-200000000000000002i−2i−2i2i-222-20000000000000000
χ502-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-2−2i2i−2i2i2-20000000000000000−2i2i2i−2i2-2-220000000000000000
χ512-22-2-22-22−2i2i−2i2i2i−2i2i−2i-222i−2i2i−2i-22000000002i−2i−2i2i-222-2000000000000000000000000
χ522-22-2-22-22−2i2i−2i2i2i−2i2i−2i-222i−2i2i−2i-2200000000−2i2i2i−2i2-2-22000000000000000000000000
χ532-2-22-222-22i−2i−2i2i−2i2i2i−2i2-22i−2i−2i2i-220000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ542-2-22-222-22i−2i−2i2i−2i2i2i−2i2-22i−2i−2i2i-22000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ552-2-22-222-22i−2i−2i2i−2i2i2i−2i-22−2i2i2i−2i2-2000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ562-2-22-222-22i−2i−2i2i−2i2i2i−2i-22−2i2i2i−2i2-200000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ572-2-22-222-2−2i2i2i−2i2i−2i−2i2i2-2−2i2i2i−2i-220000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ582-2-22-222-2−2i2i2i−2i2i−2i−2i2i2-2−2i2i2i−2i-22000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ592-2-22-222-2−2i2i2i−2i2i−2i−2i2i-222i−2i−2i2i2-2000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ602-2-22-222-2−2i2i2i−2i2i−2i−2i2i-222i−2i−2i2i2-200000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ6144-4-4-4-44444-4-4-4-444000000000000000000000000000000000000000000000000
χ6244-4-4-4-444-4-44444-4-4000000000000000000000000000000000000000000000000
χ634-4-444-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000
χ644-4-444-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000

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