Finite Group Databasebeta

← Group #8709

Character table — Group #8709

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111111111111111222222224444444444444444444444448888888888888888
order1222222244444444444444442244444488888888888888884444444488888888
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
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−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
χ1922222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ2122-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000002i−2i002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ2222-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000002i−2i002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ2322-22-2-22-22i2i−2i−2i2i2i−2i−2i0000000000−2i2i00-221+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ2422-22-2-22-22i2i−2i−2i2i2i−2i−2i0000000000−2i2i00-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ2522-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000002i−2i00-221−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ2622-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000002i−2i00-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ2722-22-2-22-2−2i−2i2i2i−2i−2i2i2i0000000000−2i2i002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ2822-22-2-22-2−2i−2i2i2i−2i−2i2i2i0000000000−2i2i002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ2922-2-22-2-222i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3022-2-22-2-222i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3122-2-22-2-222i−2i2i−2i2i−2i2i−2i-2-222−2i−2i2i2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3222-2-22-2-222i−2i2i−2i2i−2i2i−2i-2-222−2i−2i2i2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3322-2-22-2-22−2i2i−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3422-2-22-2-22−2i2i−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3522-2-22-2-22−2i2i−2i2i−2i2i−2i2i-2-2222i2i−2i−2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3622-2-22-2-22−2i2i−2i2i−2i2i−2i2i-2-2222i2i−2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ372-22-22-22-22i2i−2i−2i−2i−2i2i2i2-22-22i−2i2i−2i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ382-22-22-22-22i2i−2i−2i−2i−2i2i2i2-22-22i−2i2i−2i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ392-22-22-22-22i2i−2i−2i−2i−2i2i2i-22-22−2i2i−2i2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ402-22-22-22-22i2i−2i−2i−2i−2i2i2i-22-22−2i2i−2i2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ412-22-22-22-2−2i−2i2i2i2i2i−2i−2i2-22-2−2i2i−2i2i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ422-22-22-22-2−2i−2i2i2i2i2i−2i−2i2-22-2−2i2i−2i2i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ432-22-22-22-2−2i−2i2i2i2i2i−2i−2i-22-222i−2i2i−2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ442-22-22-22-2−2i−2i2i2i2i2i−2i−2i-22-222i−2i2i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ452-2-2222-2-22-2-22-222-22-2-222-2-220000000000000000000000002i−2i2i−2i000000000000
χ462-2-2222-2-22-2-22-222-22-2-222-2-22000000000000000000000000−2i2i−2i2i000000000000
χ472-2-2222-2-22-2-22-222-2-222-2-222-200000000000000000000000000002i−2i2i−2i00000000
χ482-2-2222-2-22-2-22-222-2-222-2-222-20000000000000000000000000000−2i2i−2i2i00000000
χ492-2-2222-2-2-222-22-2-222-2-22-222-20000000000000000000000002i−2i−2i2i000000000000
χ502-2-2222-2-2-222-22-2-222-2-22-222-2000000000000000000000000−2i2i2i−2i000000000000
χ512-2-2222-2-2-222-22-2-22-222-22-2-2200000000000000000000000000002i−2i−2i2i00000000
χ522-2-2222-2-2-222-22-2-22-222-22-2-220000000000000000000000000000−2i2i2i−2i00000000
χ532-2-2-2-22222222-2-2-2-2000000002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ542-2-2-2-22222222-2-2-2-2000000002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ552-2-2-2-22222222-2-2-2-200000000-2200-2200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ562-2-2-2-22222222-2-2-2-200000000-2200-2200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ572-2-2-2-2222-2-2-2-22222000000002-200-22002−2−22−222−22−2−22−222−20000000000000000
χ582-2-2-2-2222-2-2-2-22222000000002-200-2200−222−22−2−22−222−22−2−220000000000000000
χ592-2-2-2-2222-2-2-2-2222200000000-22002-2002−2−22−222−2−222−22−2−220000000000000000
χ602-2-2-2-2222-2-2-2-2222200000000-22002-200−222−22−2−222−2−22−222−20000000000000000
χ61444-4-44-4-44-4-444-4-44000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-444-4-444-4000000000000000000000000000000000000000000000000
χ634-444-4-4-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000
χ644-444-4-4-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000

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