Finite Group Databasebeta

← Group #11221

Character table — Group #11221

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111111111111111222222224444444444444444444444448888888888888888
order1222222244444444222244444444444488888888888888884444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1-1-111−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-11111-1-1ii−i−i−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i
χ172222222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-200000000-2-222-2-222000000000000000000000000
χ1922222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-22222-2-2-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ21222-2-22-2-22222-2-2-2-222-2-22-2-22000000000000000022-2-222-2-20000000000000000
χ22222-2-22-2-22222-2-2-2-222-2-22-2-220000000000000000-2-222-2-2220000000000000000
χ23222-2-22-2-22222-2-2-2-2-2-222-222-222-2-222-2-200000000000000000000000000000000
χ24222-2-22-2-22222-2-2-2-2-2-222-222-2-2-222-2-22200000000000000000000000000000000
χ25222-2-22-2-2-2-2-2-2222222-2-2-222-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ26222-2-22-2-2-2-2-2-2222222-2-2-222-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ27222-2-22-2-2-2-2-2-22222-2-2222-2-22000000000000000022-2-2-2-2220000000000000000
χ28222-2-22-2-2-2-2-2-22222-2-2222-2-220000000000000000-2-22222-2-20000000000000000
χ2922-22-2-22-22i2i−2i−2i2i−2i2i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζi2−i2i2−i22−22−20000000000000000
χ3022-22-2-22-22i2i−2i−2i2i−2i2i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ−i2i2−i2i2−22−220000000000000000
χ3122-22-2-22-22i2i−2i−2i2i−2i2i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ−i2i2−i2i2−22−220000000000000000
χ3222-22-2-22-22i2i−2i−2i2i−2i2i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζi2−i2i2−i22−22−20000000000000000
χ3322-22-2-22-2−2i−2i2i2i−2i2i−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ3i2−i2i2−i2−22−220000000000000000
χ3422-22-2-22-2−2i−2i2i2i−2i2i−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ3−i2i2−i2i22−22−20000000000000000
χ3522-22-2-22-2−2i−2i2i2i−2i2i−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ3−i2i2−i2i22−22−20000000000000000
χ3622-22-2-22-2−2i−2i2i2i−2i2i−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ3i2−i2i2−i2−22−220000000000000000
χ3722-2-22-2-222i2i−2i−2i−2i2i−2i2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ00i2−i2−i2i22−2−220000000000000000
χ3822-2-22-2-222i2i−2i−2i−2i2i−2i2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ00−i2i2i2−i2−222−20000000000000000
χ3922-2-22-2-222i2i−2i−2i−2i2i−2i2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ00−i2i2i2−i2−222−20000000000000000
χ4022-2-22-2-222i2i−2i−2i−2i2i−2i2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ00i2−i2−i2i22−2−220000000000000000
χ4122-2-22-2-22−2i−2i2i2i2i−2i2i−2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ300i2−i2−i2i2−222−20000000000000000
χ4222-2-22-2-22−2i−2i2i2i2i−2i2i−2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300−i2i2i2−i22−2−220000000000000000
χ4322-2-22-2-22−2i−2i2i2i2i−2i2i−2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ300−i2i2i2−i22−2−220000000000000000
χ4422-2-22-2-22−2i−2i2i2i2i−2i2i−2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300i2−i2−i2i2−222−20000000000000000
χ452-2-2222-2-22-22-222-2-22-22-222-2-2000000000000000000000000000000002-22-20000
χ462-2-2222-2-22-22-222-2-22-22-222-2-200000000000000000000000000000000-22-220000
χ472-2-2222-2-22-22-222-2-2-22-22-2-22200000000000000000000000000002i−2i2i−2i00000000
χ482-2-2222-2-22-22-222-2-2-22-22-2-2220000000000000000000000000000−2i2i−2i2i00000000
χ492-2-2222-2-2-22-22-2-2222-22-2-2-22200000000000000000000000000002i−2i−2i2i00000000
χ502-2-2222-2-2-22-22-2-2222-22-2-2-2220000000000000000000000000000−2i2i2i−2i00000000
χ512-2-2222-2-2-22-22-2-222-22-2222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ522-2-2222-2-2-22-22-2-222-22-2222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ532-2-2-2-22222-22-2-2-2222-2-222-22-20000000000000000000000000000000000002-22-2
χ542-2-2-2-22222-22-2-2-2222-2-222-22-2000000000000000000000000000000000000-22-22
χ552-2-2-2-22222-22-2-2-222-222-2-22-220000000000000000000000002-22-2000000000000
χ562-2-2-2-22222-22-2-2-222-222-2-22-22000000000000000000000000-22-22000000000000
χ572-2-2-2-2222-22-2222-2-22-2-22-22-220000000000000000000000002-2-22000000000000
χ582-2-2-2-2222-22-2222-2-22-2-22-22-22000000000000000000000000-222-2000000000000
χ592-2-2-2-2222-22-2222-2-2-222-22-22-20000000000000000000000000000000000002i−2i−2i2i
χ602-2-2-2-2222-22-2222-2-2-222-22-22-2000000000000000000000000000000000000−2i2i2i−2i
χ614-444-4-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000
χ624-444-4-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000
χ634-44-44-44-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000
χ644-44-44-44-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000

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