Finite Group Databasebeta

← Group #7113

Character table — Group #7113

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order12222222444444448888888844888816161616161616161616161616161616888888884444
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
χ511111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ9111-1-1-1-11i−i1-11-1i−iii−i−iii−i−ii−i11-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2i−i1-1
χ10111-1-1-1-11i−i1-11-1i−iii−i−iii−i−ii−i11-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii-11
χ11111-1-1-1-11i−i1-11-1i−iii−i−iii−i−ii−i11-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii-11
χ12111-1-1-1-11i−i1-11-1i−iii−i−iii−i−ii−i11-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2i−i1-1
χ13111-1-1-1-11−ii1-11-1−ii−i−iii−i−iii−ii11-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ii1-1
χ14111-1-1-1-11−ii1-11-1−ii−i−iii−i−iii−ii11-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−i-11
χ15111-1-1-1-11−ii1-11-1−ii−i−iii−i−iii−ii11-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−i-11
χ16111-1-1-1-11−ii1-11-1−ii−i−iii−i−iii−ii11-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ii1-1
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222-2-2-2-22200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ192222222222-2-2-2-22200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ2022222222-2-22222-2-222222222-2-2-2-2-2-20000000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2222222222-2-2-2-2-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ23222-2-2-2-222i−2i2-22-22i−2i−2i−2i2i2i−2i−2i2i2i2i−2i-2-2220000000000000000000000000000
χ24222-2-2-2-222i−2i-22-222i−2i00000000−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000
χ25222-2-2-2-222i−2i-22-222i−2i00000000−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000
χ26222-2-2-2-22−2i2i2-22-2−2i2i2i2i−2i−2i2i2i−2i−2i−2i2i-2-2220000000000000000000000000000
χ27222-2-2-2-22−2i2i-22-22−2i2i000000002i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000
χ28222-2-2-2-22−2i2i-22-22−2i2i000000002i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000
χ2922-222-2-2-2220000-2-22−22−22−22−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3022-222-2-2-2220000-2-22−22−22−22−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3122-222-2-2-2220000-2-2−22−22−22−2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ3222-222-2-2-2220000-2-2−22−22−22−2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3322-222-2-2-2-2-20000222−22−22−22−200−22−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3422-222-2-2-2-2-20000222−22−22−22−200−22−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3522-222-2-2-2-2-2000022−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3622-222-2-2-2-2-2000022−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3722-2-2-222-22i−2i0000−2i2ii2−i2−i2i2i2−i2−i2i2002−2−22ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3000000000000
χ3822-2-2-222-22i−2i0000−2i2ii2−i2−i2i2i2−i2−i2i2002−2−22−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3000000000000
χ3922-2-2-222-22i−2i0000−2i2i−i2i2i2−i2−i2i2i2−i200−222−2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ4022-2-2-222-22i−2i0000−2i2i−i2i2i2−i2−i2i2i2−i200−222−2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ4122-2-2-222-2−2i2i00002i−2ii2−i2−i2i2i2−i2−i2i200−222−2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3000000000000
χ4222-2-2-222-2−2i2i00002i−2ii2−i2−i2i2i2−i2−i2i200−222−2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3000000000000
χ4322-2-2-222-2−2i2i00002i−2i−i2i2i2−i2−i2i2i2−i2002−2−22ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ4422-2-2-222-2−2i2i00002i−2i−i2i2i2−i2−i2i2i2−i2002−2−22−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ452-2-22-2-222002-2-22002222-2-2-2-20000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ462-2-22-2-222002-2-22002222-2-2-2-20000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ472-2-22-2-222002-2-2200-2-2-2-2222200000000000000000000002−22−2−22−220000
χ482-2-22-2-222002-2-2200-2-2-2-222220000000000000000000000−22−222−22−20000
χ492-2-2-222-220022-2-2002i2i−2i−2i−2i−2i2i2i00000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ502-2-2-222-220022-2-2002i2i−2i−2i−2i−2i2i2i0000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ512-2-2-222-220022-2-200−2i−2i2i2i2i2i−2i−2i00000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ522-2-2-222-220022-2-200−2i−2i2i2i2i2i−2i−2i0000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ534-444-44-4-40000000022−2222−22−2222−22220000000000000000000000000000000000
χ544-444-44-4-400000000−2222−222222−2222−220000000000000000000000000000000000
χ554-44-44-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ564-44-44-44-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ574-4-44-4-44400-444-400000000000000000000000000000000000000000000
χ584-4-4-444-4400-4-44400000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.