Finite Group Databasebeta

← Group #152860

Character table — Group #152860

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444488888816161616161616164488161616163232323232323232323232323232323244444488
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ91111-1-11-11-11111-1-111-1-111-1-1i−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i
χ101111-1-11-11-11111-1-111-1-111-1-1i−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii
χ111111-1-11-11-11111-1-111-1-111-1-1i−ii−iii−i−i-1-1-1-11111−i−i−i−iiiii1-1-11−iii−i
χ121111-1-11-11-11111-1-111-1-111-1-1i−ii−iii−i−i-1-1-1-11111−i−i−i−iiiii-111-1i−i−ii
χ131111-1-11-11-11111-1-111-1-111-1-1−ii−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii
χ141111-1-11-11-11111-1-111-1-111-1-1−ii−ii−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i
χ151111-1-11-11-11111-1-111-1-111-1-1−ii−ii−i−iii-1-1-1-11111iiii−i−i−i−i1-1-11i−i−ii
χ161111-1-11-11-11111-1-111-1-111-1-1−ii−ii−i−iii-1-1-1-11111iiii−i−i−i−i-111-1−iii−i
χ172222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-2-2-20000000022-2-2000022−2−222−2−222−2−222−2−200000000
χ202222222222-2-2-2-2-2-20000000022-2-20000−2−222−2−222−2−222−2−22200000000
χ212222222222-2-2-2-2-2-200000000-2-222000022−2−222−2−2−2−222−2−22200000000
χ222222222222-2-2-2-2-2-200000000-2-2220000−2−222−2−22222−2−222−2−200000000
χ232222-2-22-22-22222-2-2-2-222-2-2222i−2i2i−2i−2i−2i2i2i000000000000000000000000
χ242222-2-22-22-22222-2-2-2-222-2-222−2i2i−2i2i2i2i−2i−2i000000000000000000000000
χ252222-2-22-22-2-2-2-2-222000000002i−2i−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000
χ262222-2-22-22-2-2-2-2-222000000002i−2i−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000
χ272222-2-22-22-2-2-2-2-22200000000−2i2i2i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000
χ282222-2-22-22-2-2-2-2-22200000000−2i2i2i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000
χ2922-2-22-2-222-222-2-2-220000000000002-22-22−22−22−22−22−22−22−22−200000000
χ3022-2-22-2-222-222-2-2-220000000000002-22-2−22−22−22−22−22−22−22−2200000000
χ3122-2-22-2-222-222-2-2-22000000000000-22-222−22−22−22−2−22−22−22−2200000000
χ3222-2-22-2-222-222-2-2-22000000000000-22-22−22−22−22−222−22−22−22−200000000
χ3322-2-22-2-222-2-2-2222-222-2-2-2-22200000000000000002-2-222-2-2200000000
χ3422-2-22-2-222-2-2-2222-222-2-2-2-2220000000000000000-222-2-222-200000000
χ3522-2-22-2-222-2-2-2222-2-2-22222-2-2000000002-2-222-2-220000000000000000
χ3622-2-22-2-222-2-2-2222-2-2-22222-2-200000000-222-2-222-20000000000000000
χ3722-2-2-22-2-22222-2-22-20000000000002i−2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ3822-2-2-22-2-22222-2-22-20000000000002i−2i−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ3922-2-2-22-2-22222-2-22-2000000000000−2i2i2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ4022-2-2-22-2-22222-2-22-2000000000000−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ4122-2-2-22-2-222-2-222-222222-2-2-2-200000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ4222-2-2-22-2-222-2-222-222222-2-2-2-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ4322-2-2-22-2-222-2-222-22-2-2-2-22222000000002-2-22-222-20000000000000000
χ4422-2-2-22-2-222-2-222-22-2-2-2-2222200000000-222-22-2-220000000000000000
χ45444444-4-4-4-400000022−2222−2222−2222−2200000000000000000000000000000000
χ46444444-4-4-4-4000000−2222−2222−2222−222200000000000000000000000000000000
χ474444-4-4-44-4400000022−22−222222−22−222200000000000000000000000000000000
χ484444-4-4-44-44000000−222222−22−222222−2200000000000000000000000000000000
χ4944-4-44-44-4-4400000022−22−2222−222222−2200000000000000000000000000000000
χ5044-4-44-44-4-44000000−222222−2222−22−222200000000000000000000000000000000
χ5144-4-4-4444-4-400000022−2222−22−2222−222200000000000000000000000000000000
χ5244-4-4-4444-4-4000000−2222−222222−2222−2200000000000000000000000000000000
χ538-88-800000042−4242−42000000000000000000000000000000000000000000
χ548-88-8000000−4242−4242000000000000000000000000000000000000000000
χ558-8-8800000042−42−4242000000000000000000000000000000000000000000
χ568-8-88000000−424242−42000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).