Finite Group Databasebeta

← Group #120556

Character table — Group #120556

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222244444444444416161616161616161616161616161616161616161616161616161616
order12224444442224444444448888888888888888888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ51111111111111111111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-11-1-1-111-1-11111-1-1-11-111ii−i−iii−i−iii−i−i-1-111-1-1ii−i−i11-1-1
χ101111-11-1-1-111-1-11111-1-1-11-111ii−i−iii−i−i−i−iii-1-1-1-111−i−iii-1-111
χ111111-11-1-1-111-1-11111-1-1-11-111−i−iii−i−iiiii−i−i-1-1-1-111ii−i−i-1-111
χ121111-11-1-1-111-1-11111-1-1-11-111−i−iii−i−iii−i−iii-1-111-1-1−i−iii11-1-1
χ131111-11-1-1-111-1-11111-1-1-11-1-1-1ii−i−i−i−iiiii−i−i1111-1-1−i−iii-1-111
χ141111-11-1-1-111-1-11111-1-1-11-1-1-1ii−i−i−i−iii−i−iii11-1-111ii−i−i11-1-1
χ151111-11-1-1-111-1-11111-1-1-11-1-1-1−i−iiiii−i−iii−i−i11-1-111−i−iii11-1-1
χ161111-11-1-1-111-1-11111-1-1-11-1-1-1−i−iiiii−i−i−i−iii1111-1-1ii−i−i-1-111
χ172222222222-22-222-2-22-2-2-2-2002-22-20000000000000000000000
χ182222222222-22-222-2-22-2-2-2-200-22-220000000000000000000000
χ192222222-2-222-2-2-2-2-2-222-22200000000000000002-22-200000000
χ202222222-2-222-2-2-2-2-2-222-2220000000000000000-22-2200000000
χ212222222-2-22-2-22-2-2222-22-2-200000000002i−2i2i−2i00000000000000
χ222222222-2-22-2-22-2-2222-22-2-20000000000−2i2i−2i2i00000000000000
χ2322222-2222-22-2-22-22-2-222-2-2000000000000000000002i−2i2i−2i0000
χ2422222-2222-22-2-22-22-2-222-2-200000000000000000000−2i2i−2i2i0000
χ2522222-2222-2-2-222-2-22-2-2-2220000000000000000000000002-22-2
χ2622222-2222-2-2-222-2-22-2-2-222000000000000000000000000-22-22
χ2722222-22-2-2-2222-22-22-22-2-2-20000002-22-2000000000000000000
χ2822222-22-2-2-2222-22-22-22-2-2-2000000-22-22000000000000000000
χ2922222-22-2-2-2-22-2-222-2-2-22222i−2i0000000000002i−2i000000000000
χ3022222-22-2-2-2-22-2-222-2-2-2222−2i2i000000000000−2i2i000000000000
χ312222-22-2222222-2-2-2-2-2-222-200000000000000002-2-2200000000
χ322222-22-2222222-2-2-2-2-2-222-20000000000000000-222-200000000
χ332222-22-2222-22-2-2-222-22-2-2200000000002-2-2200000000000000
χ342222-22-2222-22-2-2-222-22-2-220000000000-222-200000000000000
χ352222-22-2-2-22-2-2222-2-2-222-22002i−2i−2i2i0000000000000000000000
χ362222-22-2-2-22-2-2222-2-2-222-2200−2i2i2i−2i0000000000000000000000
χ372222-2-2-222-22-2-2-22-222-22-220000002i−2i−2i2i000000000000000000
χ382222-2-2-222-22-2-2-22-222-22-22000000−2i2i2i−2i000000000000000000
χ392222-2-2-222-2-2-22-222-222-22-22i−2i000000000000−2i2i000000000000
χ402222-2-2-222-2-2-22-222-222-22-2−2i2i0000000000002i−2i000000000000
χ412222-2-2-2-2-2-22222-22-22-2-2-22000000000000000000002-2-220000
χ422222-2-2-2-2-2-22222-22-22-2-2-2200000000000000000000-222-20000
χ432222-2-2-2-2-2-2-22-22-2-222222-20000000000000000000000002-2-22
χ442222-2-2-2-2-2-2-22-22-2-222222-2000000000000000000000000-222-2
χ4588-8-80008i−8i00000000000000000000000000000000000000000
χ4688-8-8000−8i8i00000000000000000000000000000000000000000
χ478-88-808000-80000000000000000000000000000000000000000
χ488-88-80-800080000000000000000000000000000000000000000
χ498-8-8880-80000000000000000000000000000000000000000000
χ508-8-88-8080000000000000000000000000000000000000000000

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