Finite Group Databasebeta

← Group #236413

Character table — Group #236413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222244444444444416161616161616161616161616161616161616161616161616161616
order12222244442244444444442222244444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-111-1-11-1-111-1-1-1111-1111-11-1-1-11-111-1-111-1-111-1-111-1-1
χ10111111-1-111-1-11-1-111-1-1-1111-111-111-1-1-1-1111-1-1-1-111-1-111-1-111
χ11111111-1-111-1-11-1-111-1-1-1111-1-1-11-11-1111-1-1-11111-1-1-1-111-1-111
χ12111111-1-111-1-11-1-111-1-1-1111-1-1-1-111-111-11-1-111-1-11111-1-111-1-1
χ13111111-1-111-1-11-1-111-1-1-111-11111-1-11-1-11-1-1-111-1-11111-1-1-1-111
χ14111111-1-111-1-11-1-111-1-1-111-1111-11-11-1-1-11-1-11111-1-1-1-11111-1-1
χ15111111-1-111-1-11-1-111-1-1-111-11-1-11-1-11111-111-1-1-1-111-1-11111-1-1
χ16111111-1-111-1-11-1-111-1-1-111-11-1-1-11-1111-1111-1-111-1-111-1-1-1-111
χ172222222222-2-2-2222-22-2-2-2-22-20000-2200000000000000000000
χ182222222222-2-2-2222-22-2-2-2-2-2200002-200000000000000000000
χ1922222222-2-222-2-2-2-222-2-2-22002-200002-2000000000000000000
χ2022222222-2-222-2-2-2-222-2-2-2200-220000-22000000000000000000
χ2122222222-2-2-2-22-2-2-2-22222-20000000000002-22-2000000000000
χ2222222222-2-2-2-22-2-2-2-22222-2000000000000-22-22000000000000
χ23222222-2-22222-2-2-22-2-222-2-2220000-2-200000000000000000000
χ24222222-2-22222-2-2-22-2-222-2-2-2-200002200000000000000000000
χ25222222-2-2-2-222222-2-2-2-2-22-20000000000002-2-22000000000000
χ26222222-2-2-2-222222-2-2-2-2-22-2000000000000-222-2000000000000
χ27222222-2-2-2-2-2-2-222-22-222-22002-20000-22000000000000000000
χ28222222-2-2-2-2-2-2-222-22-222-2200-2200002-2000000000000000000
χ292222-2-222222-222-2-2-2-22-2-2200002-20000-220000000000000000
χ302222-2-222222-222-2-2-2-22-2-220000-2200002-20000000000000000
χ312222-2-22222-22-22-2-22-2-222-200000000000000002-22-200000000
χ322222-2-22222-22-22-2-22-2-222-20000000000000000-22-2200000000
χ332222-2-222-2-22-2-2-222-2-2-2222000000000000000000002-22-20000
χ342222-2-222-2-22-2-2-222-2-2-222200000000000000000000-22-220000
χ352222-2-222-2-2-222-2222-22-2-2-20000000000000000000000002i−2i2i−2i
χ362222-2-222-2-2-222-2222-22-2-2-2000000000000000000000000−2i2i−2i2i
χ372222-2-2-2-2222-2-2-22-2222-22-200000000000000002-2-2200000000
χ382222-2-2-2-2222-2-2-22-2222-22-20000000000000000-222-200000000
χ392222-2-2-2-222-222-22-2-22-22-220000220000-2-20000000000000000
χ402222-2-2-2-222-222-22-2-22-22-220000-2-20000220000000000000000
χ412222-2-2-2-2-2-22-222-2222-22-2-20000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-2-22-222-2222-22-2-2000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-2-2-22-22-22-222-222000000000000000000002-2-220000
χ442222-2-2-2-2-2-2-22-22-22-222-22200000000000000000000-222-20000
χ4588-8-8008i−8i000000000000000000000000000000000000000000
χ4688-8-800−8i8i000000000000000000000000000000000000000000
χ478-88-800008-80000000000000000000000000000000000000000
χ488-88-80000-880000000000000000000000000000000000000000
χ498-8-888-800000000000000000000000000000000000000000000
χ508-8-88-8800000000000000000000000000000000000000000000

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