Finite Group Databasebeta

← Group #114709

Character table — Group #114709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222244444444444416161616161616161616161616161616161616161616161616161616
order12222244442244444444442222444488888888888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1-1-111-1111-1-1-1-11-11-11-11-11-1ii−i−i11-1-1ii−i−iii−i−iii−i−i
χ10111111-1-1-1-111-1111-1-1-1-11-11-11-11-11-1−i−iii11-1-1−i−iii−i−iii−i−iii
χ11111111-1-1-1-111-1111-1-1-1-11-11-1-111-1-11ii−i−i-1-111ii−i−i−i−iii−i−iii
χ12111111-1-1-1-111-1111-1-1-1-11-11-1-111-1-11−i−iii-1-111−i−iiiii−i−iii−i−i
χ13111111-1-1-1-111-1111-1-1-1-11-1-111-1-111-1ii−i−i-1-111−i−iiiii−i−i−i−iii
χ14111111-1-1-1-111-1111-1-1-1-11-1-111-1-111-1−i−iii-1-111ii−i−i−i−iiiii−i−i
χ15111111-1-1-1-111-1111-1-1-1-11-1-11-11-11-11ii−i−i11-1-1−i−iii−i−iiiii−i−i
χ16111111-1-1-1-111-1111-1-1-1-11-1-11-11-11-11−i−iii11-1-1ii−i−iii−i−i−i−iii
χ172222222222-2-222-2-2-2-2-2-222002200-2-200000000000000000000
χ182222222222-2-222-2-2-2-2-2-22200-2-2002200000000000000000000
χ192222222-2-22222-2-2-2-2-222-2-200000000000000002-22-200000000
χ202222222-2-22222-2-2-2-2-222-2-20000000000000000-22-2200000000
χ212222222-2-22-2-22-22222-2-2-2-20000000000000000000000002i−2i2i−2i
χ222222222-2-22-2-22-22222-2-2-2-2000000000000000000000000−2i2i−2i2i
χ23222222-222-222-2-2-2-222-2-2-2200000000000000002i−2i−2i2i00000000
χ24222222-222-222-2-2-2-222-2-2-220000000000000000−2i2i2i−2i00000000
χ25222222-222-2-2-2-2-222-2-222-220000000000000000000000002-2-22
χ26222222-222-2-2-2-2-222-2-222-22000000000000000000000000-222-2
χ27222222-2-2-2-2-2-2-22-2-222222-2002-200-2200000000000000000000
χ28222222-2-2-2-2-2-2-22-2-222222-200-22002-200000000000000000000
χ292222-2-222222-2-2-22-22-22-22-20000000000002-22-2000000000000
χ302222-2-222222-2-2-22-22-22-22-2000000000000-22-22000000000000
χ312222-2-22222-22-2-2-22-22-222-22200-2-20000000000000000000000
χ322222-2-22222-22-2-2-22-22-222-2-2-200220000000000000000000000
χ332222-2-22-2-222-2-22-22-222-2-22000000000000000000002-22-20000
χ342222-2-22-2-222-2-22-22-222-2-2200000000000000000000-22-220000
χ352222-2-22-2-22-22-222-22-2-22-22000000002-22-20000000000000000
χ362222-2-22-2-22-22-222-22-2-22-2200000000-22-220000000000000000
χ372222-2-2-222-22-222-222-2-22-2-2000000000000000000002i−2i−2i2i0000
χ382222-2-2-222-22-222-222-2-22-2-200000000000000000000−2i2i2i−2i0000
χ392222-2-2-222-2-22222-2-222-2-2-2000000002i−2i−2i2i0000000000000000
χ402222-2-2-222-2-22222-2-222-2-2-200000000−2i2i2i−2i0000000000000000
χ412222-2-2-2-2-2-22-22-22-2-22-22220000000000002-2-22000000000000
χ422222-2-2-2-2-2-22-22-22-2-22-2222000000000000-222-2000000000000
χ432222-2-2-2-2-2-2-222-2-222-22-2222-200-220000000000000000000000
χ442222-2-2-2-2-2-2-222-2-222-22-222-22002-20000000000000000000000
χ4588-8-800800-80000000000000000000000000000000000000000
χ4688-8-800-80080000000000000000000000000000000000000000
χ478-88-80008-800000000000000000000000000000000000000000
χ488-88-8000-8800000000000000000000000000000000000000000
χ498-8-888-800000000000000000000000000000000000000000000
χ508-8-88-8800000000000000000000000000000000000000000000

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