Finite Group Databasebeta

← Group #137804

Character table — Group #137804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12222244442244444444442244444488884444888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-222-2-2-2-2-2-22222-2-222-2-200000000000000000000000000
χ182222222222-2-222-2-2-2-2-2-222-2-222-2-22200000000000000000000000000
χ192222222222-2-2-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000
χ202222222222-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000
χ21222222-2-2-2-22222-2-2-2-222-2-2000000000000000000000000002i−2i2i−2i0000
χ22222222-2-2-2-22222-2-2-2-222-2-200000000000000000000000000−2i2i−2i2i0000
χ23222222-2-2-2-222-2-2-2-222-2-222000000000000000000000000002-2-220000
χ24222222-2-2-2-222-2-2-2-222-2-22200000000000000000000000000-222-20000
χ25222222-2-2-2-2-2-2222222-2-2-2-20000000000000000000000000000002i−2i2i−2i
χ26222222-2-2-2-2-2-2222222-2-2-2-2000000000000000000000000000000−2i2i−2i2i
χ27222222-2-2-2-2-2-2-2-222-2-222220000000000000000000000000000002-2-22
χ28222222-2-2-2-2-2-2-2-222-2-22222000000000000000000000000000000-222-2
χ292-22-2-222-22-22-22i−2i2-22i−2i2i−2i2i−2i0000000000002i−2i2-2000000000000000000
χ302-22-2-222-22-22-22i−2i2-22i−2i2i−2i2i−2i000000000000−2i2i-22000000000000000000
χ312-22-2-222-22-22-2−2i2i2-2−2i2i−2i2i−2i2i0000000000002i−2i-22000000000000000000
χ322-22-2-222-22-22-2−2i2i2-2−2i2i−2i2i−2i2i000000000000−2i2i2-2000000000000000000
χ332-22-2-222-22-2-222i−2i-22−2i2i−2i2i2i−2i0000000022-2-200002i−2i0000000000000000
χ342-22-2-222-22-2-222i−2i-22−2i2i−2i2i2i−2i00000000-2-2220000−2i2i0000000000000000
χ352-22-2-222-22-2-22−2i2i-222i−2i2i−2i−2i2i0000000022-2-20000−2i2i0000000000000000
χ362-22-2-222-22-2-22−2i2i-222i−2i2i−2i−2i2i00000000-2-22200002i−2i0000000000000000
χ372-22-2-22-22-222-22i−2i-22−2i2i2i−2i−2i2i00000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ382-22-2-22-22-222-22i−2i-22−2i2i2i−2i−2i2i0000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ392-22-2-22-22-222-2−2i2i-222i−2i−2i2i2i−2i00000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ402-22-2-22-22-222-2−2i2i-222i−2i−2i2i2i−2i0000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ412-22-2-22-22-22-222i−2i2-22i−2i−2i2i−2i2i0000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ422-22-2-22-22-22-222i−2i2-22i−2i−2i2i−2i2i000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ432-22-2-22-22-22-22−2i2i2-2−2i2i2i−2i2i−2i0000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ442-22-2-22-22-22-22−2i2i2-2−2i2i2i−2i2i−2i000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ454444-4-44-4-440000000000004-400000000000000000000000000000000
χ464444-4-44-4-44000000000000-4400000000000000000000000000000000
χ474444-4-4-444-400000000000000004-40000000000000000000000000000
χ484444-4-4-444-40000000000000000-440000000000000000000000000000
χ494-44-44-444-4-4000000000000004-4000000000000000000000000000000
χ504-44-44-444-4-400000000000000-44000000000000000000000000000000
χ514-44-44-4-4-4440000000000000000004i−4i00000000000000000000000000
χ524-44-44-4-4-444000000000000000000−4i4i00000000000000000000000000
χ5388-8-80000000000000000000000000022−2222−220000000000000000000000
χ5488-8-800000000000000000000000000−2222−22220000000000000000000000
χ558-8-880000000000000000000000000022−22−22220000000000000000000000
χ568-8-8800000000000000000000000000−222222−220000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.