Finite Group Databasebeta

← Group #145308

Character table — Group #145308

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222444444444444488888888161616161616161616161616323232323232
order12224444244448888888816161616161616162488888816161616248888
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ92222222222222-2-2-2-2-2-2-2-20000000022-2-200000000000000
χ102222222222222-2-2-2-2-2-2-2-200000000-2-22200000000000000
χ1122222222-2-22-2-222-2-222-2-200000000000000000000002-200
χ1222222222-2-22-2-222-2-222-2-20000000000000000000000-2200
χ1322222222-2-22-2-2-2-222-2-222000000000000000000002-20000
χ1422222222-2-22-2-2-2-222-2-22200000000000000000000-220000
χ1522222-2-22-2-2-222000000002222−2−2−2−22-200000022−2−2000000
χ1622222-2-22-2-2-222000000002222−2−2−2−2-22000000−2−222000000
χ1722222-2-22-2-2-22200000000−2−2−2−222222-2000000−2−222000000
χ1822222-2-22-2-2-22200000000−2−2−2−22222-2200000022−2−2000000
χ192222-222-22-2-2-222222-2-2-2-200000000000000002i−2i2i−2i000000
χ202222-222-22-2-2-222222-2-2-2-20000000000000000−2i2i−2i2i000000
χ212222-222-22-2-2-22-2-2-2-2222222-2-222-2-2000000000000000000
χ222222-222-22-2-2-22-2-2-2-22222-2-222-2-222000000000000000000
χ232222-222-2-22-22-222-2-2-2-2220000000000000000000000002i−2i
χ242222-222-2-22-22-222-2-2-2-222000000000000000000000000−2i2i
χ252222-222-2-22-22-2-2-22222-2-20000000000002i2i−2i−2i0000000000
χ262222-222-2-22-22-2-2-22222-2-2000000000000−2i−2i2i2i0000000000
χ272222-2-2-2-2-222-220000000022−2−2−2−222002i−2i0000i2−i2−i2i2000000
χ282222-2-2-2-2-222-220000000022−2−2−2−22200−2i2i0000−i2i2i2−i2000000
χ292222-2-2-2-2-222-2200000000−2−22222−2−2002i−2i0000−i2i2i2−i2000000
χ302222-2-2-2-2-222-2200000000−2−22222−2−200−2i2i0000i2−i2−i2i2000000
χ3144444-4-4444-4-4-40000000000000000000000000000000000
χ324444-4-4-4-44-444-40000000000000000000000000000000000
χ3344-4-4400-4000000022−220022−22ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000000
χ3444-4-4400-4000000022−220022−22−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000000
χ3544-4-4400-40000000−222200−2222ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000000
χ3644-4-4400-40000000−222200−2222−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000000
χ3744-4-4-4004000000022−2200−2222ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000000
χ3844-4-4-4004000000022−2200−2222−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000000
χ3944-4-4-40040000000−22220022−22ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000000
χ4044-4-4-40040000000−22220022−22−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000000
χ414-44-404-40000004i−4i0000000000000000002ζ2−2ζ22ζ6−2ζ60000000000
χ424-44-404-40000004i−4i000000000000000000−2ζ22ζ2−2ζ62ζ60000000000
χ434-44-404-4000000−4i4i0000000000000000002ζ6−2ζ62ζ2−2ζ20000000000
χ444-44-404-4000000−4i4i000000000000000000−2ζ62ζ6−2ζ22ζ20000000000
χ458-88-80-880000000000000000000000000000000000000000
χ468-8-88000000000000042−420000000000000000000000000000
χ478-8-880000000000000−42420000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.