Finite Group Databasebeta

← Group #146136

Character table — Group #146136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222224444444444888888888161616161616161616161616323232323232
order12224444442444888888816161616161616164488888816161616888888
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
χ5111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ922222222222222-2-2-2-2-2-2-20000000022-2-200000000000000
χ1022222222222222-2-2-2-2-2-2-200000000-2-22200000000000000
χ11222222-2-222-22-2-22222-2-2-2000000000000000000002i−2i0000
χ12222222-2-222-22-2-22222-2-2-200000000000000000000−2i2i0000
χ13222222-2-222-22-2-2-2-2-2-22220000000000002i2i−2i−2i0000000000
χ14222222-2-222-22-2-2-2-2-2-2222000000000000−2i−2i2i2i0000000000
χ1522222-2-2-2-222-22-20000000i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i2000000
χ1622222-2-2-2-222-22-20000000i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i2000000
χ1722222-2-2-2-222-22-20000000−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i2000000
χ1822222-2-2-2-222-22-20000000−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i2000000
χ192222-22222-22-2-2-222-2-222-20000000000000000000000002i−2i
χ202222-22222-22-2-2-222-2-222-2000000000000000000000000−2i2i
χ212222-22222-22-2-2-2-2-222-2-2200000000000000000000002i−2i00
χ222222-22222-22-2-2-2-2-222-2-220000000000000000000000−2i2i00
χ232222-22-2-22-2-2-22222-2-2-2-222i2i−2i−2i2i2i−2i−2i000000000000000000
χ242222-22-2-22-2-2-22222-2-2-2-22−2i−2i2i2i−2i−2i2i2i000000000000000000
χ252222-22-2-22-2-2-222-2-22222-200000000000000002-22-2000000
χ262222-22-2-22-2-2-222-2-22222-20000000000000000-22-22000000
χ272222-2-222-2-2-222-2000000022−2−2−2−222002i−2i0000i2−i2−i2i2000000
χ282222-2-222-2-2-222-2000000022−2−2−2−22200−2i2i0000−i2i2i2−i2000000
χ292222-2-222-2-2-222-20000000−2−22222−2−2002i−2i0000−i2i2i2−i2000000
χ302222-2-222-2-2-222-20000000−2−22222−2−200−2i2i0000i2−i2−i2i2000000
χ3144444-444-44-4-4-44000000000000000000000000000000000
χ324444-4-4-4-4-4-444-44000000000000000000000000000000000
χ3344-4-40-400400000004i−4i0000000000000002ζ2−2ζ22ζ6−2ζ60000000000
χ3444-4-40-400400000004i−4i000000000000000−2ζ22ζ2−2ζ62ζ60000000000
χ3544-4-40-40040000000−4i4i0000000000000002ζ6−2ζ62ζ2−2ζ20000000000
χ3644-4-40-40040000000−4i4i000000000000000−2ζ62ζ6−2ζ22ζ20000000000
χ374-44-4004i−4i00000022−22002i2−2i20ζ+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
χ384-44-4004i−4i00000022−22002i2−2i20−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
χ394-44-4004i−4i000000−222200−2i22i20ζ+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
χ404-44-4004i−4i000000−222200−2i22i20−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
χ414-44-400−4i4i00000022−2200−2i22i20ζ−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
χ424-44-400−4i4i00000022−2200−2i22i20−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
χ434-44-400−4i4i000000−2222002i2−2i20ζ−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
χ444-44-400−4i4i000000−2222002i2−2i20−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
χ4588-8-80800-800000000000000000000000000000000000000
χ468-8-8880000-80000000000000000000000000000000000000
χ478-8-88-8000080000000000000000000000000000000000000

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