Finite Group Databasebeta

← Group #326554

Character table — Group #326554

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444224488888888444488884444444444448888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2222222-2-2000000000000-2-20000-2-20000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-222000000000000220000-2-20000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222000000000000-2-20000220000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000220000220000000000000000
χ212222-2-2-2-222-2-2000000002-22-22i2i−2i−2i0000000022-2-22i2i−2i−2i2i−2i0000000000000000000000
χ222222-2-2-2-222-2-2000000002-22-22i2i−2i−2i00000000-2-222−2i−2i2i2i2i−2i0000000000000000000000
χ232222-2-2-2-222-2-2000000002-22-2−2i−2i2i2i0000000022-2-2−2i−2i2i2i−2i2i0000000000000000000000
χ242222-2-2-2-222-2-2000000002-22-2−2i−2i2i2i00000000-2-2222i2i−2i−2i−2i2i0000000000000000000000
χ252222-2-2-2-222-2-200000000-22-222i2i−2i−2i000022-2-200000000−2i2i2i2i−2i−2i000000000000000000
χ262222-2-2-2-222-2-200000000-22-222i2i−2i−2i0000-2-22200000000−2i2i−2i−2i2i2i000000000000000000
χ272222-2-2-2-222-2-200000000-22-22−2i−2i2i2i000022-2-2000000002i−2i−2i−2i2i2i000000000000000000
χ282222-2-2-2-222-2-200000000-22-22−2i−2i2i2i0000-2-222000000002i−2i2i2i−2i−2i000000000000000000
χ292222-2-2-2-2-2-2222222-2-2-2-222-2-2000000000000000000000000002-22-22-2000000000000
χ302222-2-2-2-2-2-2222222-2-2-2-222-2-2000000000000000000000000002-2-22-22000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-2-2-22200000000000000000000000000-2200002i−2i2i−2i00000000
χ322222-2-2-2-2-2-2222222-2-2-2-2-2-22200000000000000000000000000-220000−2i2i−2i2i00000000
χ332222-2-2-2-2-2-222-2-2-2-2222222-2-200000000000000000000000000-222-2-22000000000000
χ342222-2-2-2-2-2-222-2-2-2-2222222-2-200000000000000000000000000-22-222-2000000000000
χ352222-2-2-2-2-2-222-2-2-2-22222-2-222000000000000000000000000002-200002i−2i−2i2i00000000
χ362222-2-2-2-2-2-222-2-2-2-22222-2-222000000000000000000000000002-20000−2i2i2i−2i00000000
χ3722-2-2-2-2222-22-222-2-222-2-200002i−2i2i−2i2i−2i0000000000000000000000000000002−22−2i2−i2i2−i2
χ3822-2-2-2-2222-22-222-2-222-2-200002i−2i2i−2i2i−2i000000000000000000000000000000−22−22−i2i2−i2i2
χ3922-2-2-2-2222-22-222-2-222-2-20000−2i2i−2i2i−2i2i0000000000000000000000000000002−22−2−i2i2−i2i2
χ4022-2-2-2-2222-22-222-2-222-2-20000−2i2i−2i2i−2i2i000000000000000000000000000000−22−22i2−i2i2−i2
χ4122-2-2-2-2222-22-2-2-222-2-22200002i−2i2i−2i−2i2i0000000000000000000000000000002−2−22i2−i2−i2i2
χ4222-2-2-2-2222-22-2-2-222-2-22200002i−2i2i−2i−2i2i000000000000000000000000000000−222−2−i2i2i2−i2
χ4322-2-2-2-2222-22-2-2-222-2-2220000−2i2i−2i2i2i−2i0000000000000000000000000000002−2−22−i2i2i2−i2
χ4422-2-2-2-2222-22-2-2-222-2-2220000−2i2i−2i2i2i−2i000000000000000000000000000000−222−2i2−i2−i2i2
χ4544444444-4-4-4-4000000004-4-4400000000000000000000000000000000000000000000
χ4644444444-4-4-4-400000000-444-400000000000000000000000000000000000000000000
χ4744-4-444-4-44-4-440000000000004-4-440000000000000000000000000000000000000000
χ4844-4-444-4-44-4-44000000000000-444-40000000000000000000000000000000000000000
χ4944-4-444-4-4-444-444-4-4-4-444000000000000000000000000000000000000000000000000
χ5044-4-444-4-4-444-4-4-44444-4-4000000000000000000000000000000000000000000000000
χ5144-4-4-4-444-44-440000000000000000004i−4i000000000000000000000000000000000000
χ5244-4-4-4-444-44-44000000000000000000−4i4i000000000000000000000000000000000000
χ534-44-44i−4i4i−4i00002i2−2i22i2−2i222−2222−220000000000002-22i−2i00002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ544-44-44i−4i4i−4i00002i2−2i22i2−2i222−2222−22000000000000-22−2i2i0000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ554-44-44i−4i4i−4i0000−2i22i2−2i22i2−2222−22220000000000002-22i−2i0000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ564-44-44i−4i4i−4i0000−2i22i2−2i22i2−2222−2222000000000000-22−2i2i00002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ574-44-4−4i4i−4i4i00002i2−2i22i2−2i2−2222−22220000000000002-2−2i2i00002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ584-44-4−4i4i−4i4i00002i2−2i22i2−2i2−2222−2222000000000000-222i−2i0000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ594-44-4−4i4i−4i4i0000−2i22i2−2i22i222−2222−220000000000002-2−2i2i0000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ604-44-4−4i4i−4i4i0000−2i22i2−2i22i222−2222−22000000000000-222i−2i00002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ614-4-444i−4i−4i4i00002i2−2i2−2i22i2−222222−2200000000000000002-22i−2i0000002ζ3−2ζ32ζ−2ζ000000000000000000
χ624-4-444i−4i−4i4i00002i2−2i2−2i22i2−222222−220000000000000000-22−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ634-4-444i−4i−4i4i0000−2i22i22i2−2i222−22−222200000000000000002-22i−2i000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ644-4-444i−4i−4i4i0000−2i22i22i2−2i222−22−22220000000000000000-22−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000000000
χ654-4-44−4i4i4i−4i00002i2−2i2−2i22i222−22−222200000000000000002-2−2i2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ664-4-44−4i4i4i−4i00002i2−2i2−2i22i222−22−22220000000000000000-222i−2i000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ674-4-44−4i4i4i−4i0000−2i22i22i2−2i2−222222−2200000000000000002-2−2i2i000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ684-4-44−4i4i4i−4i0000−2i22i22i2−2i2−222222−220000000000000000-222i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000

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