Finite Group Databasebeta

← Group #459709

Character table — Group #459709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12224444222222444444444444448888888888888888224444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-111-1-11-111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-11-1-1-1-1-11-1-111-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1-11111-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-11111-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-111-1-111-1-111-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-11-1-1111111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-1-1-111-1-111-1-1111111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1111-1-1-1-1-1-11111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1-111-1-1
χ172222-2-2-2-22-22-2-2-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i0200000-2000000002i−2i000000
χ182222-2-2-2-22-22-2-2-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i0-200000200000000−2i2i000000
χ192222-2-2-2-22-22-2-2-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i0200000-200000000−2i2i000000
χ202222-2-2-2-22-22-2-2-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i0-2000002000000002i−2i000000
χ212222-2-2-2-2-22-22-2-222-22-22000000002i2i2i2i−2i−2i−2i−2i0000000000002-20000000000002i−2i0000
χ222222-2-2-2-2-22-22-2-222-22-22000000002i2i2i2i−2i−2i−2i−2i000000000000-22000000000000−2i2i0000
χ232222-2-2-2-2-22-22-2-222-22-2200000000−2i−2i−2i−2i2i2i2i2i0000000000002-2000000000000−2i2i0000
χ242222-2-2-2-2-22-22-2-222-22-2200000000−2i−2i−2i−2i2i2i2i2i000000000000-220000000000002i−2i0000
χ252222-2-2-2-2-2-2-2-222-2-222222222-2-2-2-20000000000000000202-200-200000000000000000
χ262222-2-2-2-2-2-2-2-222-2-222222222-2-2-2-20000000000000000-20-2200200000000000000000
χ272222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222000000000000000020-2200-200000000000000000
χ282222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222220000000000000000-202-200200000000000000000
χ292-2-2222-2-2-2-2222-22-2-222-22i2i−2i−2i2i2i−2i−2i22-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302-2-2222-2-2-2-2222-22-2-222-22i2i−2i−2i2i2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312-2-2222-2-2-2-2222-22-2-222-2−2i−2i2i2i−2i−2i2i2i22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ322-2-2222-2-2-2-2222-22-2-222-2−2i−2i2i2i−2i−2i2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ332-2-22-2-22222-2-22-2-22-222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000002-200002i−2i00000000
χ342-2-22-2-22222-2-22-2-22-222-22i2i−2i−2i−2i−2i2i2i000000000000000000000000-220000−2i2i00000000
χ352-2-22-2-22222-2-22-2-22-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-20000−2i2i00000000
χ362-2-22-2-22222-2-22-2-22-222-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000-2200002i−2i00000000
χ372-2-22-2-2222-2-22-222-222-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000002-2000000002i−2i
χ382-2-22-2-2222-2-22-222-222-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000-2200000000−2i2i
χ392-2-22-2-2222-2-22-222-222-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000002-200000000−2i2i
χ402-2-22-2-2222-2-22-222-222-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000-22000000002i−2i
χ412-2-22-2-222-222-2-222-2-2-222000000000000000022-2-2-2-22200000000002-2000000002-200
χ422-2-22-2-222-222-2-222-2-2-222000000000000000022-2-2-2-2220000000000-2200000000-2200
χ432-2-22-2-222-222-2-222-2-2-2220000000000000000-2-22222-2-200000000002-200000000-2200
χ442-2-22-2-222-222-2-222-2-2-2220000000000000000-2-22222-2-20000000000-22000000002-200
χ45444444444-44-4-4-4-4-4-44-44000000000000000000000000000000000000000000000000
χ4644444444-44-44-4-4-4-44-44-4000000000000000000000000000000000000000000000000
χ4744444444-4-4-4-44444-4-4-4-4000000000000000000000000000000000000000000000000
χ484444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ4944-4-44i−4i4i−4i0000000000002-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5044-4-44i−4i4i−4i0000000000002-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ5144-4-44i−4i4i−4i000000000000-22-22−2i2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ5244-4-44i−4i4i−4i000000000000-22-22−2i2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5344-4-4−4i4i−4i4i0000000000002-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5444-4-4−4i4i−4i4i0000000000002-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ5544-4-4−4i4i−4i4i000000000000-22-222i−2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ5644-4-4−4i4i−4i4i000000000000-22-222i−2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ574-44-44i−4i−4i4i0000000000002i−2i−2i2i-222-22ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ584-44-44i−4i−4i4i0000000000002i−2i−2i2i-222-2−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ594-44-44i−4i−4i4i000000000000−2i2i2i−2i2-2-222ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ604-44-44i−4i−4i4i000000000000−2i2i2i−2i2-2-22−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ614-44-4−4i4i4i−4i0000000000002i−2i−2i2i2-2-222ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ624-44-4−4i4i4i−4i0000000000002i−2i−2i2i2-2-22−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ634-44-4−4i4i4i−4i000000000000−2i2i2i−2i-222-22ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ644-44-4−4i4i4i−4i000000000000−2i2i2i−2i-222-2−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ654-4-4444-4-444-4-44-44-44-4-44000000000000000000000000000000000000000000000000
χ664-4-4444-4-44-4-44-44-44-4-444000000000000000000000000000000000000000000000000
χ674-4-4444-4-4-444-4-44-4444-4-4000000000000000000000000000000000000000000000000
χ684-4-44-4-444-4-4444-4-444-4-44000000000000000000000000000000000000000000000000

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