Finite Group Databasebeta

← Group #506406

Character table — Group #506406

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1244222444888888888888444444444444888888888822224444888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1111-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1111-11-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-11-1111111-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-111111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-1111-11111-1-1-1-1-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-1-1-11-1-1-111-1-11111-1-111-1-111
χ11111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1111-1111-1-111-1-1-1-1-1-111-1-111
χ12111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-11-1-1-11-1-1-1-111111111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-11-11-11-1-1-111-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-111-1-11-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-111-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-11-11-1111-1-111-1-111-1-1-1-111
χ172222222222-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000
χ182222222222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222-2-2000000000000000000000000
χ192222222222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ2122-2-22-2-222-222000022-2-2-2-2000022-2-2000000002-2002-20000000000002i−2i2i−2i00000000
χ2222-2-22-2-222-222000022-2-2-2-2000022-2-2000000002-2002-2000000000000−2i2i−2i2i00000000
χ2322-2-22-2-222-2220000-2-222-2-20000-2-222000000002-200-220000000000002i−2i−2i2i00000000
χ2422-2-22-2-222-2220000-2-222-2-20000-2-222000000002-200-22000000000000−2i2i2i−2i00000000
χ2522-2-22-2-222-2-2-2000022-2-2220000-2-22200000000-22002-2002200-2-20000000000000000
χ2622-2-22-2-222-2-2-2000022-2-2220000-2-22200000000-22002-200-2-200220000000000000000
χ2722-2-22-2-222-2-2-20000-2-22222000022-2-200000000-2200-22002-200-220000000000000000
χ2822-2-22-2-222-2-2-20000-2-22222000022-2-200000000-2200-2200-22002-20000000000000000
χ2922-2-2-22-22-222222-2-20000-2-222-2-2000000000000-222-200000000002i−2i2i−2i000000000000
χ3022-2-2-22-22-222222-2-20000-2-222-2-2000000000000-222-20000000000−2i2i−2i2i000000000000
χ3122-2-2-22-22-2222-2-2220000-2-2-2-222000000000000-22-2200000000002i−2i−2i2i000000000000
χ3222-2-2-22-22-2222-2-2220000-2-2-2-222000000000000-22-220000000000−2i2i2i−2i000000000000
χ3322-2-2-22-22-22-2-222-2-2000022-2-2220000000000002-22-2002200-2-2000000000000000000
χ3422-2-2-22-22-22-2-222-2-2000022-2-2220000000000002-22-200-2-20022000000000000000000
χ3522-2-2-22-22-22-2-2-2-22200002222-2-20000000000002-2-22002-200-22000000000000000000
χ3622-2-2-22-22-22-2-2-2-22200002222-2-20000000000002-2-2200-22002-2000000000000000000
χ3722-2-2-2-22-2220022-2-222-2-2000000000022-2-2000000-22-2200000000000000002−22−22−22−2
χ3822-2-2-2-22-2220022-2-222-2-2000000000022-2-2000000-22-220000000000000000−22−22−22−22
χ3922-2-2-2-22-2220022-2-2-2-2220000000000-2-222000000-222-200000000000000002−22−2−22−22
χ4022-2-2-2-22-2220022-2-2-2-2220000000000-2-222000000-222-20000000000000000−22−222−22−2
χ4122-2-2-2-22-22200-2-22222-2-20000000000-2-2220000002-2-2200000000000000002−2−222−2−22
χ4222-2-2-2-22-22200-2-22222-2-20000000000-2-2220000002-2-220000000000000000−222−2−222−2
χ4322-2-2-2-22-22200-2-222-2-222000000000022-2-20000002-22-200000000000000002−2−22−222−2
χ4422-2-2-2-22-22200-2-222-2-222000000000022-2-20000002-22-20000000000000000−222−22−2−22
χ4544444-4-4-4-44004444000000000000000000000000-4-400000000000000000000000000
χ4644444-4-4-4-4400-4-4-4-40000000000000000000000004400000000000000000000000000
χ474444-44-4-44-400000044440000000000000000000000-4-4000000000000000000000000
χ484444-44-4-44-4000000-4-4-4-4000000000000000000000044000000000000000000000000
χ494444-4-444-4-44400000000440000000000000000-4-40000000000000000000000000000
χ504444-4-444-4-4-4-400000000-4-40000000000000000440000000000000000000000000000
χ5144-4-4444-4-4-40000000000000000000000004i4i−4i−4i000000000000000000000000000000
χ5244-4-4444-4-4-4000000000000000000000000−4i−4i4i4i000000000000000000000000000000
χ534-44i−4i0000002i2−2i222−222i2−2i222−222i2−2i222−222i−2i2-22i−2i2-22-22i−2i2ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ544-44i−4i0000002i2−2i222−222i2−2i2−2222−2i22i222−222i−2i2-2−2i2i-22-22−2i2i−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ554-44i−4i0000002i2−2i2−2222−2i22i222−222i2−2i222−22−2i2i-222i−2i2-2-22−2i2i−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ564-44i−4i0000002i2−2i2−2222−2i22i2−2222−2i22i222−22−2i2i-22−2i2i-222-22i−2i2ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ574-44i−4i000000−2i22i222−222i2−2i222−222i2−2i2−2222−2i2i-22−2i2i-222-22i−2i−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ584-44i−4i000000−2i22i222−222i2−2i2−2222−2i22i2−2222−2i2i-222i−2i2-2-22−2i2i2ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ594-44i−4i000000−2i22i2−2222−2i22i222−222i2−2i2−22222i−2i2-2−2i2i-22-22−2i2i2ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ604-44i−4i000000−2i22i2−2222−2i22i2−2222−2i22i2−22222i−2i2-22i−2i2-22-22i−2i−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ614-4−4i4i0000002i2−2i222−22−2i22i222−22−2i22i2−22222i−2i-222i−2i-222-2−2i2i2ζ3−2ζ32ζ−2ζ000000000000000000000000000000
χ624-4−4i4i0000002i2−2i222−22−2i22i2−22222i2−2i2−22222i−2i-22−2i2i2-2-222i−2i−2ζ32ζ3−2ζ2ζ000000000000000000000000000000
χ634-4−4i4i0000002i2−2i2−22222i2−2i222−22−2i22i2−2222−2i2i2-22i−2i-22-222i−2i−2ζ32ζ3−2ζ2ζ000000000000000000000000000000
χ644-4−4i4i0000002i2−2i2−22222i2−2i2−22222i2−2i2−2222−2i2i2-2−2i2i2-22-2−2i2i2ζ3−2ζ32ζ−2ζ000000000000000000000000000000
χ654-4−4i4i000000−2i22i222−22−2i22i222−22−2i22i222−22−2i2i2-2−2i2i2-22-2−2i2i−2ζ32ζ3−2ζ2ζ000000000000000000000000000000
χ664-4−4i4i000000−2i22i222−22−2i22i2−22222i2−2i222−22−2i2i2-22i−2i-22-222i−2i2ζ3−2ζ32ζ−2ζ000000000000000000000000000000
χ674-4−4i4i000000−2i22i2−22222i2−2i222−22−2i22i222−222i−2i-22−2i2i2-2-222i−2i2ζ3−2ζ32ζ−2ζ000000000000000000000000000000
χ684-4−4i4i000000−2i22i2−22222i2−2i2−22222i2−2i222−222i−2i-222i−2i-222-2−2i2i−2ζ32ζ3−2ζ2ζ000000000000000000000000000000

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