Finite Group Databasebeta

← Group #105147

Character table — Group #105147

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222444444444444444448888888888888888444488888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ92222222222222222-2-2-22-2-22-2-20000000000000000000022-2-20000000000
χ102222222222222222-2-2-22-2-22-2-200000000000000000000-2-2220000000000
χ11222222222222-2-2-2-222-2-22-2-22-200000000000000000000000000002i2i−2i−2i00
χ12222222222222-2-2-2-222-2-22-2-22-20000000000000000000000000000−2i−2i2i2i00
χ13222222222222-2-2-2-2-2-22-2-22-2-22000000002i2i2i2i−2i−2i−2i−2i000000000000000000
χ14222222222222-2-2-2-2-2-22-2-22-2-2200000000−2i−2i−2i−2i2i2i2i2i000000000000000000
χ1522222222-2-2-2-22222222-2-22-2-2-2000000000000000022-2-200000000000000
χ1622222222-2-2-2-22222222-2-22-2-2-20000000000000000-2-22200000000000000
χ1722222222-2-2-2-22222-2-2-2-22-2-222000000000000000000000000000000002-2
χ1822222222-2-2-2-22222-2-2-2-22-2-22200000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-2-2-222-22-2-22-220000000000000000000000002i2i−2i−2i000000
χ2022222222-2-2-2-2-2-2-2-222-22-2-22-22000000000000000000000000−2i−2i2i2i000000
χ2122222222-2-2-2-2-2-2-2-2-2-2222222-22222-2-2-2-200000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2222200000000000000000000000000
χ23222-22-2-2-200002-2-222-2-2002000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-200000000000000
χ24222-22-2-2-200002-2-222-2-2002000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200-2200000000000000
χ25222-22-2-2-200002-2-222-2-2002000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200-2200000000000000
χ26222-22-2-2-200002-2-222-2-2002000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-200000000000000
χ27222-22-2-2-20000-222-2-22-2002000i2i2−i2−i2−i2−i2i2i222−2−2−2−2222i−2i0000000000000000
χ28222-22-2-2-20000-222-2-22-2002000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−2i2i0000000000000000
χ29222-22-2-2-20000-222-2-22-2002000−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2i2i0000000000000000
χ30222-22-2-2-20000-222-2-22-2002000−i2−i2i2i2i2i2−i2−i2−2−22222−2−22i−2i0000000000000000
χ312-2-2222-2-222-2-222-2-2000-200200000000002−22−22−22−20000002i−2i0000i2−i2i2−i200
χ322-2-2222-2-222-2-222-2-2000-200200000000002−22−22−22−2000000−2i2i0000−i2i2−i2i200
χ332-2-2222-2-222-2-222-2-2000-20020000000000−22−22−22−220000002i−2i0000−i2i2−i2i200
χ342-2-2222-2-222-2-222-2-2000-20020000000000−22−22−22−22000000−2i2i0000i2−i2i2−i200
χ352-2-2222-2-222-2-2-2-222000200-20000000000i2−i2i2−i2−i2i2−i2i200002i−2i0000002−2−2200
χ362-2-2222-2-222-2-2-2-222000200-20000000000i2−i2i2−i2−i2i2−i2i20000−2i2i000000−222−200
χ372-2-2222-2-222-2-2-2-222000200-20000000000−i2i2−i2i2i2−i2i2−i200002i−2i000000−222−200
χ382-2-2222-2-222-2-2-2-222000200-20000000000−i2i2−i2i2i2−i2i2−i20000−2i2i0000002−2−2200
χ39444-44-4-4-400004-4-44-44400-40000000000000000000000000000000000000
χ40444-44-4-4-40000-444-44-4400-40000000000000000000000000000000000000
χ4144-44-4-44-4000000000000400-40000022−2222−2200000000000000000000000000
χ4244-44-4-44-4000000000000400-400000−2222−222200000000000000000000000000
χ4344-44-4-44-4000000000000-400402i2−2i22i2−2i2000000000000000000000000000000
χ4444-44-4-44-4000000000000-40040−2i22i2−2i22i2000000000000000000000000000000
χ4544-4-4-44-444i−4i4i−4i00000000000002-2-222i−2i−2i2i00000000000000000000000000
χ4644-4-4-44-444i−4i4i−4i0000000000000-222-2−2i2i2i−2i00000000000000000000000000
χ4744-4-4-44-44−4i4i−4i4i00000000000002-2-22−2i2i2i−2i00000000000000000000000000
χ4844-4-4-44-44−4i4i−4i4i0000000000000-222-22i−2i−2i2i00000000000000000000000000
χ494-44-4-444-44i−4i−4i4i00000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ504-44-4-444-44i−4i−4i4i0000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ514-44-4-444-4−4i4i4i−4i00000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ524-44-4-444-4−4i4i4i−4i0000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ534-4-4444-4-4-4-44444-4-4000400-4000000000000000000000000000000000000
χ544-4-4444-4-4-4-444-4-444000-4004000000000000000000000000000000000000
χ554-4-4-44-44400004-44-4000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ564-4-4-44-44400004-44-400000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ574-4-4-44-4440000-44-44000000000000000002-2-22-222-2000000000000000000
χ584-4-4-44-4440000-44-4400000000000000000-222-22-2-22000000000000000000
χ598-888-8-8-88000000000000000000000000000000000000000000000000000

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