Finite Group Databasebeta

← Group #349109

Character table — Group #349109

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444444444448888888888222444444488888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-11-11-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111-1-1-11-11-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ61111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-111111111-1-1-1-1111-1-11
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1111111-1-11111-1-1-111-1
χ91111111111111-1-11-1-11111111-1-1-1-111-1-1-1-111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-111
χ101111111111111-1-11-1-11111111-1-1-1-111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1111111-1-1
χ111111111111111-1-11-1-11111111-1-1-1-1-1-11-11-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1
χ121111111111111-1-11-1-11111111-1-1-1-1-1-11-11-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ131111111111111-1-11-1-11-1-1-1-1-1-1111111-1-1-1-111-1-111-111-1-1-1-11111-1-1-1-111-111-1
χ141111111111111-1-11-1-11-1-1-1-1-1-1111111-1-1-1-111-1-111-111-1-1-1-111-1-11111-1-11-1-11
χ151111111111111-1-11-1-11-1-1-1-1-1-11111-1-11-11-1-1-111-1-1-1111111-1-111-1-111-1-1-11-11
χ161111111111111-1-11-1-11-1-1-1-1-1-11111-1-11-11-1-1-111-1-1-1111111-1-1-1-111-1-1111-11-1
χ172222222-2-22-2-2222-2-2-2-2000000000000020-200002i−2i0002i2i−2i−2i2i−2i000000000000
χ182222222-2-22-2-2222-2-2-2-2000000000000020-20000−2i2i000−2i−2i2i2i−2i2i000000000000
χ192222222-2-22-2-22-2-2-222-20000000000000-20200002i−2i000−2i−2i2i2i2i−2i000000000000
χ202222222-2-22-2-22-2-2-222-20000000000000-2020000−2i2i0002i2i−2i−2i−2i2i000000000000
χ21222222-222-222-200-200-22222-2-200000020-20002-2-2-2-200000022000000000000
χ22222222-222-222-200-200-22222-2-2000000-202000-2222-2000000-2-2000000000000
χ23222222-222-222-200-200-2-2-2-2-22200000020-20002-2222000000-2-2000000000000
χ24222222-222-222-200-200-2-2-2-2-222000000-202000-22-2-2200000022000000000000
χ25222222-2-2-2-2-2-2-20020020000002i2i−2i−2i2-200002-2002i−2i02i−2i0000−2i2i000000000000
χ26222222-2-2-2-2-2-2-20020020000002i2i−2i−2i-220000-2200−2i2i02i−2i00002i−2i000000000000
χ27222222-2-2-2-2-2-2-2002002000000−2i−2i2i2i2-200002-200−2i2i0−2i2i00002i−2i000000000000
χ28222222-2-2-2-2-2-2-2002002000000−2i−2i2i2i-220000-22002i−2i0−2i2i0000−2i2i000000000000
χ292222-2-222-222-2-222-2-2-220000000000222-222-2-2-2-200000000000000000000000
χ302222-2-222-222-2-222-2-2-220000000000-2-2-2-2-22222200000000000000000000000
χ312222-2-222-222-2-2-2-2-2222000000000022-22-2-2-2-22200000000000000000000000
χ322222-2-222-222-2-2-2-2-22220000000000-2-2222-222-2-200000000000000000000000
χ332222-2-22-222-22-222222-222-2-2222222000-20-2000000-2-2-2000000000000000000
χ342222-2-22-222-22-222222-2-2-222-2-2-2-2-2-2000-20-2000000222000000000000000000
χ352222-2-22-222-22-2-2-22-2-2-222-2-222-2-2-2-2000202000000-222000000000000000000
χ362222-2-22-222-22-2-2-22-2-2-2-2-222-2-222220002020000002-2-2000000000000000000
χ372222-2-2-22-2-22-2200200-20000002i2i−2i−2i0020-2000-22000−2i2i2i−2i2i−2i00000000000000
χ382222-2-2-22-2-22-2200200-20000002i2i−2i−2i00-2020002-2000−2i2i−2i2i−2i2i00000000000000
χ392222-2-2-22-2-22-2200200-2000000−2i−2i2i2i0020-2000-220002i−2i−2i2i−2i2i00000000000000
χ402222-2-2-22-2-22-2200200-2000000−2i−2i2i2i00-2020002-20002i−2i2i−2i2i−2i00000000000000
χ412222-2-2-2-22-2-22200-200222-2-2-2-200002-20000-220000200-222-200000000000000
χ422222-2-2-2-22-2-22200-200222-2-2-2-20000-2200002-200002002-2-2200000000000000
χ432222-2-2-2-22-2-22200-2002-2-2222200002-20000-220000-2002-2-2200000000000000
χ442222-2-2-2-22-2-22200-2002-2-222220000-2200002-20000-200-222-200000000000000
χ4544-4-400400-40004-4000022−220022−2222−2222−22000000000000000000000000000000000
χ4644-4-400400-40004-40000−222200−2222−2222−2222000000000000000000000000000000000
χ4744-4-400400-4000-44000022−220022−22−2222−2222000000000000000000000000000000000
χ4844-4-400400-4000-440000−222200−222222−2222−22000000000000000000000000000000000
χ4944-4-400-40040000004i−4i022−2200−22222i2−2i2−2i22i2000000000000000000000000000000000
χ5044-4-400-40040000004i−4i0−22220022−22−2i22i22i2−2i2000000000000000000000000000000000
χ5144-4-400-4004000000−4i4i022−2200−2222−2i22i22i2−2i2000000000000000000000000000000000
χ5244-4-400-4004000000−4i4i0−22220022−222i2−2i2−2i22i2000000000000000000000000000000000
χ534-44-44-40440-4-40000000000000000000000000000000000000000000022−220000
χ544-44-44-40440-4-400000000000000000000000000000000000000000000−22220000
χ554-44-44-40-4-40440000000000000000000000000000000000000022−220000000000
χ564-44-44-40-4-404400000000000000000000000000000000000000−22220000000000
χ574-44-4-4404-40-4400000000000000000000000000000000000000002i2−2i200000000
χ584-44-4-4404-40-440000000000000000000000000000000000000000−2i22i200000000
χ594-44-4-440-4404-40000000000000000000000000000000000000000002i2−2i2000000
χ604-44-4-440-4404-4000000000000000000000000000000000000000000−2i22i2000000
χ618-8-88000000000000000004i2−4i2000000000000000000000000000000000000000
χ628-8-8800000000000000000−4i24i2000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).