Finite Group Databasebeta

← Group #511935

Character table — Group #511935

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222244444444444444444444444444444488888888888888816161616323232323232
order12442488882224444444444444448888888888882224448888888882244888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-11-1-111111-1-1-1-1111111-1-1-1-1
χ411111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-11-1-111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-11-1111-1-111-1-11111-1-111-1-1
χ61111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-11-1111-1-111-1-1-1-1-1-111-1-111
χ71111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-1111111-1-1-1-111
χ81111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1
χ9111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-11-11-11-1
χ10111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-11-11-11
χ11111111-1-1-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-11-1-1-1-1-1-1-111111-11-11-1-11-11
χ12111111-1-1-1-11111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-11-1-1-1-1-1-1-11111-11-11-111-11-1
χ13111111-1-1-1-1111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-11-1-11-1-1-1-111-1-1111-11-1-111-1-11
χ14111111-1-1-1-1111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-11-1-11-1-1-1-111-1-111-11-111-1-111-1
χ15111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11-1-11-1-1-11111-1-11-11-1-11-111-1
χ16111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11-1-11-1-1-11111-1-1-11-111-11-1-11
χ1722222222222-2-20000000022222-2-200000000222200-200-22-2-20000-2-20000000000
χ1822222222222-2-200000000-2-2-2-22-2-200000000-2-2-2-20020022-2-20000220000000000
χ192222222222-22-2000022220000-22-20000222200000-200-20-22-200-2-2000000000000
χ202222222222-22-20000-2-2-2-20000-22-20000-2-2-2-20000020020-22-20022000000000000
χ212222222222-2-22222200000000-2-22222200000000-200-200-2-22-2-200000000000000
χ222222222222-2-22-2-2-2-200000000-2-22-2-2-2-200000000200200-2-222200000000000000
χ23222222-2-2-2-22-2-20000000022222-2-200000000-2-2-2-200-200-2-2220000220000000000
χ24222222-2-2-2-22-2-200000000-2-2-2-22-2-2000000002222002002-2220000-2-20000000000
χ25222222-2-2-2-2-22-2000022220000-22-20000-2-2-2-200000-200-202-220022000000000000
χ26222222-2-2-2-2-22-20000-2-2-2-20000-22-20000222200000200202-2200-2-2000000000000
χ27222222-2-2-2-2-2-22222200000000-2-22-2-2-2-200000000-200-20022-22200000000000000
χ28222222-2-2-2-2-2-22-2-2-2-200000000-2-2222220000000020020022-2-2-200000000000000
χ2922-2-22-2000022-222-2-200000000-2-2200002i2i−2i−2i2i2i−2i−2i200-200000002i−2i2i−2i0000000000
χ3022-2-22-2000022-222-2-200000000-2-220000−2i−2i2i2i−2i−2i2i2i200-20000000−2i2i−2i2i0000000000
χ3122-2-22-2000022-2-2-22200000000-2-2200002i2i−2i−2i−2i−2i2i2i-200200000002i−2i−2i2i0000000000
χ3222-2-22-2000022-2-2-22200000000-2-220000−2i−2i2i2i2i2i−2i−2i-20020000000−2i2i2i−2i0000000000
χ3322-2-22-200002-22000022-2-20000-22-22i2i−2i−2i00002i2i−2i−2i0200-200002i−2i00−2i2i0000000000
χ3422-2-22-200002-22000022-2-20000-22-2−2i−2i2i2i0000−2i−2i2i2i0200-20000−2i2i002i−2i0000000000
χ3522-2-22-200002-220000-2-2220000-22-22i2i−2i−2i0000−2i−2i2i2i0-200200002i−2i002i−2i0000000000
χ3622-2-22-200002-220000-2-2220000-22-2−2i−2i2i2i00002i2i−2i−2i0-20020000−2i2i00−2i2i0000000000
χ3722-2-22-20000-2220000000022-2-22-2-22i2i−2i−2i2i2i−2i−2i000000200-2000−2i2i−2i2i000000000000
χ3822-2-22-20000-2220000000022-2-22-2-2−2i−2i2i2i−2i−2i2i2i000000200-20002i−2i2i−2i000000000000
χ3922-2-22-20000-22200000000-2-2222-2-22i2i−2i−2i−2i−2i2i2i000000-2002000−2i2i2i−2i000000000000
χ4022-2-22-20000-22200000000-2-2222-2-2−2i−2i2i2i2i2i−2i−2i000000-20020002i−2i−2i2i000000000000
χ4122-2-22-20000-2-2-222-2-222-2-222-2-2222000000000000-2-2-22220000000000000000000
χ4222-2-22-20000-2-2-222-2-2-2-222-2-222222000000000000-2222-2-20000000000000000000
χ4322-2-22-20000-2-2-2-2-22222-2-2-2-2222220000000000002-22-22-20000000000000000000
χ4422-2-22-20000-2-2-2-2-222-2-22222-2-222200000000000022-2-2-220000000000000000000
χ4544-4-4-4444-4-400000000000000000000000000000000000000000000022-2-2000000
χ4644-4-4-4444-4-4000000000000000000000000000000000000000000000-2-222000000
χ4744-4-4-44-4-4440000000000000000000000000000000000000000000002-2-22000000
χ4844-4-4-44-4-444000000000000000000000000000000000000000000000-222-2000000
χ494-44i−4i0022−222i2−2i20002-22i−2i2-22i−2i2-22i−2i0002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ504-44i−4i0022−222i2−2i20002-22i−2i-22−2i2i-22−2i2i0002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ514-44i−4i0022−222i2−2i2000-22−2i2i2-22i−2i-22−2i2i000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ524-44i−4i0022−222i2−2i2000-22−2i2i-22−2i2i2-22i−2i000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ534-44i−4i00−2222−2i22i20002-22i−2i2-22i−2i2-22i−2i000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ544-44i−4i00−2222−2i22i20002-22i−2i-22−2i2i-22−2i2i000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ554-44i−4i00−2222−2i22i2000-22−2i2i2-22i−2i-22−2i2i0002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ564-44i−4i00−2222−2i22i2000-22−2i2i-22−2i2i2-22i−2i0002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ574-4−4i4i0022−22−2i22i20002-2−2i2i2-2−2i2i2-2−2i2i000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ584-4−4i4i0022−22−2i22i20002-2−2i2i-222i−2i-222i−2i000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ594-4−4i4i0022−22−2i22i2000-222i−2i2-2−2i2i-222i−2i0002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ604-4−4i4i0022−22−2i22i2000-222i−2i-222i−2i2-2−2i2i0002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ614-4−4i4i00−22222i2−2i20002-2−2i2i2-2−2i2i2-2−2i2i0002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ624-4−4i4i00−22222i2−2i20002-2−2i2i-222i−2i-222i−2i0002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ634-4−4i4i00−22222i2−2i2000-222i−2i2-2−2i2i-222i−2i000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ644-4−4i4i00−22222i2−2i2000-222i−2i-222i−2i2-2−2i2i000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ658888-8-800000000000000000000000000000000000000000000000000000000000

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