Finite Group Databasebeta

← Group #145584

Character table — Group #145584

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order122244442244444444888888888888888816161616161616161616161616161616444488882244
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ9222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ10222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222222-2-2-2-222-2-20000000022-2-200002222−2−2−2−22222−2−2−2−2000000000000
χ122222222222-2-2-2-222-2-20000000022-2-20000−2−2−2−22222−2−2−2−22222000000000000
χ132222222222-2-2-2-222-2-200000000-2-22200002222−2−2−2−2−2−2−2−22222000000000000
χ142222222222-2-2-2-222-2-200000000-2-2220000−2−2−2−222222222−2−2−2−2000000000000
χ1522222222-2-22222-2-2-2-222-2-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ1622222222-2-22222-2-2-2-222-2-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ1722222222-2-22222-2-2-2-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ1822222222-2-22222-2-2-2-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ1922222222-2-2-2-2-2-2-2-22200000000000022-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2022222222-2-2-2-2-2-2-2-22200000000000022-2-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2122222222-2-2-2-2-2-2-2-222000000000000-2-222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2222222222-2-2-2-2-2-2-2-222000000000000-2-222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ232222-2-2-2-222-2-222-2-22-22222-2-2-2-200000000000000000000000000002i2i−2i−2i0000
χ242222-2-2-2-222-2-222-2-22-22222-2-2-2-20000000000000000000000000000−2i−2i2i2i0000
χ252222-2-2-2-222-2-222-2-22-2-2-2-2-2222200000000000000000000000022-2-200000000
χ262222-2-2-2-222-2-222-2-22-2-2-2-2-22222000000000000000000000000-2-22200000000
χ272222-2-2-2-2-2-2-2-22222-2222-2-2-2-2220000000000000000000000000000000020-20
χ282222-2-2-2-2-2-2-2-22222-2222-2-2-2-22200000000000000000000000000000000-2020
χ292222-2-2-2-2-2-2-2-22222-22-2-22222-2-200000000000000000000000000000000020-2
χ302222-2-2-2-2-2-2-2-22222-22-2-22222-2-2000000000000000000000000000000000-202
χ312-2-2222-2-22-200002-2002−22−22−22−22-2002−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ322-2-2222-2-22-200002-2002−22−22−22−22-2002−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ332-2-2222-2-22-200002-2002−22−22−22−2-2200−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ342-2-2222-2-22-200002-2002−22−22−22−2-2200−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ352-2-2222-2-22-200002-200−22−22−22−222-200−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000000000
χ362-2-2222-2-22-200002-200−22−22−22−222-200−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000000000
χ372-2-2222-2-22-200002-200−22−22−22−22-22002−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000000000
χ382-2-2222-2-22-200002-200−22−22−22−22-22002−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000000000
χ392-2-2222-2-2-220000-22002−2−222−2−22002-22−2−22ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7000000000000
χ402-2-2222-2-2-220000-22002−2−222−2−22002-22−2−22−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7000000000000
χ412-2-2222-2-2-220000-22002−2−222−2−2200-22−222−2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7000000000000
χ422-2-2222-2-2-220000-22002−2−222−2−2200-22−222−2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7000000000000
χ432-2-2222-2-2-220000-2200−222−2−222−2002-2−222−2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5000000000000
χ442-2-2222-2-2-220000-2200−222−2−222−2002-2−222−2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5000000000000
χ452-2-2222-2-2-220000-2200−222−2−222−200-222−2−22ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5000000000000
χ462-2-2222-2-2-220000-2200−222−2−222−200-222−2−22−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5000000000000
χ474444-4-4-4-44444-4-4-4-4-4400000000000000000000000000000000000000000000
χ484444-4-4-4-4-4-444-4-4444-400000000000000000000000000000000000000000000
χ4944-4-44i−4i4i−4i004i−4i4-40000000000000000000000000000000000002-22i−2i00000000
χ5044-4-44i−4i4i−4i004i−4i4-4000000000000000000000000000000000000-22−2i2i00000000
χ5144-4-44i−4i4i−4i00−4i4i-4400000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ5244-4-44i−4i4i−4i00−4i4i-440000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ5344-4-4−4i4i−4i4i004i−4i-4400000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ5444-4-4−4i4i−4i4i004i−4i-440000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ5544-4-4−4i4i−4i4i00−4i4i4-40000000000000000000000000000000000002-2−2i2i00000000
χ5644-4-4−4i4i−4i4i00−4i4i4-4000000000000000000000000000000000000-222i−2i00000000
χ574-4-44-4-4444-40000-440022−2222−22−2222−2222000000000000000000000000000000000000
χ584-4-44-4-4444-40000-4400−2222−222222−2222−22000000000000000000000000000000000000
χ594-4-44-4-444-4400004-40022−22−2222−222222−22000000000000000000000000000000000000
χ604-4-44-4-444-4400004-400−222222−2222−22−2222000000000000000000000000000000000000
χ618-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.