Finite Group Databasebeta

← Group #239877

Character table — Group #239877

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444422444444444444888888888888888888888888222444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111-1-1-1-1-1-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111111-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111111
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1111
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-111-1-11
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-111-1-111-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-11111-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-11
χ172222222222-2-22222222222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ182222222222-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-222-2-2-2-222000000000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-2222222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000002-2-20000002
χ2222222222-2-2222222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000-222000000-2
χ2322222222-2-222-2-2-2-22222-2-222-2-222-2-200000000000000000000000000000000002-22000000-2
χ2422222222-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000000000-22-20000002
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-200000002-20
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-220000000-220
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000002-20000000-220
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000-2200000002-20
χ2922-22-22-2-22-2002i2i−2i−2i2i2i−2i−2i2-200000000002-2002i−2ii2i2−i2−i222−2−200000000i2i2−i2−i222−2−2000000000000
χ3022-22-22-2-22-2002i2i−2i−2i2i2i−2i−2i2-200000000002-2002i−2i−i2−i2i2i2−2−22200000000−i2−i2i2i2−2−222000000000000
χ3122-22-22-2-22-2002i2i−2i−2i2i2i−2i−2i2-20000000000-2200−2i2ii2i2−i2−i222−2−200000000−i2−i2i2i2−2−222000000000000
χ3222-22-22-2-22-2002i2i−2i−2i2i2i−2i−2i2-20000000000-2200−2i2i−i2−i2i2i2−2−22200000000i2i2−i2−i222−2−2000000000000
χ3322-22-22-2-22-200−2i−2i2i2i−2i−2i2i2i2-200000000002-200−2i2ii2i2−i2−i2−2−22200000000i2i2−i2−i2−2−222000000000000
χ3422-22-22-2-22-200−2i−2i2i2i−2i−2i2i2i2-200000000002-200−2i2i−i2−i2i2i222−2−200000000−i2−i2i2i222−2−2000000000000
χ3522-22-22-2-22-200−2i−2i2i2i−2i−2i2i2i2-20000000000-22002i−2ii2i2−i2−i2−2−22200000000−i2−i2i2i222−2−2000000000000
χ3622-22-22-2-22-200−2i−2i2i2i−2i−2i2i2i2-20000000000-22002i−2i−i2−i2i2i222−2−200000000i2i2−i2−i2−2−222000000000000
χ372-222-2-22-22-2002i−2i2i−2i2i−2i2i−2i-22000000002-2002i−2i002−22−2i2−i2i2−i2000000002−22−2i2−i2i2−i2000000000000
χ382-222-2-22-22-2002i−2i2i−2i2i−2i2i−2i-22000000002-2002i−2i00−22−22−i2i2−i2i200000000−22−22−i2i2−i2i2000000000000
χ392-222-2-22-22-2002i−2i2i−2i2i−2i2i−2i-2200000000-2200−2i2i002−22−2i2−i2i2−i200000000−22−22−i2i2−i2i2000000000000
χ402-222-2-22-22-2002i−2i2i−2i2i−2i2i−2i-2200000000-2200−2i2i00−22−22−i2i2−i2i2000000002−22−2i2−i2i2−i2000000000000
χ412-222-2-22-22-200−2i2i−2i2i−2i2i−2i2i-22000000002-200−2i2i002−22−2−i2i2−i2i2000000002−22−2−i2i2−i2i2000000000000
χ422-222-2-22-22-200−2i2i−2i2i−2i2i−2i2i-22000000002-200−2i2i00−22−22i2−i2i2−i200000000−22−22i2−i2i2−i2000000000000
χ432-222-2-22-22-200−2i2i−2i2i−2i2i−2i2i-2200000000-22002i−2i002−22−2−i2i2−i2i200000000−22−22i2−i2i2−i2000000000000
χ442-222-2-22-22-200−2i2i−2i2i−2i2i−2i2i-2200000000-22002i−2i00−22−22i2−i2i2−i2000000002−22−2−i2i2−i2i2000000000000
χ452-2-222-2-2222222-2-222-2-22-2-2-2-22-22-2-22000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ462-2-222-2-2222222-2-222-2-22-2-2-2-22-22-2-2200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ472-2-222-2-222222-222-2-222-2-2-2-2-2-22-22-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ482-2-222-2-222222-222-2-222-2-2-2-2-2-22-22-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ492-2-222-2-2222-2-22-2-222-2-22-2-222-22-222-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ502-2-222-2-2222-2-22-2-222-2-22-2-222-22-222-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ512-2-222-2-2222-2-2-222-2-222-2-2-2222-22-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ522-2-222-2-2222-2-2-222-2-222-2-2-2222-22-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ532-2-222-2-22-2-2222-2-22-222-222-2-22-2-222-200000000000000000000000000000000000002i−2i2i−2i000
χ542-2-222-2-22-2-2222-2-22-222-222-2-22-2-222-20000000000000000000000000000000000000−2i2i−2i2i000
χ552-2-222-2-22-2-222-222-22-2-2222-2-2-222-22-200000000000000000000000000000000000002i−2i−2i2i000
χ562-2-222-2-22-2-222-222-22-2-2222-2-2-222-22-20000000000000000000000000000000000000−2i2i2i−2i000
χ572-2-222-2-22-2-2-2-22-2-22-222-22222-222-2-22000000000000000022-2-222-2-200000000000000000000
χ582-2-222-2-22-2-2-2-22-2-22-222-22222-222-2-220000000000000000-2-222-2-22200000000000000000000
χ592-2-222-2-22-2-2-2-2-222-22-2-2222222-2-22-22000000000000000022-2-2-2-22200000000000000000000
χ602-2-222-2-22-2-2-2-2-222-22-2-2222222-2-22-220000000000000000-2-22222-2-200000000000000000000
χ61444-44-4-4-4004-400000000004-4000000000000000000000022−2222−22000000000000000000000000
χ62444-44-4-4-4004-400000000004-40000000000000000000000−2222−2222000000000000000000000000
χ63444-44-4-4-400-440000000000-440000000000000000000000000022−2222−2200000000000000000000
χ64444-44-4-4-400-440000000000-4400000000000000000000000000−2222−222200000000000000000000
χ6544-44-44-4-4-44004i4i−4i−4i−4i−4i4i4i-440000000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-4400−4i−4i4i4i4i4i−4i−4i-440000000000000000000000000000000000000000000000000000
χ674-444-4-44-4-44004i−4i4i−4i−4i4i−4i4i4-40000000000000000000000000000000000000000000000000000
χ684-444-4-44-4-4400−4i4i−4i4i4i−4i4i−4i4-40000000000000000000000000000000000000000000000000000
χ694-4-4-4444-4004-40000000000-440000000000000000000000000022−22−222200000000000000000000
χ704-4-4-4444-4004-40000000000-4400000000000000000000000000−222222−2200000000000000000000
χ714-4-4-4444-400-4400000000004-4000000000000000000000022−22−2222000000000000000000000000
χ724-4-4-4444-400-4400000000004-40000000000000000000000−222222−22000000000000000000000000
χ7388-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000

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