Finite Group Databasebeta

← Group #242003

Character table — Group #242003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444444444448888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-11111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ121111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ131111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ141111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-2-222-2-222-2-2-2-22200002200-2-2-2-2000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-20000-2-2002222000000000000000000000000000000
χ192222222222-2-2-2-22222-2-222-2-2-2-222-2-2220000-2-20022-2-2000000000000000000000000000000
χ202222222222-2-2-2-22222-2-222-2-2-2-222-2-2-2-200002200-2-222000000000000000000000000000000
χ2122222222-2-22222222222-2-222-2-2-2-2-2-200222200-2-20000-2-20000000000000000000000000000
χ2222222222-2-22222222222-2-222-2-2-2-2-2-200-2-2-2-200220000220000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-22-200000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-22-2200000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-20022-2-200-2-20000220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-200-2-22200220000-2-20000000000000000000000000000
χ2922-22-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-2000000000000002i−2i00002-2i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000
χ3022-22-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-2000000000000002i−2i00002-2−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000
χ3122-22-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-200000000000000−2i2i0000-22i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000
χ3222-22-2-2-22002i2i−2i−2i2i2i−2i−2i2-2002-200000000000000−2i2i0000-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000
χ3322-22-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-2000000000000002i−2i0000-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000
χ3422-22-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-2000000000000002i−2i0000-22−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000
χ3522-22-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-200000000000000−2i2i00002-2i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000
χ3622-22-2-2-2200−2i−2i2i2i−2i−2i2i2i2-2002-200000000000000−2i2i00002-2−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000
χ372-22-22-2-222-22i−2i2i−2i2i−2i2i−2i2-22-2-222i−2i2i−2i2-20000000000000000000000002i−2i2i−2i2-22-2000000000000
χ382-22-22-2-222-22i−2i2i−2i2i−2i2i−2i2-22-2-222i−2i2i−2i2-2000000000000000000000000−2i2i−2i2i-22-22000000000000
χ392-22-22-2-222-22i−2i2i−2i−2i2i−2i2i-222-22-22i−2i−2i2i-2200000000000000000000000000000000000000002-22i−2i
χ402-22-22-2-222-22i−2i2i−2i−2i2i−2i2i-222-22-22i−2i−2i2i-220000000000000000000000000000000000000000-22−2i2i
χ412-22-22-2-222-2−2i2i−2i2i2i−2i2i−2i-222-22-2−2i2i2i−2i-2200000000000000000000000000000000000000002-2−2i2i
χ422-22-22-2-222-2−2i2i−2i2i2i−2i2i−2i-222-22-2−2i2i2i−2i-220000000000000000000000000000000000000000-222i−2i
χ432-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i2-22-2-22−2i2i−2i2i2-20000000000000000000000002i−2i2i−2i-22-22000000000000
χ442-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i2-22-2-22−2i2i−2i2i2-2000000000000000000000000−2i2i−2i2i2-22-2000000000000
χ452-22-22-2-22-222i−2i2i−2i2i−2i2i−2i2-2-22-22−2i2i−2i2i-2200000000000000002i−2i2i−2i2-22-200000000000000000000
χ462-22-22-2-22-222i−2i2i−2i2i−2i2i−2i2-2-22-22−2i2i−2i2i-220000000000000000−2i2i−2i2i-22-2200000000000000000000
χ472-22-22-2-22-222i−2i2i−2i−2i2i−2i2i-22-222-2−2i2i2i−2i2-20000000000000000000000000000000000002i−2i2-20000
χ482-22-22-2-22-222i−2i2i−2i−2i2i−2i2i-22-222-2−2i2i2i−2i2-2000000000000000000000000000000000000−2i2i-220000
χ492-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222-22i−2i−2i2i2-20000000000000000000000000000000000002i−2i-220000
χ502-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222-22i−2i−2i2i2-2000000000000000000000000000000000000−2i2i2-20000
χ512-22-22-2-22-22−2i2i−2i2i−2i2i−2i2i2-2-22-222i−2i2i−2i-2200000000000000002i−2i2i−2i-22-2200000000000000000000
χ522-22-22-2-22-22−2i2i−2i2i−2i2i−2i2i2-2-22-222i−2i2i−2i-220000000000000000−2i2i−2i2i2-22-200000000000000000000
χ532-2-2-2-2222002-2-222-2-222200-2-2000000002i−2i2i−2i00000000002−2−222−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ542-2-2-2-2222002-2-222-2-222200-2-2000000002i−2i2i−2i0000000000−222−2−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ552-2-2-2-2222002-2-222-2-222200-2-200000000−2i2i−2i2i00000000002−2−222−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ562-2-2-2-2222002-2-222-2-222200-2-200000000−2i2i−2i2i0000000000−222−2−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ572-2-2-2-222200-222-2-222-22200-2-2000000002i−2i−2i2i00000000002−2−22−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ582-2-2-2-222200-222-2-222-22200-2-2000000002i−2i−2i2i0000000000−222−22−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ592-2-2-2-222200-222-2-222-22200-2-200000000−2i2i2i−2i00000000002−2−22−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-2-2-222200-222-2-222-22200-2-200000000−2i2i2i−2i0000000000−222−22−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ6144-44-4-4-44004i4i−4i−4i−4i−4i4i4i-4400-4400000000000000000000000000000000000000000000000000
χ6244-44-4-4-4400−4i−4i4i4i4i4i−4i−4i-4400-4400000000000000000000000000000000000000000000000000
χ6344-4-444-4-4440000000000-4-4000000004-4000000000000000000000000000000000000000000
χ6444-4-444-4-4440000000000-4-400000000-44000000000000000000000000000000000000000000
χ6544-4-444-4-4-4-40000000000440000000000000000004i−4i00000000000000000000000000000000
χ6644-4-444-4-4-4-4000000000044000000000000000000−4i4i00000000000000000000000000000000
χ674-4-444-44-44-40000000000-44000000000000000000004i−4i000000000000000000000000000000
χ684-4-444-44-44-40000000000-4400000000000000000000−4i4i000000000000000000000000000000
χ694-4-444-44-4-4400000000004-4000000000000004i−4i000000000000000000000000000000000000
χ704-4-444-44-4-4400000000004-400000000000000−4i4i000000000000000000000000000000000000
χ714-4-4-4-4444004-4-44-444-4-4-4004400000000000000000000000000000000000000000000000000
χ724-4-4-4-444400-444-44-4-44-4-4004400000000000000000000000000000000000000000000000000
χ73888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000

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