Finite Group Databasebeta

← Group #239496

Character table — Group #239496

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222224444444422444444444444444444448888888888888888244444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-11-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-111111
χ91111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-11111-1-1
χ111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-111-11-1-1-111
χ121111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-111-1-11-11-1-111
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-1-111
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-111-1-11-1111-1-1
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-111-11-111-1-1
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000002222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-2-22222222222-2-2-2-2-2-20000000022-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-2-22222222222-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000
χ2122222222-2-22222-2-22222-2-2-2-2-2-22-22-2000000000000000000000000000000002-200-20020000
χ2222222222-2-22222-2-22222-2-2-2-2-2-22-22-200000000000000000000000000000000-2200200-20000
χ2322222222-2-22222-2-2-2-2-2-22222-2-2-22-220000000000000000000000000000000000220-2-200000
χ2422222222-2-22222-2-2-2-2-2-22222-2-2-22-220000000000000000000000000000000000-2-202200000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-222-22-2200000000000000000000000000000000002-20-2200000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-222-22-220000000000000000000000000000000000-2202-200000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222-22-2000000000000000000000000000000002200-200-20000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222222-22-200000000000000000000000000000000-2-20020020000
χ2922-2-222-2-22-200002-22i2i−2i−2i2i2i−2i−2i00000000000000002-22i−2i0022−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000
χ3022-2-222-2-22-200002-22i2i−2i−2i2i2i−2i−2i00000000000000002-22i−2i00−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000
χ3122-2-222-2-22-200002-22i2i−2i−2i2i2i−2i−2i0000000000000000-22−2i2i0022−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000
χ3222-2-222-2-22-200002-22i2i−2i−2i2i2i−2i−2i0000000000000000-22−2i2i00−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000
χ3322-2-222-2-22-200002-2−2i−2i2i2i−2i−2i2i2i00000000000000002-2−2i2i0022−2−2−i2−i2i2i2−i2−i2i2i222−2−2000000000000
χ3422-2-222-2-22-200002-2−2i−2i2i2i−2i−2i2i2i00000000000000002-2−2i2i00−2−222i2i2−i2−i2i2i2−i2−i2−2−222000000000000
χ3522-2-222-2-22-200002-2−2i−2i2i2i−2i−2i2i2i0000000000000000-222i−2i0022−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000
χ3622-2-222-2-22-200002-2−2i−2i2i2i−2i−2i2i2i0000000000000000-222i−2i00−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000
χ372-22-22-22-2-2200002-22i−2i2i−2i2i−2i2i−2i000000000000002-200002i−2ii2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-22-22-22-2-2200002-22i−2i2i−2i2i−2i2i−2i000000000000002-200002i−2i−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-22-22-22-2-2200002-22i−2i2i−2i2i−2i2i−2i00000000000000-220000−2i2ii2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ402-22-22-22-2-2200002-22i−2i2i−2i2i−2i2i−2i00000000000000-220000−2i2i−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ412-22-22-22-2-2200002-2−2i2i−2i2i−2i2i−2i2i000000000000002-20000−2i2ii2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ422-22-22-22-2-2200002-2−2i2i−2i2i−2i2i−2i2i000000000000002-20000−2i2i−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ432-22-22-22-2-2200002-2−2i2i−2i2i−2i2i−2i2i00000000000000-2200002i−2ii2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-22-22-22-2-2200002-2−2i2i−2i2i−2i2i−2i2i00000000000000-2200002i−2i−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-2-222-2-222222-2-2-2-22-2-22-222-22-22-2-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ462-2-222-2-222222-2-2-2-22-2-22-222-22-22-2-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ472-2-222-2-222222-2-2-2-2-222-22-2-222-2-222-200000000000000000000000000000000000000002i−2i2i−2i
χ482-2-222-2-222222-2-2-2-2-222-22-2-222-2-222-20000000000000000000000000000000000000000−2i2i−2i2i
χ492-2-222-2-2222-2-222-2-22-2-22-222-2-22-222-200000000000000000000000000000000000000002i−2i−2i2i
χ502-2-222-2-2222-2-222-2-22-2-22-222-2-22-222-20000000000000000000000000000000000000000−2i2i2i−2i
χ512-2-222-2-2222-2-222-2-2-222-22-2-22-222-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ522-2-222-2-2222-2-222-2-2-222-22-2-22-222-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ532-2-222-2-22-2-222-2-2222-2-222-2-22-2222-2-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ542-2-222-2-22-2-222-2-2222-2-222-2-22-2222-2-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ552-2-222-2-22-2-222-2-222-222-2-222-2-22-2-2220000000000000000000000002-2-22-222-2000000000000
χ562-2-222-2-22-2-222-2-222-222-2-222-2-22-2-222000000000000000000000000-222-22-2-22000000000000
χ572-2-222-2-22-2-2-2-222222-2-222-2-222-2-2-2220000000000000000000000002-2-222-2-22000000000000
χ582-2-222-2-22-2-2-2-222222-2-222-2-222-2-2-222000000000000000000000000-222-2-222-2000000000000
χ592-2-222-2-22-2-2-2-22222-222-2-222-22-222-2-200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ602-2-222-2-22-2-2-2-22222-222-2-222-22-222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ61444-4-4-4-44004-44-400000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ62444-4-4-4-44004-44-40000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ63444-4-4-4-4400-44-4400000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ64444-4-4-4-4400-44-440000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ6544-4-444-4-4-440000-444i4i−4i−4i−4i−4i4i4i00000000000000000000000000000000000000000000000000
χ6644-4-444-4-4-440000-44−4i−4i4i4i4i4i−4i−4i00000000000000000000000000000000000000000000000000
χ674-44-44-44-44-40000-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ684-44-44-44-44-40000-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-4-4-4444004-4-4400000000000000002-2-222-2-22000000000000000000000000000000000000
χ704-4-4-4-4444004-4-440000000000000000-222-2-222-2000000000000000000000000000000000000
χ714-4-4-4-444400-444-400000000000000002-2-22-222-2000000000000000000000000000000000000
χ724-4-4-4-444400-444-40000000000000000-222-22-2-22000000000000000000000000000000000000
χ7388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000

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