Finite Group Databasebeta

← Group #239885

Character table — Group #239885

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444422444444444444888888888888888888888888222444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-1-11
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
χ91111111111-1-1-1-1111-1-1-1-1111-1-11-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1
χ101111111111-1-1-1-1111-1-1-1-1111-1-11-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1111
χ111111111111-1-1-1-1111-1-1-1-1111-1-11-1-1111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111
χ121111111111-1-1-1-1111-1-1-1-1111-1-11-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1
χ131111111111-1-1-1-1111-1-1-1-1111-1-11-1-11-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-111-1-11
χ141111111111-1-1-1-1111-1-1-1-1111-1-11-1-11-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11111-1
χ151111111111-1-1-1-1111-1-1-1-1111-1-11-1-11-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1-111-1
χ161111111111-1-1-1-1111-1-1-1-1111-1-11-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-11
χ1722222222222222-2-2-2222222-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-222-222-222-222-2-2-2-222000000000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-222-222-222-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-22222222-2-2-2-2-2-22-2-2-222-200000000000000000000000000000000002-2-20000002
χ2222222222-2-22222222-2-2-2-2-2-22-2-2-222-20000000000000000000000000000000000-222000000-2
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2222-2-22000000000000000000000000000000002-200000002-20
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2222-2-2200000000000000000000000000000000-220000000-220
χ2522222222-2-2-2-2-2-22222222-2-2222-2-2-2-200000000000000000000000000000000002-22000000-2
χ2622222222-2-2-2-2-2-22222222-2-2222-2-2-2-20000000000000000000000000000000000-22-20000002
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-22222000000000000000000000000000000002-20000000-220
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2222200000000000000000000000000000000-2200000002-20
χ2922-22-22-2-22-22i2i−2i−2i0002i2i−2i−2i2-2000000000002-22i−2i0000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i2000000000000
χ3022-22-22-2-22-22i2i−2i−2i0002i2i−2i−2i2-2000000000002-22i−2i00000000−2−222−i2−i2i2i2−2−222−i2−i2i2i2000000000000
χ3122-22-22-2-22-22i2i−2i−2i0002i2i−2i−2i2-200000000000-22−2i2i0000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ3222-22-22-2-22-22i2i−2i−2i0002i2i−2i−2i2-200000000000-22−2i2i00000000−2−222−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ3322-22-22-2-22-2−2i−2i2i2i000−2i−2i2i2i2-2000000000002-2−2i2i0000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i2000000000000
χ3422-22-22-2-22-2−2i−2i2i2i000−2i−2i2i2i2-2000000000002-2−2i2i00000000−2−222i2i2−i2−i2−2−222i2i2−i2−i2000000000000
χ3522-22-22-2-22-2−2i−2i2i2i000−2i−2i2i2i2-200000000000-222i−2i0000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ3622-22-22-2-22-2−2i−2i2i2i000−2i−2i2i2i2-200000000000-222i−2i00000000−2−222i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ372-222-2-22-22-22i−2i2i−2i0002i−2i2i−2i-2200000002-22i−2i000000000000i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-222-2-22-22-22i−2i2i−2i0002i−2i2i−2i-2200000002-22i−2i000000000000−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-222-2-22-22-22i−2i2i−2i0002i−2i2i−2i-220000000-22−2i2i000000000000i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ402-222-2-22-22-22i−2i2i−2i0002i−2i2i−2i-220000000-22−2i2i000000000000−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ412-222-2-22-22-2−2i2i−2i2i000−2i2i−2i2i-2200000002-2−2i2i000000000000i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ422-222-2-22-22-2−2i2i−2i2i000−2i2i−2i2i-2200000002-2−2i2i000000000000−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ432-222-2-22-22-2−2i2i−2i2i000−2i2i−2i2i-220000000-222i−2i000000000000i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-222-2-22-22-2−2i2i−2i2i000−2i2i−2i2i-220000000-222i−2i000000000000−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-2-222-2-22222-2-2222-22-2-22-2-2-22-2-22-2200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ462-2-222-2-22222-2-2222-22-2-22-2-2-22-2-22-220000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ472-2-222-2-22222-2-22-2-222-2-22-2-22-222-22-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ482-2-222-2-22222-2-22-2-222-2-22-2-22-222-22-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ492-2-222-2-2222-222-222-2-222-2-2-2-2-22-2-22200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ502-2-222-2-2222-222-222-2-222-2-2-2-2-22-2-2220000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ512-2-222-2-2222-222-2-2-22-222-2-2-222-222-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ522-2-222-2-2222-222-2-2-22-222-2-2-222-222-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ532-2-222-2-22-2-22-2-2222-2-222-222-2-2222-2-200000000000000000000000000000000000002i−2i2i−2i000
χ542-2-222-2-22-2-22-2-2222-2-222-222-2-2222-2-20000000000000000000000000000000000000−2i2i−2i2i000
χ552-2-222-2-22-2-22-2-22-2-22-222-22222-2-2-2220000000022-2-222-2-20000000000000000000000000000
χ562-2-222-2-22-2-22-2-22-2-22-222-22222-2-2-22200000000-2-222-2-2220000000000000000000000000000
χ572-2-222-2-22-2-2-222-222-22-2-2222-22-22-22-200000000000000000000000000000000000002i−2i−2i2i000
χ582-2-222-2-22-2-2-222-222-22-2-2222-22-22-22-20000000000000000000000000000000000000−2i2i2i−2i000
χ592-2-222-2-22-2-2-222-2-2-222-2-22222-22-22-220000000022-2-2-2-2220000000000000000000000000000
χ602-2-222-2-22-2-2-222-2-2-222-2-22222-22-22-2200000000-2-22222-2-20000000000000000000000000000
χ6144-44-44-4-4-444i4i−4i−4i000−4i−4i4i4i-44000000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-44−4i−4i4i4i0004i4i−4i−4i-44000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4440000004-44000000-40000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ6444-4-4-4-4440000004-44000000-4000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ6544-4-4-4-444000000-44-400000040000000000000022−2222−2200000000000000000000000000000000
χ6644-4-4-4-444000000-44-4000000400000000000000−2222−222200000000000000000000000000000000
χ674-444-4-44-4-444i−4i4i−4i000−4i4i−4i4i4-4000000000000000000000000000000000000000000000000000
χ684-444-4-44-4-44−4i4i−4i4i0004i−4i4i−4i4-4000000000000000000000000000000000000000000000000000
χ694-44-4-44-440000004-4-400000040000000000000022−22−222200000000000000000000000000000000
χ704-44-4-44-440000004-4-4000000400000000000000−222222−2200000000000000000000000000000000
χ714-44-4-44-44000000-444000000-40000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ724-44-4-44-44000000-444000000-4000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ73888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000

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