Finite Group Databasebeta

← Group #242520

Character table — Group #242520

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444422444444444444888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ91111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111
χ121111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ141111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ151111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ161111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ1722222222222222-2-2-2-2-2-22-2-2222-2-2-2-20000000022-2-200000000-2-22200000000000000000000
χ1822222222222222-2-2-2-2-2-22-2-2222-2-2-2-200000000-2-2220000000022-2-200000000000000000000
χ192222222222-2-2-2-2-2-222222-2-22-2-2-2-22200000000222200000000-2-2-2-200000000000000000000
χ202222222222-2-2-2-2-2-222222-2-22-2-2-2-22200000000-2-2-2-200000000222200000000000000000000
χ2122222222-2-22222222222-222-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2222222222-2-22222222222-222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2522222222-2-2-2-2-2-222-2-2-2-2-222-222-2-22222-2-2-2-222000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-2-222-222-2-222-2-22222-2-2000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i02-2000000000002i−2i2-2i2−i22−200000000i2−i22−22−22−2i2−i2i2−i2000000000000
χ3022-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i02-2000000000002i−2i2-2−i2i2−2200000000−i2i2−22−22−22−i2i2−i2i2000000000000
χ3122-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i02-200000000000−2i2i-22i2−i22−200000000i2−i22−2−22−22−i2i2−i2i2000000000000
χ3222-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i02-200000000000−2i2i-22−i2i2−2200000000−i2i2−222−22−2i2−i2i2−i2000000000000
χ3322-2-222-2-2002i2i−2i−2i-22−2i−2i2i2i0-2200000002-22i−2i0000i2−i2−2200000000−i2i22−2i2−i2−i2i2−222−2000000000000
χ3422-2-222-2-2002i2i−2i−2i-22−2i−2i2i2i0-2200000002-22i−2i0000−i2i22−200000000i2−i2−22−i2i2i2−i22−2−22000000000000
χ3522-2-222-2-2002i2i−2i−2i-22−2i−2i2i2i0-220000000-22−2i2i0000i2−i2−2200000000−i2i22−2−i2i2i2−i22−2−22000000000000
χ3622-2-222-2-2002i2i−2i−2i-22−2i−2i2i2i0-220000000-22−2i2i0000−i2i22−200000000i2−i2−22i2−i2−i2i2−222−2000000000000
χ3722-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i02-2000000000002i−2i-22i2−i2−2200000000i2−i2−222−22−2−i2i2−i2i2000000000000
χ3822-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i02-2000000000002i−2i-22−i2i22−200000000−i2i22−2−22−22i2−i2i2−i2000000000000
χ3922-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i02-200000000000−2i2i2-2i2−i2−2200000000i2−i2−22−22−22i2−i2i2−i2000000000000
χ4022-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i02-200000000000−2i2i2-2−i2i22−200000000−i2i22−22−22−2−i2i2−i2i2000000000000
χ4122-2-222-2-200−2i−2i2i2i-222i2i−2i−2i0-2200000002-2−2i2i0000i2−i22−200000000−i2i2−22i2−i2−i2i22−2−22000000000000
χ4222-2-222-2-200−2i−2i2i2i-222i2i−2i−2i0-2200000002-2−2i2i0000−i2i2−2200000000i2−i22−2−i2i2i2−i2−222−2000000000000
χ4322-2-222-2-200−2i−2i2i2i-222i2i−2i−2i0-220000000-222i−2i0000i2−i22−200000000−i2i2−22−i2i2i2−i2−222−2000000000000
χ4422-2-222-2-200−2i−2i2i2i-222i2i−2i−2i0-220000000-222i−2i0000−i2i2−2200000000i2−i22−2i2−i2−i2i22−2−22000000000000
χ452-22-22-22-2222-22-2222-22-2-2-2-2-22-22-22-20000000000000000000000000000000000002-22-20000
χ462-22-22-22-2222-22-2222-22-2-2-2-2-22-22-22-2000000000000000000000000000000000000-22-220000
χ472-22-22-22-2222-22-2-2-2-22-22-222-22-2-22-22000000000000000000000000000000002i−2i2i−2i00000000
χ482-22-22-22-2222-22-2-2-2-22-22-222-22-2-22-2200000000000000000000000000000000−2i2i−2i2i00000000
χ492-22-22-22-222-22-2222-22-22-2-2-2-2-222-2-220000000000000000000000000000000000002-2-220000
χ502-22-22-22-222-22-2222-22-22-2-2-2-2-222-2-22000000000000000000000000000000000000-222-20000
χ512-22-22-22-222-22-22-2-22-22-2-222-2-22-222-2000000000000000000000000000000002i−2i−2i2i00000000
χ522-22-22-22-222-22-22-2-22-22-2-222-2-22-222-200000000000000000000000000000000−2i2i2i−2i00000000
χ532-22-22-22-2-2-22-22-2222-22-22-2-22-22-22-2200000000000000000000000000000000000000002i−2i2i−2i
χ542-22-22-22-2-2-22-22-2222-22-22-2-22-22-22-220000000000000000000000000000000000000000−2i2i−2i2i
χ552-22-22-22-2-2-22-22-2-2-2-22-222222-222-22-200000000000022-2-222-2-2000000000000000000000000
χ562-22-22-22-2-2-22-22-2-2-2-22-222222-222-22-2000000000000-2-222-2-222000000000000000000000000
χ572-22-22-22-2-2-2-22-2222-22-222-2-222-2-222-200000000000000000000000000000000000000002i−2i−2i2i
χ582-22-22-22-2-2-2-22-2222-22-222-2-222-2-222-20000000000000000000000000000000000000000−2i2i2i−2i
χ592-22-22-22-2-2-2-22-22-2-22-22-222222-22-2-2200000000000022-2-2-2-222000000000000000000000000
χ602-22-22-22-2-2-2-22-22-2-22-22-222222-22-2-22000000000000-2-22222-2-2000000000000000000000000
χ61444-4-4-4-444-40000000000400-400000000000000000022−2222−220000000000000000000000000000
χ62444-4-4-4-444-40000000000400-4000000000000000000−2222−22220000000000000000000000000000
χ63444-4-4-4-44-440000000000-400400000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ64444-4-4-4-44-440000000000-40040000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ654-444-44-4-44-40000000000-400400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ664-444-44-4-44-40000000000-40040000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ674-444-44-4-4-440000000000400-400000000000000000022−22−22220000000000000000000000000000
χ684-444-44-4-4-440000000000400-4000000000000000000−222222−220000000000000000000000000000
χ694-4-444-4-44004i−4i−4i4i4-44i−4i−4i4i0-44000000000000000000000000000000000000000000000000000
χ704-4-444-4-44004i−4i−4i4i-44−4i4i4i−4i04-4000000000000000000000000000000000000000000000000000
χ714-4-444-4-4400−4i4i4i−4i4-4−4i4i4i−4i0-44000000000000000000000000000000000000000000000000000
χ724-4-444-4-4400−4i4i4i−4i-444i−4i−4i4i04-4000000000000000000000000000000000000000000000000000
χ7388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000

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