Finite Group Databasebeta

← Group #396451

Character table — Group #396451

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422222244444444448888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ9111111111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ10111111111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ11111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ12111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ13111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1
χ14111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111
χ15111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ16111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ17222222222222-2-2-22222-2-2-2-2-2-2-2-2-222000000000000000000000000000000000000002i−2i2i−2i00
χ18222222222222-2-2-22222-2-2-2-2-2-2-2-2-22200000000000000000000000000000000000000−2i2i−2i2i00
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000002i−2i−2i2i00
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000−2i2i2i−2i00
χ2122222222-2-2-2-222-22222-2-222-222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ2222222222-2-2-2-222-22222-2-222-222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2222200000000000000000000000022-2-2-2-222000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-2-222-2-2-22222000000000000000000000000-2-22222-2-2000000000000
χ2522222222-2-2-2-2-2-22222222-2-22-2-222-2-2000022-2-2-2-20000220000000000000000000000000000
χ2622222222-2-2-2-2-2-22222222-2-22-2-222-2-20000-2-222220000-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-22-2-2-2-222-2-2222-2-222000022-2-2220000-2-20000000000000000000000000000
χ2822222222-2-2-2-2-2-22-2-2-2-222-2-2222-2-2220000-2-222-2-20000220000000000000000000000000000
χ29222-22-2-2-222-2-222200002-2-2-2-200000022-2-22-22-20000000022-2-2000000000000000000000000
χ30222-22-2-2-222-2-222200002-2-2-2-200000022-2-2-22-2200000000-2-222000000000000000000000000
χ31222-22-2-2-222-2-222200002-2-2-2-2000000-2-2222-22-200000000-2-222000000000000000000000000
χ32222-22-2-2-222-2-222200002-2-2-2-2000000-2-222-22-220000000022-2-2000000000000000000000000
χ33222-22-2-2-2-2-222-2-2200002-222-200000000002-2-22002i2i−2i−2i0000002i2i−2i−2i00000000000000000000
χ34222-22-2-2-2-2-222-2-2200002-222-200000000002-2-2200−2i−2i2i2i000000−2i−2i2i2i00000000000000000000
χ35222-22-2-2-2-2-222-2-2200002-222-20000000000-222-2002i2i−2i−2i000000−2i−2i2i2i00000000000000000000
χ36222-22-2-2-2-2-222-2-2200002-222-20000000000-222-200−2i−2i2i2i0000002i2i−2i−2i00000000000000000000
χ372-2-2222-2-22-22-22-222i2i−2i−2i-2-22-222i−2i2i−2i2i−2i000000000000000000000000000000002-22i−2i00000000
χ382-2-2222-2-22-22-22-222i2i−2i−2i-2-22-222i−2i2i−2i2i−2i00000000000000000000000000000000-22−2i2i00000000
χ392-2-2222-2-22-22-22-22−2i−2i2i2i-2-22-22−2i2i−2i2i−2i2i000000000000000000000000000000002-2−2i2i00000000
χ402-2-2222-2-22-22-22-22−2i−2i2i2i-2-22-22−2i2i−2i2i−2i2i00000000000000000000000000000000-222i−2i00000000
χ412-2-2222-2-22-22-2-22-22i2i−2i−2i22-22-2−2i2i−2i2i2i−2i00000000000000002-22-22i−2i2i−2i00000000000000000000
χ422-2-2222-2-22-22-2-22-22i2i−2i−2i22-22-2−2i2i−2i2i2i−2i0000000000000000-22-22−2i2i−2i2i00000000000000000000
χ432-2-2222-2-22-22-2-22-2−2i−2i2i2i22-22-22i−2i2i−2i−2i2i00000000000000002-22-2−2i2i−2i2i00000000000000000000
χ442-2-2222-2-22-22-2-22-2−2i−2i2i2i22-22-22i−2i2i−2i−2i2i0000000000000000-22-222i−2i2i−2i00000000000000000000
χ452-2-2222-2-2-22-222-2-22i2i−2i−2i222-2-22i−2i−2i2i−2i2i2-22-20000002i−2i2i−2i000000000000000000000000000000
χ462-2-2222-2-2-22-222-2-22i2i−2i−2i222-2-22i−2i−2i2i−2i2i-22-22000000−2i2i−2i2i000000000000000000000000000000
χ472-2-2222-2-2-22-222-2-2−2i−2i2i2i222-2-2−2i2i2i−2i2i−2i2-22-2000000−2i2i−2i2i000000000000000000000000000000
χ482-2-2222-2-2-22-222-2-2−2i−2i2i2i222-2-2−2i2i2i−2i2i−2i-22-220000002i−2i2i−2i000000000000000000000000000000
χ492-2-2222-2-2-22-22-2222i2i−2i−2i-2-2-222−2i2i2i−2i−2i2i0000000000000000000000000000000000002i−2i00002-2
χ502-2-2222-2-2-22-22-2222i2i−2i−2i-2-2-222−2i2i2i−2i−2i2i000000000000000000000000000000000000−2i2i0000-22
χ512-2-2222-2-2-22-22-222−2i−2i2i2i-2-2-2222i−2i−2i2i2i−2i0000000000000000000000000000000000002i−2i0000-22
χ522-2-2222-2-2-22-22-222−2i−2i2i2i-2-2-2222i−2i−2i2i2i−2i000000000000000000000000000000000000−2i2i00002-2
χ532-2-2-22-2222-2-22-22-200002-22-22000000000000002-22-2-222-22-2-22000000000000000000000000
χ542-2-2-22-2222-2-22-22-200002-22-22000000000000002-2-222-22-2-222-2000000000000000000000000
χ552-2-2-22-2222-2-22-22-200002-22-2200000000000000-222-2-22-22-222-2000000000000000000000000
χ562-2-2-22-2222-2-22-22-200002-22-2200000000000000-22-222-2-222-2-22000000000000000000000000
χ572-2-2-22-222-222-22-2-200002-2-2220000002-2-2200002-20000-220000-222-200000000000000000000
χ582-2-2-22-222-222-22-2-200002-2-2220000002-2-220000-2200002-200002-2-2200000000000000000000
χ592-2-2-22-222-222-22-2-200002-2-222000000-222-200002-20000-2200002-2-2200000000000000000000
χ602-2-2-22-222-222-22-2-200002-2-222000000-222-20000-2200002-20000-222-200000000000000000000
χ61444-44-4-4-444-4-4-4-4-40000-4444400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-44444-40000-44-4-4400000000000000000000000000000000000000000000000000
χ6344-4-4-444-400000004i−4i4i−4i000000000000000000000000000000000000022−22002i2−2i2000000000000
χ6444-4-4-444-400000004i−4i4i−4i0000000000000000000000000000000000000−222200−2i22i2000000000000
χ6544-4-4-444-40000000−4i4i−4i4i000000000000000000000000000000000000022−2200−2i22i2000000000000
χ6644-4-4-444-40000000−4i4i−4i4i0000000000000000000000000000000000000−2222002i2−2i2000000000000
χ674-44-4-44-4400000004-4-440000000000000000000000000000000000022−220022−2200000000000000
χ684-44-4-44-4400000004-4-4400000000000000000000000000000000000−222200−222200000000000000
χ694-44-4-44-440000000-444-40000000000000000000000000000000000022−2200−222200000000000000
χ704-44-4-44-440000000-444-400000000000000000000000000000000000−22220022−2200000000000000
χ714-4-4-44-4444-4-444-440000-44-44-400000000000000000000000000000000000000000000000000
χ724-4-4-44-444-444-4-4440000-444-4-400000000000000000000000000000000000000000000000000
χ7388-88-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000

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