Finite Group Databasebeta

← Group #241998

Character table — Group #241998

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422224444444444448888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111
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
χ91111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ121111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ131111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ141111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ17222222222222222222-2-222-2-2-2-2-2-2-2-2002200000022-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-222-2-2-2-2-2-2-2-200-2-2000000-2-222220000000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-20022000000-2-222-2-20000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-200-2-200000022-2-2220000000000000000000000000000
χ2122222222-2-22222-2-2-2-222-2-22222-2-2-2-22200-2-222-2-20000000000000000000000000000000000
χ2222222222-2-22222-2-2-2-222-2-22222-2-2-2-2-2-20022-2-2220000000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000002-22-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000-22-22000000
χ2522222222-2-2-2-2-2-2222222-2-222-2-222-2-22200-2-2-2-2220000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-222-2-222-2-2-2-2002222-2-20000000000000000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-2220000000000000000000000000000000000-222-2000000
χ29222-2-2-2-222-22i2i−2i−2i2i2i−2i−2i2-22-22-22i−2i2i−2i2-200000000000000000000000000000000000000002i−2i2-2
χ30222-2-2-2-222-22i2i−2i−2i2i2i−2i−2i2-22-22-22i−2i2i−2i2-20000000000000000000000000000000000000000−2i2i-22
χ31222-2-2-2-222-22i2i−2i−2i2i2i−2i−2i-222-2-22−2i2i−2i2i-22000000000000000000000000000000002i−2i00002-20000
χ32222-2-2-2-222-22i2i−2i−2i2i2i−2i−2i-222-2-22−2i2i−2i2i-2200000000000000000000000000000000−2i2i0000-220000
χ33222-2-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-22-22-2−2i2i−2i2i2-200000000000000000000000000000000000000002i−2i-22
χ34222-2-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-22-22-2−2i2i−2i2i2-20000000000000000000000000000000000000000−2i2i2-2
χ35222-2-2-2-222-2−2i−2i2i2i−2i−2i2i2i-222-2-222i−2i2i−2i-22000000000000000000000000000000002i−2i0000-220000
χ36222-2-2-2-222-2−2i−2i2i2i−2i−2i2i2i-222-2-222i−2i2i−2i-2200000000000000000000000000000000−2i2i00002-20000
χ37222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i2-2-222-22i−2i−2i2i-2200000000000000000000000022-2-22i2i−2i−2i000000000000
χ38222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i2-2-222-22i−2i−2i2i-22000000000000000000000000-2-222−2i−2i2i2i000000000000
χ39222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i-22-22-22−2i2i2i−2i2-200000000000000002i2i−2i−2i22-2-200000000000000000000
χ40222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i-22-22-22−2i2i2i−2i2-20000000000000000−2i−2i2i2i-2-22200000000000000000000
χ41222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i2-2-222-2−2i2i2i−2i-2200000000000000000000000022-2-2−2i−2i2i2i000000000000
χ42222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i2-2-222-2−2i2i2i−2i-22000000000000000000000000-2-2222i2i−2i−2i000000000000
χ43222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22-22-222i−2i−2i2i2-200000000000000002i2i−2i−2i-2-22200000000000000000000
χ44222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22-22-222i−2i−2i2i2-20000000000000000−2i−2i2i2i22-2-200000000000000000000
χ452-2222-2-2-2-2-22-22-22-22-20022000000000000000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ462-2222-2-2-2-2-22-22-22-22-20022000000000000000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ472-2222-2-2-2-2-22-22-22-22-2002200000000000000000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ482-2222-2-2-2-2-22-22-22-22-2002200000000000000000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ492-2222-2-2-2-2-2-22-22-22-220022000000000000000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ502-2222-2-2-2-2-2-22-22-22-220022000000000000000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ512-2222-2-2-2-2-2-22-22-22-22002200000000000000000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ522-2222-2-2-2-2-2-22-22-22-22002200000000000000000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ532-22-2-222-22-22i−2i−2i2i−2i2i2i−2i00-2200000000002-20000002i−2i00002−2−22−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ542-22-2-222-22-22i−2i−2i2i−2i2i2i−2i00-2200000000002-20000002i−2i0000−222−2i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ552-22-2-222-22-22i−2i−2i2i−2i2i2i−2i00-220000000000-22000000−2i2i00002−2−22−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ562-22-2-222-22-22i−2i−2i2i−2i2i2i−2i00-220000000000-22000000−2i2i0000−222−2i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ572-22-2-222-22-2−2i2i2i−2i2i−2i−2i2i00-2200000000002-2000000−2i2i00002−2−22i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ582-22-2-222-22-2−2i2i2i−2i2i−2i−2i2i00-2200000000002-2000000−2i2i0000−222−2−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ592-22-2-222-22-2−2i2i2i−2i2i−2i−2i2i00-220000000000-220000002i−2i00002−2−22i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ602-22-2-222-22-2−2i2i2i−2i2i−2i−2i2i00-220000000000-220000002i−2i0000−222−2−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ614-4444-4-4-4444-44-4-44-4400-4-40000000000000000000000000000000000000000000000000000
χ624-4444-4-4-444-44-444-44-400-4-40000000000000000000000000000000000000000000000000000
χ634-44-4-444-4-444i−4i−4i4i4i−4i−4i4i004-40000000000000000000000000000000000000000000000000000
χ644-44-4-444-4-44−4i4i4i−4i−4i4i4i−4i004-40000000000000000000000000000000000000000000000000000
χ654-4-44-44-4400000000004400-4-400000000004i−4i00000000000000000000000000000000000000
χ664-4-44-44-4400000000004400-4-40000000000−4i4i00000000000000000000000000000000000000
χ674-4-44-44-440000000000-4-400440000000000004-4000000000000000000000000000000000000
χ684-4-44-44-440000000000-4-40044000000000000-44000000000000000000000000000000000000
χ694-4-4-44-44400000000004-400-440000004-4000000000000000000000000000000000000000000
χ704-4-4-44-44400000000004-400-44000000-44000000000000000000000000000000000000000000
χ714-4-4-44-4440000000000-44004-4000000000000004-40000000000000000000000000000000000
χ724-4-4-44-4440000000000-44004-400000000000000-440000000000000000000000000000000000
χ7388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ7488-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000

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