Finite Group Databasebeta

← Group #406207

Character table — Group #406207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222224444444422444444444444888888888888888888888888244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-11111
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
χ9111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-11-1-111
χ11111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1111-11-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1111-111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1111-1-1-111
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1111-1-1
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-11-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2122222222-2-2-2-222222-222-2-22-2-2-222-2-200000000000000000000000000000000200-200-220000
χ2222222222-2-2-2-222222-222-2-22-2-2-222-2-200000000000000000000000000000000-2002002-20000
χ2322222222-2-2-2-22222-22-2-222-22-2-2-2-2220000000022-2-222-2-20000000000000000000000000000
χ2422222222-2-2-2-22222-22-2-222-22-2-2-2-22200000000-2-222-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-222-2-22-222-2-22200000000000000000000000000000000200200-2-20000
χ2622222222-2-2-2-2-2-2-2-22-222-2-22-222-2-22200000000000000000000000000000000-200-200220000
χ2722222222-2-2-2-2-2-2-2-2-22-2-222-222222-2-20000000022-2-2-2-2220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-22-2-222-222222-2-200000000-2-22222-2-20000000000000000000000000000
χ29222-2-2-22-222-2-200002-22-22-2-2200000000002i2i−2i−2i0000000000002-22-22i2i−2i−2i0000000000000000
χ30222-2-2-22-222-2-200002-22-22-2-2200000000002i2i−2i−2i000000000000-22-22−2i−2i2i2i0000000000000000
χ31222-2-2-22-222-2-200002-22-22-2-220000000000−2i−2i2i2i0000000000002-22-2−2i−2i2i2i0000000000000000
χ32222-2-2-22-222-2-200002-22-22-2-220000000000−2i−2i2i2i000000000000-22-222i2i−2i−2i0000000000000000
χ33222-2-2-22-222-2-20000-22-22-222-20000002i2i−2i−2i00000000000000002i−2i−2i2i000022-2-2000000000000
χ34222-2-2-22-222-2-20000-22-22-222-20000002i2i−2i−2i0000000000000000−2i2i2i−2i0000-2-222000000000000
χ35222-2-2-22-222-2-20000-22-22-222-2000000−2i−2i2i2i00000000000000002i−2i−2i2i0000-2-222000000000000
χ36222-2-2-22-222-2-20000-22-22-222-2000000−2i−2i2i2i0000000000000000−2i2i2i−2i000022-2-2000000000000
χ372-2-222-22-22-22-200002-2-22-22-220000002i−2i2i−2i0000000000002-22-200002i−2i2i−2i0000000000000000
χ382-2-222-22-22-22-200002-2-22-22-220000002i−2i2i−2i000000000000-22-220000−2i2i−2i2i0000000000000000
χ392-2-222-22-22-22-200002-2-22-22-22000000−2i2i−2i2i0000000000002-22-20000−2i2i−2i2i0000000000000000
χ402-2-222-22-22-22-200002-2-22-22-22000000−2i2i−2i2i000000000000-22-2200002i−2i2i−2i0000000000000000
χ412-2-222-22-22-22-20000-222-22-22-200000000002i−2i2i−2i000000002i−2i−2i2i000000002-22-2000000000000
χ422-2-222-22-22-22-20000-222-22-22-200000000002i−2i2i−2i00000000−2i2i2i−2i00000000-22-22000000000000
χ432-2-222-22-22-22-20000-222-22-22-20000000000−2i2i−2i2i000000002i−2i−2i2i00000000-22-22000000000000
χ442-2-222-22-22-22-20000-222-22-22-20000000000−2i2i−2i2i00000000−2i2i2i−2i000000002-22-2000000000000
χ452-2-2-2-22222-2-2222-2-222-2-2-2-2222-22-22-20000000000000000000000002-2-222-2-22000000000000
χ462-2-2-2-22222-2-2222-2-222-2-2-2-2222-22-22-2000000000000000000000000-222-2-222-2000000000000
χ472-2-2-2-22222-2-2222-2-2-2-22222-2-22-2-22-222-2-222-2-22000000000000000000000000000000000000
χ482-2-2-2-22222-2-2222-2-2-2-22222-2-22-2-22-22-222-2-222-2000000000000000000000000000000000000
χ492-2-2-2-22222-2-22-2-22222-2-2-2-222-22-22-220000000000000000000000002-2-22-222-2000000000000
χ502-2-2-2-22222-2-22-2-22222-2-2-2-222-22-22-22000000000000000000000000-222-22-2-22000000000000
χ512-2-2-2-22222-2-22-2-222-2-22222-2-2-222-22-22-2-22-222-2000000000000000000000000000000000000
χ522-2-2-2-22222-2-22-2-222-2-22222-2-2-222-22-2-222-22-2-22000000000000000000000000000000000000
χ532-2-2-2-2222-222-222-2-22-2-2-2222-2-222-2-220000000000000000000000000000000002-202-2000000
χ542-2-2-2-2222-222-222-2-22-2-2-2222-2-222-2-22000000000000000000000000000000000-220-22000000
χ552-2-2-2-2222-222-222-2-2-2222-2-2-22-22-222-200000000000000000000000000000000000000002-22-2
χ562-2-2-2-2222-222-222-2-2-2222-2-2-22-22-222-20000000000000000000000000000000000000000-22-22
χ572-2-2-2-2222-222-2-2-2222-2-2-2222-22-2-222-20000000000000000000000000000000002-20-22000000
χ582-2-2-2-2222-222-2-2-2222-2-2-2222-22-2-222-2000000000000000000000000000000000-2202-2000000
χ592-2-2-2-2222-222-2-2-222-2222-2-2-222-22-2-2200000000000000000000000000000000000000002-2-22
χ602-2-2-2-2222-222-2-2-222-2222-2-2-222-22-2-220000000000000000000000000000000000000000-222-2
χ61444-4-4-44-4-4-4440000444-4-44-4-400000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-4-4440000-4-4-444-44400000000000000000000000000000000000000000000000000
χ6344-44-4-4-4400004-44-40000000000000000000000002i2−2i2002i2−2i20000000000000000000000000000
χ6444-44-4-4-4400004-44-4000000000000000000000000−2i22i200−2i22i20000000000000000000000000000
χ6544-44-4-4-440000-44-440000000000000000000000002i2−2i200−2i22i20000000000000000000000000000
χ6644-44-4-4-440000-44-44000000000000000000000000−2i22i2002i2−2i20000000000000000000000000000
χ674-44-44-4-4400004-4-4400000000000000000000002i2−2i2002i2−2i2000000000000000000000000000000
χ684-44-44-4-4400004-4-440000000000000000000000−2i22i200−2i22i2000000000000000000000000000000
χ694-44-44-4-440000-444-400000000000000000000002i2−2i200−2i22i2000000000000000000000000000000
χ704-44-44-4-440000-444-40000000000000000000000−2i22i2002i2−2i2000000000000000000000000000000
χ714-4-444-44-4-44-44000044-444-4-4-400000000000000000000000000000000000000000000000000
χ724-4-444-44-4-44-440000-4-44-4-444400000000000000000000000000000000000000000000000000
χ7388-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000

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