Finite Group Databasebeta

← Group #404306

Character table — Group #404306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12222222222244444444224444444444222444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111-1-11-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-1111-1-111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-111-1-1-1-1111-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111111111111111-1-11111-1-11111-111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-11111-1-11111-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ1111111111111111111111-1-11111-1-11111-1-1-1-1-111-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1211111111111111111111-1-11111-1-11111-1-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ17222222222222-2-2-2-2-2-2-2-2220000-2-200002000000-20022-2-2000022-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2220000-2-200002000000-200-2-2220000-2-22200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-20000220000-200000020022-2-20000-2-22200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-20000220000-2000000200-2-222000022-2-200000000000000000000
χ2122222222-2-2-2-222-2-222-2-2220000220000-2220022-2-2-2000000-2-2000000000000000000000000
χ2222222222-2-2-2-222-2-222-2-2220000220000-2-2-200-2-2-22200000022000000000000000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20000-2-2000022200-2-22-2-200000022000000000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-20000-2-200002-2-20022222000000-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-20022002000000-2-200000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-22222-200-2-20020000002200000000000000000000000000
χ2722222222-2-2-2-2-2-222-2-222-2-2222222-2-2-2-2200-2-200-20000002200000000000000000000000000
χ2822222222-2-2-2-2-2-222-2-222-2-2-2-2-2-22222222002200-2000000-2-200000000000000000000000000
χ29222-2-2-22-22-22-22-2-2-22-222002i2i−2i−2i002i2i−2i−2i0000000000000000000000000000002i−2i0000002-200
χ30222-2-2-22-22-22-22-2-2-22-222002i2i−2i−2i002i2i−2i−2i000000000000000000000000000000−2i2i000000-2200
χ31222-2-2-22-22-22-22-2-2-22-22200−2i−2i2i2i00−2i−2i2i2i0000000000000000000000000000002i−2i000000-2200
χ32222-2-2-22-22-22-22-2-2-22-22200−2i−2i2i2i00−2i−2i2i2i000000000000000000000000000000−2i2i0000002-200
χ33222-2-2-22-2-22-22-22-2-2-2222002i2i−2i−2i00−2i−2i2i2i000000000000000000000000000000002i−2i0000002-2
χ34222-2-2-22-2-22-22-22-2-2-2222002i2i−2i−2i00−2i−2i2i2i00000000000000000000000000000000−2i2i000000-22
χ35222-2-2-22-2-22-22-22-2-2-222200−2i−2i2i2i002i2i−2i−2i000000000000000000000000000000002i−2i000000-22
χ36222-2-2-22-2-22-22-22-2-2-222200−2i−2i2i2i002i2i−2i−2i00000000000000000000000000000000−2i2i0000002-2
χ372-2-222-22-222-2-2-2-22-2222-2002i−2i2i−2i002i−2i2i−2i00000000000000000000002i2i−2i−2i000000002-2000000
χ382-2-222-22-222-2-2-2-22-2222-2002i−2i2i−2i002i−2i2i−2i0000000000000000000000−2i−2i2i2i00000000-22000000
χ392-2-222-22-222-2-2-2-22-2222-200−2i2i−2i2i00−2i2i−2i2i00000000000000000000002i2i−2i−2i00000000-22000000
χ402-2-222-22-222-2-2-2-22-2222-200−2i2i−2i2i00−2i2i−2i2i0000000000000000000000−2i−2i2i2i000000002-2000000
χ412-2-222-22-2-2-222222-2-2-22-2002i−2i2i−2i00−2i2i−2i2i0000000000000000000000000022-2-20000002i−2i0000
χ422-2-222-22-2-2-222222-2-2-22-2002i−2i2i−2i00−2i2i−2i2i00000000000000000000000000-2-222000000−2i2i0000
χ432-2-222-22-2-2-222222-2-2-22-200−2i2i−2i2i002i−2i2i−2i0000000000000000000000000022-2-2000000−2i2i0000
χ442-2-222-22-2-2-222222-2-2-22-200−2i2i−2i2i002i−2i2i−2i00000000000000000000000000-2-2220000002i−2i0000
χ452-2-2-2-22222-2-222-22-2-22-220000000000000002-22-200000002-22-22-22-200000000000000000000
χ462-2-2-2-22222-2-222-22-2-22-220000000000000002-2-2200000002-2-22-22-2200000000000000000000
χ472-2-2-2-22222-2-222-22-2-22-22000000000000000-222-20000000-222-2-22-2200000000000000000000
χ482-2-2-2-22222-2-222-22-2-22-22000000000000000-22-220000000-22-222-22-200000000000000000000
χ492-2-2-2-22222-2-22-22-222-22-2002-2-22002-2-2202-2000002-2000000002-2-2200000000000000000000
χ502-2-2-2-22222-2-22-22-222-22-2002-2-22002-2-220-2200000-2200000000-222-200000000000000000000
χ512-2-2-2-22222-2-22-22-222-22-200-222-200-222-202-2000002-200000000-222-200000000000000000000
χ522-2-2-2-22222-2-22-22-222-22-200-222-200-222-20-2200000-22000000002-2-2200000000000000000000
χ532-2-2-2-2222-222-22-2-22-222-2002-2-2200-222-2000002-20002-22-200-22000000000000000000000000
χ542-2-2-2-2222-222-22-2-22-222-2002-2-2200-222-200000-22000-22-22002-2000000000000000000000000
χ552-2-2-2-2222-222-22-2-22-222-200-222-2002-2-22000002-2000-22-2200-22000000000000000000000000
χ562-2-2-2-2222-222-22-2-22-222-200-222-2002-2-2200000-220002-22-2002-2000000000000000000000000
χ572-2-2-2-2222-222-2-222-22-2-2200000000000002-22-2000-222-2-22-2200000000000000000000000000
χ582-2-2-2-2222-222-2-222-22-2-2200000000000002-2-22000-22-222-22-200000000000000000000000000
χ592-2-2-2-2222-222-2-222-22-2-220000000000000-222-20002-2-222-2-2200000000000000000000000000
χ602-2-2-2-2222-222-2-222-22-2-220000000000000-22-220002-22-2-222-200000000000000000000000000
χ61444-4-4-44-44-44-4-4444-44-4-4000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-44-444-4444-4-4-4000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-40000000000004-4000000000000000000000000000000002-22-22-22-2000000000000
χ6444-44-44-4-40000000000004-400000000000000000000000000000000-22-22-22-22000000000000
χ6544-44-44-4-4000000000000-44000000000000000000000000000000002-22-2-22-22000000000000
χ6644-44-44-4-4000000000000-4400000000000000000000000000000000-22-222-22-2000000000000
χ674-444-4-4-440000000000000000004i−4i000000000000000000000000002i−2i−2i2i2-2-22000000000000
χ684-444-4-4-440000000000000000004i−4i00000000000000000000000000−2i2i2i−2i-222-2000000000000
χ694-444-4-4-44000000000000000000−4i4i000000000000000000000000002i−2i−2i2i-222-2000000000000
χ704-444-4-4-44000000000000000000−4i4i00000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ714-4-444-44-444-4-444-44-4-4-44000000000000000000000000000000000000000000000000000000
χ724-4-444-44-4-4-444-4-4-4444-44000000000000000000000000000000000000000000000000000000
χ7388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000

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