Finite Group Databasebeta

← Group #414749

Character table — Group #414749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222222222444444444422444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ911111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-11-11-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-11-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1111-11-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-11-1111-1-1
χ1722222222222-2-2-2-2-2-2-2-22222222-2-2-2-222-2-2-2-200002200000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-222220000-2-200000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2222222-2-2220000-2-200000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-22222-2-222-2-200002200000000000000000000000000000000
χ2122222222-2-2-222-2-222-2-2-22222-2-222-2-2000000000000000000000000000000002-22-200000000
χ2222222222-2-2-222-2-222-2-2-22222-2-222-2-200000000000000000000000000000000-22-2200000000
χ2322222222-2-2-222-2-222-2-2-2-2-2-2-222-2-222000000000000000000000000000000002-2-2200000000
χ2422222222-2-2-222-2-222-2-2-2-2-2-2-222-2-22200000000000000000000000000000000-222-200000000
χ2522222222-2-2-2-2-222-2-222-22222-2-2-2-2220000000000000000000000000000000000002-2-220000
χ2622222222-2-2-2-2-222-2-222-22222-2-2-2-222000000000000000000000000000000000000-222-20000
χ2722222222-2-2-2-2-222-2-222-2-2-2-2-22222-2-200000000000000000000000000000000000022-2-20000
χ2822222222-2-2-2-2-222-2-222-2-2-2-2-22222-2-2000000000000000000000000000000000000-2-2220000
χ292222-2-2-2-222-22-22-22-22-2-200000000002-22-2000000000000000022-2-2000022-2-2000000000000
χ302222-2-2-2-222-22-22-22-22-2-200000000002-22-20000000000000000-2-2220000-2-222000000000000
χ312222-2-2-2-222-22-22-22-22-2-20000000000-22-22000000000000000022-2-20000-2-222000000000000
χ322222-2-2-2-222-22-22-22-22-2-20000000000-22-220000000000000000-2-222000022-2-2000000000000
χ332222-2-2-2-222-2-22-22-22-22-200000000002-2-2200000000000022-2-2000022-2-20000000000000000
χ342222-2-2-2-222-2-22-22-22-22-200000000002-2-22000000000000-2-2220000-2-2220000000000000000
χ352222-2-2-2-222-2-22-22-22-22-20000000000-222-200000000000022-2-20000-2-2220000000000000000
χ362222-2-2-2-222-2-22-22-22-22-20000000000-222-2000000000000-2-222000022-2-20000000000000000
χ372-2-2222-2-22-2-22-22-2-22-222000000000000002i−2i00002i−2i000000002i−2i2i−2i2-22-20000000000000000
χ382-2-2222-2-22-2-22-22-2-22-222000000000000002i−2i00002i−2i00000000−2i2i−2i2i-22-220000000000000000
χ392-2-2222-2-22-2-22-22-2-22-22200000000000000−2i2i0000−2i2i000000002i−2i2i−2i-22-220000000000000000
χ402-2-2222-2-22-2-22-22-2-22-22200000000000000−2i2i0000−2i2i00000000−2i2i−2i2i2-22-20000000000000000
χ412-2-2222-2-22-2-2-22-222-22-22000000000000002i−2i0000−2i2i00002i−2i2i−2i000000002-22-2000000000000
χ422-2-2222-2-22-2-2-22-222-22-22000000000000002i−2i0000−2i2i0000−2i2i−2i2i00000000-22-22000000000000
χ432-2-2222-2-22-2-2-22-222-22-2200000000000000−2i2i00002i−2i00002i−2i2i−2i00000000-22-22000000000000
χ442-2-2222-2-22-2-2-22-222-22-2200000000000000−2i2i00002i−2i0000−2i2i−2i2i000000002-22-2000000000000
χ452-2-22-2-2222-222222-2-2-2-2-222-2-22-22-22-200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ462-2-22-2-2222-222222-2-2-2-2-222-2-22-22-22-20000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ472-2-22-2-2222-222222-2-2-2-2-2-2-222-22-22-2200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ482-2-22-2-2222-222222-2-2-2-2-2-2-222-22-22-220000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ492-2-22-2-2222-22-2-2-2-22222-222-2-22-2-22-220000000000000000000000002-2-222-2-22000000000000
χ502-2-22-2-2222-22-2-2-2-22222-222-2-22-2-22-22000000000000000000000000-222-2-222-2000000000000
χ512-2-22-2-2222-22-2-2-2-22222-2-2-222-222-22-20000000000000000000000002-2-22-222-2000000000000
χ522-2-22-2-2222-22-2-2-2-22222-2-2-222-222-22-2000000000000000000000000-222-22-2-22000000000000
χ532-2-22-2-222-22-222-2-2-2-222222-2-2-222-2-2200000022-2-20022-2-20000000000000000000000000000
χ542-2-22-2-222-22-222-2-2-2-222222-2-2-222-2-22000000-2-22200-2-2220000000000000000000000000000
χ552-2-22-2-222-22-222-2-2-2-2222-2-2222-2-222-200000022-2-200-2-2220000000000000000000000000000
χ562-2-22-2-222-22-222-2-2-2-2222-2-2222-2-222-2000000-2-2220022-2-20000000000000000000000000000
χ572-2-22-2-222-22-2-2-22222-2-2222-2-2-22-222-200000000000000000000000000000000000000002-22-2
χ582-2-22-2-222-22-2-2-22222-2-2222-2-2-22-222-20000000000000000000000000000000000000000-22-22
χ592-2-22-2-222-22-2-2-22222-2-22-2-2222-22-2-2200000000000000000000000000000000000000002-2-22
χ602-2-22-2-222-22-2-2-22222-2-22-2-2222-22-2-220000000000000000000000000000000000000000-222-2
χ614444-4-4-4-4-4-444-4-444-4-444000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44-444-4-444-44000000000000000000000000000000000000000000000000000000
χ6344-4-44-44-40000000000004i−4i4i−4i0000000000002-22-2002i−2i2i−2i0000000000000000000000000000
χ6444-4-44-44-40000000000004i−4i4i−4i000000000000-22-2200−2i2i−2i2i0000000000000000000000000000
χ6544-4-44-44-4000000000000−4i4i−4i4i0000000000002-22-200−2i2i−2i2i0000000000000000000000000000
χ6644-4-44-44-4000000000000−4i4i−4i4i000000000000-22-22002i−2i2i−2i0000000000000000000000000000
χ674-44-4-444-40000000000004i−4i−4i4i0000000000002-2-22002i−2i−2i2i0000000000000000000000000000
χ684-44-4-444-40000000000004i−4i−4i4i000000000000-222-200−2i2i2i−2i0000000000000000000000000000
χ694-44-4-444-4000000000000−4i4i4i−4i0000000000002-2-2200−2i2i2i−2i0000000000000000000000000000
χ704-44-4-444-4000000000000−4i4i4i−4i000000000000-222-2002i−2i−2i2i0000000000000000000000000000
χ714-4-4444-4-4-4444-4-44-444-4-4000000000000000000000000000000000000000000000000000000
χ724-4-4444-4-4-444-444-44-4-44-4000000000000000000000000000000000000000000000000000000
χ7388-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000

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