Finite Group Databasebeta

← Group #394723

Character table — Group #394723

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222222222444444444444444444444444444444442244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-11-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ2122222222-2-2-222-2-222-2-2-222-2-222-2-200000000000000000000000002002-20-200000000
χ2222222222-2-2-222-2-222-2-2-222-2-222-2-20000000000000000000000000-200-220200000000
χ2322222222-2-2-222-2-222-2-2-2-2-222-2-2220000000000000000000000000200-220-200000000
χ2422222222-2-2-222-2-222-2-2-2-2-222-2-2220000000000000000000000000-2002-20200000000
χ2522222222-2-2-2-2-222-2-222-222-2-2-2-222000000000000000000000000202-200-2000000000
χ2622222222-2-2-2-2-222-2-222-222-2-2-2-222000000000000000000000000-20-22002000000000
χ2722222222-2-2-2-2-222-2-222-2-2-22222-2-200000000000000000000000020-2200-2000000000
χ2822222222-2-2-2-2-222-2-222-2-2-22222-2-2000000000000000000000000-202-2002000000000
χ29222-2-2-22-22-2-22-22-22-22-2200000000002i−2i002i−2i00002i2i−2i−2i22-2-200000000000000000000
χ30222-2-2-22-22-2-22-22-22-22-2200000000002i−2i002i−2i0000−2i−2i2i2i-2-22200000000000000000000
χ31222-2-2-22-22-2-22-22-22-22-220000000000−2i2i00−2i2i00002i2i−2i−2i-2-22200000000000000000000
χ32222-2-2-22-22-2-22-22-22-22-220000000000−2i2i00−2i2i0000−2i−2i2i2i22-2-200000000000000000000
χ33222-2-2-22-22-2-2-22-22-22-22200000000002i−2i00−2i2i2i2i−2i−2i0000000022-2-20000000000000000
χ34222-2-2-22-22-2-2-22-22-22-22200000000002i−2i00−2i2i−2i−2i2i2i00000000-2-2220000000000000000
χ35222-2-2-22-22-2-2-22-22-22-2220000000000−2i2i002i−2i2i2i−2i−2i00000000-2-2220000000000000000
χ36222-2-2-22-22-2-2-22-22-22-2220000000000−2i2i002i−2i−2i−2i2i2i0000000022-2-20000000000000000
χ372-2-222-22-222-222-2-2-2-222-22-22-22-22-20000000000000000000000000000000000002i−2i2i−2i
χ382-2-222-22-222-222-2-2-2-222-22-22-22-22-2000000000000000000000000000000000000−2i2i−2i2i
χ392-2-222-22-222-222-2-2-2-222-2-22-22-22-220000000000000000000000000000000000002i−2i−2i2i
χ402-2-222-22-222-222-2-2-2-222-2-22-22-22-22000000000000000000000000000000000000−2i2i2i−2i
χ412-2-222-22-222-2-2-22222-2-2-22-22-2-22-22000000000000000000000000000000002i−2i2i−2i0000
χ422-2-222-22-222-2-2-22222-2-2-22-22-2-22-2200000000000000000000000000000000−2i2i−2i2i0000
χ432-2-222-22-222-2-2-22222-2-2-2-22-222-22-2000000000000000000000000000000002i−2i−2i2i0000
χ442-2-222-22-222-2-2-22222-2-2-2-22-222-22-200000000000000000000000000000000−2i2i2i−2i0000
χ452-2-222-22-2-2-222222-2-2-2-222-2-222-2-22000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ462-2-222-22-2-2-222222-2-2-2-222-2-222-2-2200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ472-2-222-22-2-2-222222-2-2-2-22-222-2-222-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ482-2-222-22-2-2-222222-2-2-2-22-222-2-222-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ492-2-222-22-2-2-22-2-2-2-2222222-2-22-222-200000000000000002-22-22-22-20000000000000000
χ502-2-222-22-2-2-22-2-2-2-2222222-2-22-222-20000000000000000-22-22-22-220000000000000000
χ512-2-222-22-2-2-22-2-2-2-222222-222-22-2-2200000000000000002-22-2-22-220000000000000000
χ522-2-222-22-2-2-22-2-2-2-222222-222-22-2-220000000000000000-22-222-22-20000000000000000
χ532-2-2-2-2222-22-22-22-2-22-222000000002-2002-20000002-2-2200002-2-220000000000000000
χ542-2-2-2-2222-22-22-22-2-22-222000000002-2002-2000000-222-20000-222-20000000000000000
χ552-2-2-2-2222-22-22-22-2-22-22200000000-2200-220000002-2-220000-222-20000000000000000
χ562-2-2-2-2222-22-22-22-2-22-22200000000-2200-22000000-222-200002-2-220000000000000000
χ572-2-2-2-2222-22-2-22-222-22-22000000002-200-22002-2-2200002-2-2200000000000000000000
χ582-2-2-2-2222-22-2-22-222-22-22000000002-200-2200-222-20000-222-200000000000000000000
χ592-2-2-2-2222-22-2-22-222-22-2200000000-22002-2002-2-220000-222-200000000000000000000
χ602-2-2-2-2222-22-2-22-222-22-2200000000-22002-200-222-200002-2-2200000000000000000000
χ61444-4-4-44-4-4444-4-444-4-44-4000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-444-444-4-444-4-4000000000000000000000000000000000000000000000000
χ634-4-4-4-44444-444-4-44-444-4-4000000000000000000000000000000000000000000000000
χ644-4-4-4-44444-44-444-44-4-44-4000000000000000000000000000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6688-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ678-888-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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