Finite Group Databasebeta

← Group #399151

Character table — Group #399151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size112222222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222244444444222244448888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ911111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1
χ1211111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111
χ1311111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111
χ1511111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ1611111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ1722222-2-2-2-2222-2-2-2-2222-2-222-2-2000000000000000000000000002i−2i0000002i−2i0000
χ1822222-2-2-2-2222-2-2-2-2222-2-222-2-200000000000000000000000000−2i2i000000−2i2i0000
χ1922222-2-2-2-2222-2-2-2-22-2-222-2-222000000000000000000000000002i−2i000000−2i2i0000
χ2022222-2-2-2-2222-2-2-2-22-2-222-2-22200000000000000000000000000−2i2i0000002i−2i0000
χ2122222-2-2-2-2-2-2-22222-200000000000022-2-22i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ2222222-2-2-2-2-2-2-22222-200000000000022-2-2−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ2322222-2-2-2-2-2-2-22222-2000000000000-2-2222i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ2422222-2-2-2-2-2-2-22222-2000000000000-2-222−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ25222-2-222-2-22-222-2-22-222-2-2-2-22200000000000000002i2i−2i−2i2i−2i2i−2i0000000000000000
χ26222-2-222-2-22-222-2-22-222-2-2-2-2220000000000000000−2i−2i2i2i−2i2i−2i2i0000000000000000
χ27222-2-222-2-22-222-2-22-2-2-22222-2-200000000000000002i2i−2i−2i−2i2i−2i2i0000000000000000
χ28222-2-222-2-22-222-2-22-2-2-22222-2-20000000000000000−2i−2i2i2i2i−2i2i−2i0000000000000000
χ29222-2-2-2-2222-22-222-2-22222-2-2-2-200000000000000000000000000002i−2i0000002i−2i00
χ30222-2-2-2-2222-22-222-2-22222-2-2-2-20000000000000000000000000000−2i2i000000−2i2i00
χ31222-2-2-2-2222-22-222-2-2-2-2-2-2222200000000000000000000000000002i−2i000000−2i2i00
χ32222-2-2-2-2222-22-222-2-2-2-2-2-222220000000000000000000000000000−2i2i0000002i−2i00
χ33222-2-2-2-222-22-22-2-2220000000022-2-20000000022-2-200002-2-220000000000000000
χ34222-2-2-2-222-22-22-2-2220000000022-2-200000000-2-2220000-222-20000000000000000
χ35222-2-2-2-222-22-22-2-22200000000-2-2220000000022-2-20000-222-20000000000000000
χ36222-2-2-2-222-22-22-2-22200000000-2-22200000000-2-22200002-2-220000000000000000
χ3722-22-22-22-2-222-22-22-22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ3822-22-22-22-2-222-22-22-22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ3922-22-22-22-2-222-22-22-2-22-22-22-22000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4022-22-22-22-2-222-22-22-2-22-22-22-2200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4122-22-2-22-222-2-2-22-222000000002-22-200002-2-2200002-22-200000000000000000000
χ4222-22-2-22-222-2-2-22-222000000002-22-20000-222-20000-22-2200000000000000000000
χ4322-22-2-22-222-2-2-22-22200000000-22-2200002-2-220000-22-2200000000000000000000
χ4422-22-2-22-222-2-2-22-22200000000-22-220000-222-200002-22-200000000000000000000
χ4522-22-2-22-22-2222-22-2-22-2-222-2-220000000000000000000000000000002i−2i0000002i−2i
χ4622-22-2-22-22-2222-22-2-22-2-222-2-22000000000000000000000000000000−2i2i000000−2i2i
χ4722-22-2-22-22-2222-22-2-2-222-2-222-20000000000000000000000000000002i−2i000000−2i2i
χ4822-22-2-22-22-2222-22-2-2-222-2-222-2000000000000000000000000000000−2i2i0000002i−2i
χ4922-2-222-2-22-2-22-2-22222-2-22-222-22-2-222-22-200000000000000000000000000000000
χ5022-2-222-2-22-2-22-2-22222-2-22-222-2-222-2-22-2200000000000000000000000000000000
χ5122-2-222-2-22-2-22-2-2222-222-22-2-222-2-22-22-2200000000000000000000000000000000
χ5222-2-222-2-22-2-22-2-2222-222-22-2-22-222-22-22-200000000000000000000000000000000
χ5322-2-22-222-222-2-2-222-20000000000002-2-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ5422-2-22-222-222-2-2-222-20000000000002-2-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ5522-2-22-222-222-2-2-222-2000000000000-222-200002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ5622-2-22-222-222-2-2-222-2000000000000-222-20000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ5722-2-22-222-2-2-2222-2-222-22-2-22-220000000000000000000000002-20000002-2000000
χ5822-2-22-222-2-2-2222-2-222-22-2-22-22000000000000000000000000-22000000-22000000
χ5922-2-22-222-2-2-2222-2-22-22-222-22-20000000000000000000000002-2000000-22000000
χ6022-2-22-222-2-2-2222-2-22-22-222-22-2000000000000000000000000-220000002-2000000
χ61444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ62444-4-444-4-4-44-4-444-44000000000000000000000000000000000000000000000000
χ6344-44-44-44-44-4-44-44-44000000000000000000000000000000000000000000000000
χ6444-4-444-4-4444-444-4-4-4000000000000000000000000000000000000000000000000
χ6516-16000000000000000000000000000000000000000000000000000000000000000

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