Finite Group Databasebeta

← Group #252589

Character table — Group #252589

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888822222244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ7111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111111-1-1
χ1011111111-1-1-1-111111111-1-1-1-1111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1111-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1111-1-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-111-11-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-11-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11-111-1-111
χ17222222222222222-2-2-2-2222-2-22222-2-2-2-2-2-2-2002200000000000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2222200-2-200000000000000000000000000000000
χ19222222222222-2-2-22222-2-2-2220000-2-2-200002200220000000000000000000000-2-2000000
χ20222222222222-2-2-22222-2-2-2220000-2-2-20000-2-200-2-2000000000000000000000022000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000222000000000000000000000000002-20000002-20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022200000000000000000000000000-22000000-220000
χ2322222222-2-2-2-2222-2-2-2-22-2-2222222-2-22-2-22200-2-200000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-222-2-2-2-2-2-2222-2-2002200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-20000-2-2200002200-2-200000000000000000000002-2000000
χ2622222222-2-2-2-2-2-2-22222-222-2-20000-2-220000-2-200220000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-2000000000000000000000000002-2000000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-200000000000000000000000000-220000002-20000
χ2922-222-2-2-2000022-22-22-2-200002i2i−2i−2i2-202i−2i0000000000002i2i−2i−2i0000000000002-200000000
χ3022-222-2-2-2000022-22-22-2-200002i2i−2i−2i2-202i−2i000000000000−2i−2i2i2i000000000000-2200000000
χ3122-222-2-2-2000022-22-22-2-20000−2i−2i2i2i2-20−2i2i0000000000002i2i−2i−2i000000000000-2200000000
χ3222-222-2-2-2000022-22-22-2-20000−2i−2i2i2i2-20−2i2i000000000000−2i−2i2i2i0000000000002-200000000
χ3322-222-2-2-2000022-2-22-22-200002i2i−2i−2i-220−2i2i000000002i2i−2i−2i000000000000002-20000000000
χ3422-222-2-2-2000022-2-22-22-200002i2i−2i−2i-220−2i2i00000000−2i−2i2i2i00000000000000-220000000000
χ3522-222-2-2-2000022-2-22-22-20000−2i−2i2i2i-2202i−2i000000002i2i−2i−2i00000000000000-220000000000
χ3622-222-2-2-2000022-2-22-22-20000−2i−2i2i2i-2202i−2i00000000−2i−2i2i2i000000000000002-20000000000
χ3722-2-2-222-222-2-22-220000-22-2002i−2i2i−2i0000000002i−2i000000000022−2−222−2−20000000000i2−i2i2−i2
χ3822-2-2-222-222-2-22-220000-22-2002i−2i2i−2i0000000002i−2i0000000000−2−222−2−2220000000000−i2i2−i2i2
χ3922-2-2-222-222-2-22-220000-22-200−2i2i−2i2i000000000−2i2i000000000022−2−222−2−20000000000−i2i2−i2i2
χ4022-2-2-222-222-2-22-220000-22-200−2i2i−2i2i000000000−2i2i0000000000−2−222−2−2220000000000i2−i2i2−i2
χ4122-2-2-222-2-2-2222-220000-2-22002i−2i2i−2i000000000−2i2i000000000022−2−2−2−2220000000000i2−i2−i2i2
χ4222-2-2-222-2-2-2222-220000-2-22002i−2i2i−2i000000000−2i2i0000000000−2−22222−2−20000000000−i2i2i2−i2
χ4322-2-2-222-2-2-2222-220000-2-2200−2i2i−2i2i0000000002i−2i000000000022−2−2−2−2220000000000−i2i2i2−i2
χ4422-2-2-222-2-2-2222-220000-2-2200−2i2i−2i2i0000000002i−2i0000000000−2−22222−2−20000000000i2−i2−i2i2
χ452-222-22-2-22-22-200022-2-20002-2000000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000
χ462-222-22-2-22-22-200022-2-20002-2000000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000
χ472-222-22-2-22-22-200022-2-20002-200000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000
χ482-222-22-2-22-22-200022-2-20002-200000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000
χ492-222-22-2-2-22-2200022-2-2000-22000000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000000000
χ502-222-22-2-2-22-2200022-2-2000-22000000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000000000
χ512-222-22-2-2-22-2200022-2-2000-2200000000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−200000000000000
χ522-222-22-2-2-22-2200022-2-2000-2200000000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000000000
χ53444-4-4-4-4400004-4-40000400004-4-440000000000000000000000000000000000000000000
χ54444-4-4-4-4400004-4-4000040000-444-40000000000000000000000000000000000000000000
χ55444-4-4-4-440000-4440000-400000000000004i−4i000000000000000000000000000000000000
χ56444-4-4-4-440000-4440000-40000000000000−4i4i000000000000000000000000000000000000
χ5744-444-4-4-40000-4-444-44-4400000000-4400000000000000000000000000000000000000000
χ5844-444-4-4-40000-4-44-44-444000000004-400000000000000000000000000000000000000000
χ5944-4-4-444-444-4-4-44-400004-440000000000000000000000000000000000000000000000000
χ6044-4-4-444-4-4-444-44-4000044-40000000000000000000000000000000000000000000000000
χ614-444-44-4-44-44-4000-4-444000-4400000000000000000000000000000000000000000000000
χ624-444-44-4-4-44-44000-4-4440004-400000000000000000000000000000000000000000000000
χ634-4-44-4-44400000004-4-440000000000000000000000000022−22−22220000000000000000000000
χ644-4-44-4-44400000004-4-4400000000000000000000000000−222222−220000000000000000000000
χ654-4-44-4-4440000000-444-4000000000000000000000022−22−222200000000000000000000000000
χ664-4-44-4-4440000000-444-40000000000000000000000−222222−2200000000000000000000000000
χ674-4-4-444-444-4-4400000000000000000000000000000000000002-2-222-2-2200000000000000
χ684-4-4-444-444-4-440000000000000000000000000000000000000-222-2-222-200000000000000
χ694-4-4-444-44-444-400000000000000000000000000000000000002-2-22-222-200000000000000
χ704-4-4-444-44-444-40000000000000000000000000000000000000-222-22-2-2200000000000000
χ718-88-88-88-8000000000000000000000000000000000000000000000000000000000000000

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