Finite Group Databasebeta

← Group #258376

Character table — Group #258376

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888844444444448888
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
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ711111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111-1-11111-1-11-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111-1-11111-1-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-1-1-111
χ1111111111-1-1-1-1111111111-1-11111-1-11-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111-1-11111-1-11-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-111-1-11111-1-1
χ1311111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-111-1-111
χ1411111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-11111-1-1
χ1511111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-11-1-11111-1-111-1-1
χ1611111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-1-111
χ17222222222222222-2-2-2-22-2-2-2000022-2-200000022220000000000000000-2-2000000000000
χ18222222222222222-2-2-2-22-2-2-2000022-2-2000000-2-2-2-2000000000000000022000000000000
χ19222222222222-2-2-22222-2-2222222-2-2-2-2-2-222-2-20000000000000000000000000000000000
χ20222222222222-2-2-22222-2-222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-22-2-20000-2-222000000000000000000000000000000002-22-20000
χ22222222222222-2-2-2-2-2-2-2-22-2-20000-2-22200000000000000000000000000000000-22-220000
χ2322222222-2-2-2-2222-2-2-2-22-2220000-2-2-2200000022-2-20000000000000000-22000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2220000-2-2-22000000-2-22200000000000000002-2000000000000
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2222222-22-2-2-2-2220000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-222222-2-20000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22220000222-2000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22220000222-200000000000000000000000000000000-222-20000
χ2922-22-2-2-2222-2-22-2-20000200000002-2000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000
χ3022-22-2-2-2222-2-22-2-20000200000002-2000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000
χ3122-22-2-2-2222-2-22-2-20000200000002-200000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000
χ3222-22-2-2-2222-2-22-2-20000200000002-200000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000
χ3322-22-2-2-22-2-2222-2-2000020000000-22000000002i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000
χ3422-22-2-2-22-2-2222-2-2000020000000-22000000002i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000
χ3522-22-2-2-22-2-2222-2-2000020000000-2200000000−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000
χ3622-22-2-2-22-2-2222-2-2000020000000-2200000000−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-2-222-2-22-22-2000-2-222002-222-2-20000002-200000000000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i2
χ3822-2-222-2-22-22-2000-2-222002-222-2-20000002-200000000000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i2
χ3922-2-222-2-22-22-2000-2-222002-2-2-222000000-2200000000000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i2
χ4022-2-222-2-22-22-2000-2-222002-2-2-222000000-2200000000000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i2
χ4122-2-222-2-2-22-22000-2-22200-2222-2-2000000-2200000000000000i2−i2i2−i2−i2i2−i2i20000000000i2−i2−i2i2
χ4222-2-222-2-2-22-22000-2-22200-2222-2-2000000-2200000000000000−i2i2−i2i2i2−i2i2−i20000000000−i2i2i2−i2
χ4322-2-222-2-2-22-22000-2-22200-22-2-2220000002-200000000000000i2−i2i2−i2−i2i2−i2i20000000000−i2i2i2−i2
χ4422-2-222-2-2-22-22000-2-22200-22-2-2220000002-200000000000000−i2i2−i2i2i2−i2i2−i20000000000i2−i2−i2i2
χ452-2-222-22-2000022-22-22-2-2-2002i−2i2i−2i00202i−2i0000000000002-22-20000000000002i−2i00000000
χ462-2-222-22-2000022-22-22-2-2-2002i−2i2i−2i00202i−2i000000000000-22-22000000000000−2i2i00000000
χ472-2-222-22-2000022-22-22-2-2-200−2i2i−2i2i0020−2i2i0000000000002-22-2000000000000−2i2i00000000
χ482-2-222-22-2000022-22-22-2-2-200−2i2i−2i2i0020−2i2i000000000000-22-220000000000002i−2i00000000
χ492-2-222-22-20000-2-222-22-222002i−2i2i−2i00-20−2i2i000000002i−2i2i−2i000000000000002-20000000000
χ502-2-222-22-20000-2-222-22-222002i−2i2i−2i00-20−2i2i00000000−2i2i−2i2i00000000000000-220000000000
χ512-2-222-22-20000-2-222-22-22200−2i2i−2i2i00-202i−2i000000002i−2i2i−2i00000000000000-220000000000
χ522-2-222-22-20000-2-222-22-22200−2i2i−2i2i00-202i−2i00000000−2i2i−2i2i000000000000002-20000000000
χ53444-4-4-44-44-4-4400000000000000000000000000000000000002-2-222-2-2200000000000000
χ54444-4-4-44-44-4-440000000000000000000000000000000000000-222-2-222-200000000000000
χ55444-4-4-44-4-444-400000000000000000000000000000000000002-2-22-222-200000000000000
χ56444-4-4-44-4-444-40000000000000000000000000000000000000-222-22-2-2200000000000000
χ5744-44-4-4-4444-4-4-4440000-40000000-44000000000000000000000000000000000000000000
χ5844-44-4-4-44-4-444-4440000-400000004-4000000000000000000000000000000000000000000
χ5944-4-444-4-44-44-400044-4-400-44000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-44-4400044-4-4004-4000000000000000000000000000000000000000000000000
χ614-444-44-4-400004-440000-4000000000000000000000000022−22−22220000000000000000000000
χ624-444-44-4-400004-440000-40000000000000000000000000−222222−220000000000000000000000
χ634-444-44-4-40000-44-4000040000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ644-444-44-4-40000-44-400004000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ654-44-44-4-4400000004-4-4400000000000000004i−4i0000000000000000000000000000000000
χ664-44-44-4-4400000004-4-440000000000000000−4i4i0000000000000000000000000000000000
χ674-44-44-4-440000000-444-400004i−4i−4i4i00000000000000000000000000000000000000000000
χ684-44-44-4-440000000-444-40000−4i4i4i−4i00000000000000000000000000000000000000000000
χ694-4-444-44-4000044-4-44-44-4400000000-400000000000000000000000000000000000000000
χ704-4-444-44-40000-4-44-44-444-400000000400000000000000000000000000000000000000000
χ718-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000

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