Finite Group Databasebeta

← Group #349643

Character table — Group #349643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444224444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-1-1-11-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-11
χ811111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ101111111111111111-1-1-1-111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-111111-1-1-1-1111-1-11-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-1111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-2-222-200002222-20000-2-2-222-2-2-200-2-2000000000022000000000000000000
χ182222222222-2-2-222-200002222-20000-2-2-2-2-2-22200220000000000-2-2000000000000000000
χ192222222222-2-2-222-20000-2-2-2-2-2000022-22222200-2-20000000000-2-2000000000000000000
χ202222222222-2-2-222-20000-2-2-2-2-2000022-2-2-22-2-20022000000000022000000000000000000
χ2122222222-2-2222-2-22222222-2-2-2222222-200-200-2-20000000000-2-200000000000000000000
χ2222222222-2-2222-2-222222-2-222-2-2-2-2-2-2-2-200200220000000000-2-200000000000000000000
χ2322222222-2-2222-2-22-2-2-2-222-2-2-2-2-2-2-222-200-2002200000000002200000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-222-22222-2-2-200200-2-200000000002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022-2-220000-2-2200200000022-2-222-2-20000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2000022-2-220000-2-22002000000-2-222-2-2220000000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2222000022200-200000022-2-2-2-2220000000000000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2222000022200-2000000-2-22222-2-20000000000000000000000
χ2922-2-22-22-22222-2-2-2-200000000222-2-200-22-20002-22-200002-22-20000000000000000000000
χ3022-2-22-22-22222-2-2-2-200000000222-2-200-2-220002-2-220000-22-220000000000000000000000
χ3122-2-22-22-22222-2-2-2-2000000002-2-22200-22-2000-222-20000-22-220000000000000000000000
χ3222-2-22-22-22222-2-2-2-2000000002-2-22200-2-22000-22-2200002-22-20000000000000000000000
χ3322-2-22-22-222-2-22-2-222i2i−2i−2i0000-200000022-200000-222i−2i2i−2i00002i−2i00000000000000000000
χ3422-2-22-22-222-2-22-2-222i2i−2i−2i0000-20000002-22000002-2−2i2i−2i2i00002i−2i00000000000000000000
χ3522-2-22-22-222-2-22-2-22−2i−2i2i2i0000-200000022-200000-22−2i2i−2i2i0000−2i2i00000000000000000000
χ3622-2-22-22-222-2-22-2-22−2i−2i2i2i0000-20000002-22000002-22i−2i2i−2i0000−2i2i00000000000000000000
χ3722-2-22-22-2-2-222-222-200000000-222-2-20020002i−2i-22002i−2i−2i2i0000002i−2i000000000000000000
χ3822-2-22-22-2-2-222-222-200000000-222-2-2002000−2i2i-2200−2i2i2i−2i000000−2i2i000000000000000000
χ3922-2-22-22-2-2-222-222-200000000-2-2-2220020002i−2i2-200−2i2i2i−2i0000002i−2i000000000000000000
χ4022-2-22-22-2-2-222-222-200000000-2-2-222002000−2i2i2-2002i−2i−2i2i000000−2i2i000000000000000000
χ4122-2-22-22-2-2-2-2-222222i2i−2i−2i00002000000-20002i−2i00000000-222-2−2i2i−2i2i000000000000000000
χ4222-2-22-22-2-2-2-2-222222i2i−2i−2i00002000000-2000−2i2i000000002-2-22−2i2i2i−2i000000000000000000
χ4322-2-22-22-2-2-2-2-22222−2i−2i2i2i00002000000-20002i−2i000000002-2-222i−2i−2i2i000000000000000000
χ4422-2-22-22-2-2-2-2-22222−2i−2i2i2i00002000000-2000−2i2i00000000-222-22i−2i2i−2i000000000000000000
χ452-22-22-2-22002-2200-22i−2i2i−2i2-20002i−2i2i−2i2-20000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ462-22-22-2-22002-2200-22i−2i2i−2i2-20002i−2i2i−2i2-20000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ472-22-22-2-22002-2200-22i−2i2i−2i-22000−2i2i−2i2i-220000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ482-22-22-2-22002-2200-22i−2i2i−2i-22000−2i2i−2i2i-220000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ492-22-22-2-22002-2200-2−2i2i−2i2i2-2000−2i2i−2i2i2-20000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ502-22-22-2-22002-2200-2−2i2i−2i2i2-2000−2i2i−2i2i2-20000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ512-22-22-2-22002-2200-2−2i2i−2i2i-220002i−2i2i−2i-220000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ522-22-22-2-22002-2200-2−2i2i−2i2i-220002i−2i2i−2i-220000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ53444-4-44-4-44-40004-40000000000000000000000000000000000000000000000000022−220000
χ54444-4-44-4-44-40004-400000000000000000000000000000000000000000000000000−22220000
χ55444-4-44-4-4-44000-44000000000000000000000000000000000000000000000000000022−2200
χ56444-4-44-4-4-44000-440000000000000000000000000000000000000000000000000000−222200
χ5744-44-4-4-444-4000-44000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ5844-44-4-4-444-4000-4400000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ5944-44-4-4-44-440004-40000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ6044-44-4-4-44-440004-4000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ614-44-44-4-4400-44-400400004-40000000-440000000000000000000000000000000000000000
χ624-44-44-4-4400-44-40040000-4400000004-40000000000000000000000000000000000000000
χ634-4-4444-4-4004-4-40040000000004i−4i−4i4i000000000000000000000000000000000000000000
χ644-4-4444-4-4004-4-4004000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-4444-4-400-44400-44-4-44000000000000000000000000000000000000000000000000000
χ664-4-4444-4-400-44400-4-444-4000000000000000000000000000000000000000000000000000
χ674-4-4-4-4444000000000000004-4000000000000000000000000000002-2-222-2-220000000000
χ684-4-4-4-4444000000000000004-400000000000000000000000000000-222-2-222-20000000000
χ694-4-4-4-444400000000000000-44000000000000000000000000000002-2-22-222-20000000000
χ704-4-4-4-444400000000000000-4400000000000000000000000000000-222-22-2-220000000000
χ718-888-8-88-8000000000000000000000000000000000000000000000000000000000000000

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