Finite Group Databasebeta

← Group #349688

Character table — Group #349688

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444222222444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ61111111111111111111-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1
χ81111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-111111-1-1-1-1-1-1-1-11111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-111111-1-1-1-1-1-1-1-11111111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-11-1-1-1-1-1-11111-1-111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-11-1-1-1-1-1-11111-1-111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-11-1-1-1-1-1-11111-1-11-1-1-1-111-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-11-1-1-1-1-1-11111-1-11-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222-2-2-222-222-20000-2-2000022-2000022-20000-2-2000022-2-2000000000000000000
χ182222222222-2-2-222-222-20000-2-2000022-20000-2-2-20000220000-2-222000000000000000000
χ192222222222-2-2-222-2-2-2-20000220000-2-2-200002220000-2-20000-2-222000000000000000000
χ202222222222-2-2-222-2-2-2-20000220000-2-2-20000-2-22000022000022-2-2000000000000000000
χ2122222222-2-2222-2-2222-22222-2-2-2-2-2-2-2-2-20000002-2-2220000000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-22222-2-2-2000000222-2-20000000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2222222222222-2000000-2-2-2-2-20000000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2-222-2-2-2-222-2000000-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22220000220000-2-2222-2-200-200000022-2-20000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22220000220000-2-22-2-22200-2000000-2-2220000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-220000-2-2000022222-2-2002000000-2-2220000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-220000-2-20000222-2-22200200000022-2-20000000000000000000000
χ2922-22-22-2-22222-2-2-2-200222-2-200000000-22-22-22-202-2002-200000000000000000000000000
χ3022-22-22-2-22222-2-2-2-200222-2-200000000-2-22-22-2202-200-2200000000000000000000000000
χ3122-22-22-2-22222-2-2-2-2002-2-22200000000-22-22-2-220-2200-2200000000000000000000000000
χ3222-22-22-2-22222-2-2-2-2002-2-22200000000-2-22-222-20-22002-200000000000000000000000000
χ3322-22-22-2-222-2-22-2-2200-20000002i2i−2i−2i00200002-20002i−2i-222i−2i2i−2i0000000000000000000000
χ3422-22-22-2-222-2-22-2-2200-20000002i2i−2i−2i0020000-220002i−2i2-2−2i2i−2i2i0000000000000000000000
χ3522-22-22-2-222-2-22-2-2200-2000000−2i−2i2i2i00200002-2000−2i2i-22−2i2i−2i2i0000000000000000000000
χ3622-22-22-2-222-2-22-2-2200-2000000−2i−2i2i2i0020000-22000−2i2i2-22i−2i2i−2i0000000000000000000000
χ3722-22-22-2-2-2-222-222-200-222-2-20000000020000000-2200002i−2i−2i2i2i−2i2i−2i000000000000000000
χ3822-22-22-2-2-2-222-222-200-222-2-20000000020000000-220000−2i2i2i−2i−2i2i−2i2i000000000000000000
χ3922-22-22-2-2-2-222-222-200-2-2-22200000000200000002-200002i−2i−2i2i−2i2i−2i2i000000000000000000
χ4022-22-22-2-2-2-222-222-200-2-2-22200000000200000002-20000−2i2i2i−2i2i−2i2i−2i000000000000000000
χ4122-22-22-2-2-2-2-2-222220020000002i2i−2i−2i00-22-2-2200000−2i2i000000−2i2i2i−2i000000000000000000
χ4222-22-22-2-2-2-2-2-222220020000002i2i−2i−2i00-2-222-200000−2i2i0000002i−2i−2i2i000000000000000000
χ4322-22-22-2-2-2-2-2-22222002000000−2i−2i2i2i00-22-2-22000002i−2i0000002i−2i−2i2i000000000000000000
χ4422-22-22-2-2-2-2-2-22222002000000−2i−2i2i2i00-2-222-2000002i−2i000000−2i2i2i−2i000000000000000000
χ452-2-2-2-2222002-2-20020002-22-22-22-22-22-2000000000000000000000022−2−222−2−22−22−2000000
χ462-2-2-2-2222002-2-20020002-22-22-22-22-22-20000000000000000000000−2−222−2−222−22−22000000
χ472-2-2-2-2222002-2-20020002-22-2-22-22-22-22000000000000000000000022−2−2−2−2222−2−22000000
χ482-2-2-2-2222002-2-20020002-22-2-22-22-22-220000000000000000000000−2−22222−2−2−222−2000000
χ492-2-2-2-2222002-2-2002000-22-222-2-22-222-2000000000000000000000022−2−222−2−2−22−22000000
χ502-2-2-2-2222002-2-2002000-22-222-2-22-222-20000000000000000000000−2−222−2−2222−22−2000000
χ512-2-2-2-2222002-2-2002000-22-22-222-22-2-22000000000000000000000022−2−2−2−222−222−2000000
χ522-2-2-2-2222002-2-2002000-22-22-222-22-2-220000000000000000000000−2−22222−2−22−2−22000000
χ53444-4-4-4-444-40004-400000000000000000000000000000000000000000000000000002i2−2i200
χ54444-4-4-4-444-40004-40000000000000000000000000000000000000000000000000000−2i22i200
χ55444-4-4-4-44-44000-44000000000000000000000000000000000000000000000000002i2−2i20000
χ56444-4-4-4-44-44000-4400000000000000000000000000000000000000000000000000−2i22i20000
χ5744-4-44-44-44-4000-440000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ5844-4-44-44-44-4000-44000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ5944-4-44-44-4-440004-4000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ6044-4-44-44-4-440004-400000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ614-444-4-44-4000000004-4000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ624-444-4-44-4000000004-400000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ634-444-4-44-400000000-44000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ644-444-4-44-400000000-4400000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ654-44-444-4-4004-4400-40004-4-44000000000000000000000000000000000000000000000000
χ664-44-444-4-4004-4400-4000-444-4000000000000000000000000000000000000000000000000
χ674-44-444-4-400-44-40040000000004i−4i−4i4i000000000000000000000000000000000000000000
χ684-44-444-4-400-44-4004000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ694-4-4-4-444400-44400-400000004-40000-440000000000000000000000000000000000000000
χ704-4-4-4-444400-44400-40000000-4400004-40000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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