Finite Group Databasebeta

← Group #350198

Character table — Group #350198

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444222224444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-11111-1-1-1-1-1-1-1-111-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-11111-1-1-1-1-1-1-1-111-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222-2-222-2-222000022-2-20000-2-2-20000000022-2-2220000-2-2000000000000000000
χ182222222222-2-222-2-222000022-2-20000-2-2-200000000-2-222-2-2000022000000000000000000
χ192222222222-2-222-2-2-2-20000-2-2220000-2-220000000022-2-2-2-2000022000000000000000000
χ202222222222-2-222-2-2-2-20000-2-2220000-2-2200000000-2-222220000-2-2000000000000000000
χ2122222222-2-222-2-222222222-2-2222222-2-2-20000-2-2-2-2000000000000000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-222-2-2-2-2-2-2-200002222000000000000000000000000000000
χ2322222222-2-222-2-222-2-2222222-2-2-2-2-2-2-2-220000-2-222000000000000000000000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-222-2-22222-2-22000022-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000-2-2-2-2000022222-2-2000000000022-2-200000000000000000000
χ2622222222-2-2-2-2-2-2-2-2220000-2-2-2-20000222-2-2220000000000-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-200002222000022-222-2-20000000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-200002222000022-2-2-222000000000022-2-200000000000000000000
χ2922-2-2-222-22-22-22-22-200000000002i2i−2i−2i2-200000002i−2i2i−2i2i−2i002-22-200000000000000000000
χ3022-2-2-222-22-22-22-22-200000000002i2i−2i−2i2-200000002i−2i−2i2i−2i2i00-22-2200000000000000000000
χ3122-2-2-222-22-22-22-22-20000000000−2i−2i2i2i2-20000000−2i2i2i−2i2i−2i00-22-2200000000000000000000
χ3222-2-2-222-22-22-22-22-20000000000−2i−2i2i2i2-20000000−2i2i−2i2i−2i2i002-22-200000000000000000000
χ3322-2-2-222-22-2-222-2-22002i2i−2i−2i00000000-2202-22-22i−2i002i−2i−2i2i00000000000000000000000000
χ3422-2-2-222-22-2-222-2-22002i2i−2i−2i00000000-220-22-222i−2i00−2i2i2i−2i00000000000000000000000000
χ3522-2-2-222-22-2-222-2-2200−2i−2i2i2i00000000-2202-22-2−2i2i00−2i2i2i−2i00000000000000000000000000
χ3622-2-2-222-22-2-222-2-2200−2i−2i2i2i00000000-220-22-22−2i2i002i−2i−2i2i00000000000000000000000000
χ3722-2-2-222-2-222-2-222-200000000002i2i−2i−2i-2202-2-2200−2i2i00002i−2i00002i−2i000000000000000000
χ3822-2-2-222-2-222-2-222-200000000002i2i−2i−2i-220-222-200−2i2i0000−2i2i0000−2i2i000000000000000000
χ3922-2-2-222-2-222-2-222-20000000000−2i−2i2i2i-2202-2-22002i−2i0000−2i2i0000−2i2i000000000000000000
χ4022-2-2-222-2-222-2-222-20000000000−2i−2i2i2i-220-222-2002i−2i00002i−2i00002i−2i000000000000000000
χ4122-2-2-222-2-22-22-22-22002i2i−2i−2i000000002-200000−2i2i0000002i−2i2-2-22−2i2i000000000000000000
χ4222-2-2-222-2-22-22-22-22002i2i−2i−2i000000002-200000−2i2i000000−2i2i-222-22i−2i000000000000000000
χ4322-2-2-222-2-22-22-22-2200−2i−2i2i2i000000002-2000002i−2i0000002i−2i-222-2−2i2i000000000000000000
χ4422-2-2-222-2-22-22-22-2200−2i−2i2i2i000000002-2000002i−2i000000−2i2i2-2-222i−2i000000000000000000
χ452-222-22-2-200-22002-22i−2i2-22-2002i−2i2i−2i2i−2i0000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ462-222-22-2-200-22002-22i−2i2-22-2002i−2i2i−2i2i−2i00000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ472-222-22-2-200-22002-22i−2i-22-22002i−2i−2i2i−2i2i0000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ482-222-22-2-200-22002-22i−2i-22-22002i−2i−2i2i−2i2i00000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ492-222-22-2-200-22002-2−2i2i2-22-200−2i2i−2i2i−2i2i0000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ502-222-22-2-200-22002-2−2i2i2-22-200−2i2i−2i2i−2i2i00000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ512-222-22-2-200-22002-2−2i2i-22-2200−2i2i2i−2i2i−2i0000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ522-222-22-2-200-22002-2−2i2i-22-2200−2i2i2i−2i2i−2i00000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ53444-4-4-4-44000000000000004i−4i000000000000000000000000000002i−2i2i−2i2-22-20000000000
χ54444-4-4-4-44000000000000004i−4i00000000000000000000000000000−2i2i−2i2i-22-220000000000
χ55444-4-4-4-4400000000000000−4i4i000000000000000000000000000002i−2i2i−2i-22-220000000000
χ56444-4-4-4-4400000000000000−4i4i00000000000000000000000000000−2i2i−2i2i2-22-20000000000
χ574-444-44-4-4004-400-444i−4i000000−4i4i000000000000000000000000000000000000000000000
χ584-444-44-4-4004-400-44−4i4i0000004i−4i000000000000000000000000000000000000000000000
χ594-44-44-44-44-400-4400000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ604-44-44-44-44-400-440000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ614-44-44-44-4-44004-40000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ624-44-44-44-4-44004-4000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ634-4-44-4-4444400-4-4000000000000000000000000000000000000000000000000000002i2−2i200
χ644-4-44-4-4444400-4-400000000000000000000000000000000000000000000000000000−2i22i200
χ654-4-44-4-444-4-4004400000000000000000000000000000000000000000000000000022−220000
χ664-4-44-4-444-4-40044000000000000000000000000000000000000000000000000000−22220000
χ674-4-4-444-44004400-4-4004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ684-4-4-444-44004400-4-400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ694-4-4-444-4400-4-4004400000000004-4-4400000000000000000000000000000000000000000
χ704-4-4-444-4400-4-400440000000000-444-400000000000000000000000000000000000000000
χ7188-888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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