Finite Group Databasebeta

← Group #242334

Character table — Group #242334

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444444444224444448888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1111111-111-1-1-1-1-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111111111
χ91111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-111111-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-1-1-1-1-11111111-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1111-1-1-1-1-111-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11-1-1-111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-11-1-1-1-111-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-11-11111-1-11-1-1-1-111-1-111
χ151111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111-11-1-11111-1-1-111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-11-111-1-1-1-111111-1-111-1-1
χ172222222222-2-222-2-22222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ182222222222-2-222-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000
χ2122222222-2-222-2-22222-2-222-2-2-2-2000000000000000022-2000000-20000000000
χ2222222222-2-222-2-22222-2-222-2-2-2-20000000000000000-2-2200000020000000000
χ2322222222-2-222-2-222-2-222-2-222-2-200000000000000002-2-200000020000000000
χ2422222222-2-222-2-222-2-222-2-222-2-20000000000000000-222000000-20000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000002-2002-200000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000-2200-2200000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000002-200-2200000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000-22002-200000000000
χ2922-22-2-2-222-22-22-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000002i−2i2-2
χ3022-22-2-2-222-22-22-22-22i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000000−2i2i-22
χ3122-22-2-2-222-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000002i−2i-22
χ3222-22-2-2-222-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000−2i2i2-2
χ3322-22-2-2-222-2-222-2-222i−2i2i−2i−2i2i−2i2i-220000000000000000000002i−2i0002-200000000
χ3422-22-2-2-222-2-222-2-222i−2i2i−2i−2i2i−2i2i-22000000000000000000000−2i2i000-2200000000
χ3522-22-2-2-222-2-222-2-22−2i2i−2i2i2i−2i2i−2i-220000000000000000000002i−2i000-2200000000
χ3622-22-2-2-222-2-222-2-22−2i2i−2i2i2i−2i2i−2i-22000000000000000000000−2i2i0002-200000000
χ3722-22-2-2-22-222-2-222-22i−2i−2i2i2i−2i−2i2i-22000000002i2i−2i−2i22-2-200000000000000000000
χ3822-22-2-2-22-222-2-222-22i−2i−2i2i2i−2i−2i2i-2200000000−2i−2i2i2i-2-22200000000000000000000
χ3922-22-2-2-22-222-2-222-2−2i2i2i−2i−2i2i2i−2i-22000000002i2i−2i−2i-2-22200000000000000000000
χ4022-22-2-2-22-222-2-222-2−2i2i2i−2i−2i2i2i−2i-2200000000−2i−2i2i2i22-2-200000000000000000000
χ4122-22-2-2-22-22-22-22-222i−2i−2i2i−2i2i2i−2i2-200000000000000000000000000002-22i−2i0000
χ4222-22-2-2-22-22-22-22-222i−2i−2i2i−2i2i2i−2i2-20000000000000000000000000000-22−2i2i0000
χ4322-22-2-2-22-22-22-22-22−2i2i2i−2i2i−2i−2i2i2-200000000000000000000000000002-2−2i2i0000
χ4422-22-2-2-22-22-22-22-22−2i2i2i−2i2i−2i−2i2i2-20000000000000000000000000000-222i−2i0000
χ454-4444-4-4-44400-4-40000000000004-40000000000000000000000000000000000
χ464-4444-4-4-44400-4-4000000000000-440000000000000000000000000000000000
χ474-4444-4-4-4-4-4004400000000000000004i−4i000000000000000000000000000000
χ484-4444-4-4-4-4-400440000000000000000−4i4i000000000000000000000000000000
χ494-44-4-44-44004-400-4400000000000000000000002i2−2i22i2−2i200000000000000000000
χ504-44-4-44-44004-400-440000000000000000000000−2i22i2−2i22i200000000000000000000
χ514-44-4-44-4400-44004-40000000000000000002i2−2i22i2−2i2000000000000000000000000
χ524-44-4-44-4400-44004-4000000000000000000−2i22i2−2i22i2000000000000000000000000
χ534-4-44-444-44-400-44000000000000004i−4i00000000000000000000000000000000
χ544-4-44-444-44-400-4400000000000000−4i4i00000000000000000000000000000000
χ554-4-44-444-4-44004-40000000000000000004i−4i0000000000000000000000000000
χ564-4-44-444-4-44004-4000000000000000000−4i4i0000000000000000000000000000
χ574-4-4-44-444004400-4-400000000000000000000002i2−2i2−2i22i200000000000000000000
χ584-4-4-44-444004400-4-40000000000000000000000−2i22i22i2−2i200000000000000000000
χ594-4-4-44-44400-4-4004400000000000000000022−22−2222000000000000000000000000
χ604-4-4-44-44400-4-40044000000000000000000−222222−22000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-8-888-8-8000000000000000000000000000000000000000000000000000000

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