Finite Group Databasebeta

← Group #331125

Character table — Group #331125

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244444444444444444444444488888888888888883232323232323232
order12222222444444444444224444448888888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-11-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-11
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111-11-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1-11
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1-11-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-111-1-1
χ172222222222-2-2-2-222-2-2-2-22222-2-2-2-200000000000000000000000022-2-222-2-200000000
χ182222222222-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000-2-222-2-22200000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000022-2-2-2-22200000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000-2-22222-2-200000000
χ2122222222-2-222-2-2-2-222-2-222-2-222-2-2000000000000000022-2-222-2-20000000000000000
χ2222222222-2-222-2-2-2-222-2-222-2-222-2-20000000000000000-2-222-2-2220000000000000000
χ2322222222-2-222-2-2-2-222-2-2-2-222-2-222000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-222-2-2-2-222-2-2-2-222-2-2220000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-222-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2922-22-22-2-2002-200002-2002-2002-20022−2−222−2−222−2−222−2−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i200000000
χ3022-22-22-2-2002-200002-2002-2002-20022−2−222−2−222−2−222−2−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i200000000
χ3122-22-22-2-2002-200002-2002-2002-200−2−222−2−222−2−222−2−222002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200000000
χ3222-22-22-2-2002-200002-2002-2002-200−2−222−2−222−2−222−2−22200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200000000
χ3322-22-22-2-2002-200002-200-2200-220022−2−222−2−2−2−222−2−222002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i200000000
χ3422-22-22-2-2002-200002-200-2200-220022−2−222−2−2−2−222−2−22200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i200000000
χ3522-22-22-2-2002-200002-200-2200-2200−2−222−2−22222−2−222−2−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i200000000
χ3622-22-22-2-2002-200002-200-2200-2200−2−222−2−22222−2−222−2−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i200000000
χ3722-22-22-2-200-220000-22002-200-220022−2−2−2−22222−2−2−2−2222i−2i002i−2i00i2−i2−i2i2i2−i2−i2i200000000
χ3822-22-22-2-200-220000-22002-200-220022−2−2−2−22222−2−2−2−222−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i200000000
χ3922-22-22-2-200-220000-22002-200-2200−2−22222−2−2−2−22222−2−22i−2i002i−2i00−i2i2i2−i2−i2i2i2−i200000000
χ4022-22-22-2-200-220000-22002-200-2200−2−22222−2−2−2−22222−2−2−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i200000000
χ4122-22-22-2-200-220000-2200-22002-20022−2−2−2−222−2−22222−2−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i200000000
χ4222-22-22-2-200-220000-2200-22002-20022−2−2−2−222−2−22222−2−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i200000000
χ4322-22-22-2-200-220000-2200-22002-200−2−22222−2−222−2−2−2−2222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i200000000
χ4422-22-22-2-200-220000-2200-22002-200−2−22222−2−222−2−2−2−222−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i200000000
χ45444-44-4-4-44-400004-400000000000022−2222−2222−2222−2200000000000000000000000000000000
χ46444-44-4-4-44-400004-4000000000000−2222−2222−2222−222200000000000000000000000000000000
χ47444-44-4-4-4-440000-4400000000000022−2222−22−2222−222200000000000000000000000000000000
χ48444-44-4-4-4-440000-44000000000000−2222−222222−2222−2200000000000000000000000000000000
χ4944-4-4-4-44400004-400004-40000000000004-4-4400000000000000000000000000000000
χ5044-4-4-4-44400004-400004-4000000000000-444-400000000000000000000000000000000
χ5144-4-4-4-4440000-440000-44000000004-4-44000000000000000000000000000000000000
χ5244-4-4-4-4440000-440000-4400000000-444-4000000000000000000000000000000000000
χ534-444-4-44-4004-40000-4400004i−4i004i−4i0000000000000000000000000000000000000000
χ544-444-4-44-4004-40000-440000−4i4i00−4i4i0000000000000000000000000000000000000000
χ554-444-4-44-400-4400004-400004i−4i00−4i4i0000000000000000000000000000000000000000
χ564-444-4-44-400-4400004-40000−4i4i004i−4i0000000000000000000000000000000000000000
χ574-44-4-44-4400004-40000-4400000000000000004-44-40000000000000000000000000000
χ584-44-4-44-4400004-40000-440000000000000000-44-440000000000000000000000000000
χ594-44-4-44-440000-4400004-4000000000000000000004-44-4000000000000000000000000
χ604-44-4-44-440000-4400004-400000000000000000000-44-44000000000000000000000000
χ614-4-444-4-44444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ624-4-444-4-4444-4-4-4-4-4-44444000000000000000000000000000000000000000000000000
χ634-4-444-4-44-4-444-4-444-4-444000000000000000000000000000000000000000000000000
χ644-4-444-4-44-4-4-4-4444444-4-4000000000000000000000000000000000000000000000000
χ654-4-4-4444-44-40000-440000000000000000000022−22−222222−22−2222000000000000000000000000
χ664-4-4-4444-44-40000-4400000000000000000000−222222−22−222222−22000000000000000000000000
χ674-4-4-4444-4-4400004-40000000000000000000022−22−2222−222222−22000000000000000000000000
χ684-4-4-4444-4-4400004-400000000000000000000−222222−2222−22−2222000000000000000000000000

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