Finite Group Databasebeta

← Group #288680

Character table — Group #288680

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222244444444488888888888888888161616161616161616161616161616163232
order12222244444444488888888888888888888888244444448888888824
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-1
χ311111111111111111111111-1-11-1-11111111111-1-11-11-111-111-1-1-1-1-1-1-1
χ411111111111111111111111-1-11-1-1-1-1-1-111111111-11-11-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111-1-1111111111-1-1-1-1-1-111-11-11111-1-11-1-1-1-1-1-1
χ6111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-11111-1-1
χ9111111111111111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1111-1-11-1
χ10111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-111111-1-1-11
χ11111111111111111-1-1-1-1-1-111-1-1-111111111-1-1-1-1111-11-1-1-11-1-1-1-1-111-11
χ12111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1111111-1-1-1111-1
χ13111111111111111-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-11-11-1-1-1111-1-111-11
χ14111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111-11-111-1-1-11-1-1111-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1111-111-1-11-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111111-1-1-111-1-1-11
χ172222222-2222-2-2-2-22222-2-20022-222000000000000000000-200-2000000
χ182222222-2222-2-2-2-22222-2-200-2-2-2-2-20000000000000000002002000000
χ192222222-2222-2-2-2-2-2-2-2-22200222-2-2000000000000000000200-2000000
χ202222222-2222-2-2-2-2-2-2-2-22200-2-2222000000000000000000-2002000000
χ21222222-2-2-2-2-2-2-22200000000000002i2i−2i−2i0022-2-20000000002i−2i0000000
χ22222222-2-2-2-2-2-2-22200000000000002i2i−2i−2i00-2-222000000000−2i2i0000000
χ23222222-2-2-2-2-2-2-2220000000000000−2i−2i2i2i0022-2-2000000000−2i2i0000000
χ24222222-2-2-2-2-2-2-2220000000000000−2i−2i2i2i00-2-2220000000002i−2i0000000
χ252222-2-222-22-22-2-2222-2-2220000-20000000000002-20-202000000000000
χ262222-2-222-22-22-2-2222-2-2220000-2000000000000-22020-2000000000000
χ272222-2-222-22-22-2-22-2-222-2-2000020000000000002-2020-2000000000000
χ282222-2-222-22-22-2-22-2-222-2-200002000000000000-220-202000000000000
χ292222-2-22-2-22-2-222-222-2-2-2-200002002i−2i2i−2i0000000000002i−2i0000000000
χ302222-2-22-2-22-2-222-222-2-2-2-20000200−2i2i−2i2i000000000000−2i2i0000000000
χ312222-2-22-2-22-2-222-2-2-222220000-2002i−2i2i−2i000000000000−2i2i0000000000
χ322222-2-22-2-22-2-222-2-2-222220000-200−2i2i−2i2i0000000000002i−2i0000000000
χ332222-2-2-222-222-22-200000022000002-2-22-2-200000020-20000000000000
χ342222-2-2-222-222-22-20000002200000-222-2-2-2000000-2020000000000000
χ352222-2-2-222-222-22-2000000-2-2000002-2-2222000000-2020000000000000
χ362222-2-2-222-222-22-2000000-2-200000-222-22200000020-20000000000000
χ3722-2-22-2-20-22200002i−2i2i−2i00i2−i22i−2i02-20000i2−i22−22−20000000000002−2i2−i200
χ3822-2-22-2-20-22200002i−2i2i−2i00i2−i2−2i2i0-220000i2−i22−22−2000000000000−22−i2i200
χ3922-2-22-2-20-22200002i−2i2i−2i00−i2i22i−2i02-20000−i2i2−22−22000000000000−22−i2i200
χ4022-2-22-2-20-22200002i−2i2i−2i00−i2i2−2i2i0-220000−i2i2−22−220000000000002−2i2−i200
χ4122-2-22-2-20-2220000−2i2i−2i2i00i2−i22i−2i0-220000i2−i2−22−220000000000002−2−i2i200
χ4222-2-22-2-20-2220000−2i2i−2i2i00i2−i2−2i2i02-20000i2−i2−22−22000000000000−22i2−i200
χ4322-2-22-2-20-2220000−2i2i−2i2i00−i2i22i−2i0-220000−i2i22−22−2000000000000−22i2−i200
χ4422-2-22-2-20-2220000−2i2i−2i2i00−i2i2−2i2i02-20000−i2i22−22−20000000000002−2−i2i200
χ45444444-44-4-4-444-4-400000000000000000000000000000000000000000
χ464444-4-4-4-44-44-44-4400000000000000000000000000000000000000000
χ4744-4-44-4404-4-40000000000000000000000022−22−2222000000000000000000
χ4844-4-44-4404-4-400000000000000000000000−222222−22000000000000000000
χ4944-4-4-4440-4-4400000000002i2−2i2000000000−2i22i20000000000000000000000
χ5044-4-4-4440-4-440000000000−2i22i20000000002i2−2i20000000000000000000000
χ5144-4-4-44-4044-400004i−4i−4i4i0000000000000000000000000000000000000
χ5244-4-4-44-4044-40000−4i4i4i−4i0000000000000000000000000000000000000
χ538-88-80008000-800000000000000000000000000000000000000000000
χ548-88-8000-8000800000000000000000000000000000000000000000000
χ558-8-8800000000000000042−4200000000000000000000000000000000000
χ568-8-88000000000000000−424200000000000000000000000000000000000

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