Finite Group Databasebeta

← Group #272178

Character table — Group #272178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444422444444488884444444888888888824444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111-11-1-11-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-11111
χ51111111111111111-1-111111111-11-1-11111-1-11111111-1-1-1-1111-1-1-1-1-111-1-1
χ61111111111111111-1-111111111-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-111
χ71111111111111111-1-1111-1-1-1-11-11-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11-1-1111-1-111
χ81111111111111111-1-1111-1-1-1-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111-111-11111111-1-1
χ9111111111111-1-1-1-1111111111-11-11111-1-11111-1-1-1-11-111-111-1-1-11-1-1-1-11-1
χ10111111111111-1-1-1-1111111111-11-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-11
χ11111111111111-1-1-1-111111-1-1-1-1-11-11111-1-1-1-1-1-111111-111-1-1-1-1-1-1-11111-11
χ12111111111111-1-1-1-111111-1-1-1-1-11-111-1-111-1-1-1-11111-1-1-1-1-111111-111-1-11-1
χ13111111111111-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1111-111-111-1-1-11
χ14111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-11-1-1-111111-1
χ15111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-11-1-1-1111-1-1111-1
χ16111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11111111-1-11-1-1-1-1-11
χ172222222-2-2222222200-2-2-20000-20-200222200000000-2000000-2000000000
χ182222222-2-2222222200-2-2-20000-20-200-2-2-2-20000000020000002000000000
χ192222222-2-2222-2-2-2-200-2-2-200002020022-2-200000000-20000002000000000
χ202222222-2-2222-2-2-2-200-2-2-2000020200-2-222000000002000000-2000000000
χ21222222-222-2-2-20000222-2-20000020-2-2000000002i2i−2i−2i000000000002i−2i0000
χ22222222-222-2-2-20000222-2-20000020-2-200000000−2i−2i2i2i00000000000−2i2i0000
χ23222222-222-2-2-20000-2-22-2-200000-2022000000002i2i−2i−2i00000000000−2i2i0000
χ24222222-222-2-2-20000-2-22-2-200000-202200000000−2i−2i2i2i000000000002i−2i0000
χ252222-2-2222-2-22000022-2-2222220-202-2000022-2-200000000000000-2000000
χ262222-2-2222-2-22000022-2-22-2-2-2-20-202-20000-2-222000000000000002000000
χ272222-2-2222-2-220000-2-2-2-222222020-220000-2-2-2-2000000000000002000000
χ282222-2-2222-2-220000-2-2-2-22-2-2-2-2020-220000222200000000000000-2000000
χ292222-2-2-22222-222-2-222-22-20000-2-22-220000000000000200-2000000000000
χ302222-2-2-22222-222-2-2-2-2-22-20000-2222-20000000000000-2002000000000000
χ312222-2-2-22222-2-2-22222-22-200002-2-2-220000000000000-2002000000000000
χ322222-2-2-22222-2-2-222-2-2-22-2000022-22-20000000000000200-2000000000000
χ332222-2-2-2-2-222-222-2-2002-22000020-200000000000000002-200002-20000000
χ342222-2-2-2-2-222-222-2-2002-22000020-20000000000000000-220000-220000000
χ352222-2-2-2-2-222-2-2-222002-220000-20200000000000000002-20000-220000000
χ362222-2-2-2-2-222-2-2-222002-220000-2020000000000000000-2200002-20000000
χ3722-2-22-2-2002-222-22-200000i2i2−i2−i2000002i−2i2i−2i00i2−i2i2−i2i2−i2000002−20000002−200
χ3822-2-22-2-2002-222-22-200000i2i2−i2−i200000−2i2i−2i2i00i2−i2i2−i2i2−i200000−22000000−2200
χ3922-2-22-2-2002-222-22-200000−i2−i2i2i2000002i−2i2i−2i00−i2i2−i2i2−i2i200000−22000000−2200
χ4022-2-22-2-2002-222-22-200000−i2−i2i2i200000−2i2i−2i2i00−i2i2−i2i2−i2i2000002−20000002−200
χ4122-2-22-2-2002-22-22-2200000i2i2−i2−i2000002i−2i−2i2i00i2−i2−i2i2−i2i2000002−2000000−2200
χ4222-2-22-2-2002-22-22-2200000i2i2−i2−i200000−2i2i2i−2i00i2−i2−i2i2−i2i200000−220000002−200
χ4322-2-22-2-2002-22-22-2200000−i2−i2i2i2000002i−2i−2i2i00−i2i2i2−i2i2−i200000−220000002−200
χ4422-2-22-2-2002-22-22-2200000−i2−i2i2i200000−2i2i2i−2i00−i2i2i2−i2i2−i2000002−2000000−2200
χ45444444-4-4-4-4-4-4000000-44400000000000000000000000000000000000000
χ464444-4-44-4-4-4-4400000044-400000000000000000000000000000000000000
χ4744-4-44-4400-44-40000000000000000000000000022−22−222200000000000000000
χ4844-4-44-4400-44-400000000000000000000000000−222222−2200000000000000000
χ4944-4-4-444004-4-44-4-440000000000000000000000000000000000000000000
χ5044-4-4-444004-4-4-444-40000000000000000000000000000000000000000000
χ5144-4-4-44-400-4440000000002i22i2−2i2−2i200000000000−2i22i2000000000000000000000
χ5244-4-4-44-400-444000000000−2i2−2i22i22i2000000000002i2−2i2000000000000000000000
χ534-4-440004-400000004i−4i0002i2−2i22i2−2i200000000022−2200000000000000000000000
χ544-4-440004-400000004i−4i000−2i22i2−2i22i2000000000−222200000000000000000000000
χ554-4-440004-40000000−4i4i0002i2−2i22i2−2i2000000000−222200000000000000000000000
χ564-4-440004-40000000−4i4i000−2i22i2−2i22i200000000022−2200000000000000000000000
χ578-88-8000000000000000004-4-440000000000000000000000000000000000
χ588-88-800000000000000000-444-40000000000000000000000000000000000
χ598-8-88000-8800000000000000000000000000000000000000000000000000

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