Finite Group Databasebeta

← Group #272249

Character table — Group #272249

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444444488882224444888888888844444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-11111111-11-1-1-1111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1
χ4111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111-1-11111
χ511111111111111-1-11111111111-1-11-111-1-111111111-11-1-1-11-1-1-111-1-111-1-1
χ611111111111111-1-11111111111-1-11-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-1-111
χ711111111111111-1-111111-1-1-1-11-1-11-1111111-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-111
χ811111111111111-1-111111-1-1-1-11-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1111111111-1-1
χ9111111111111-1-1111-1-1111111-111-111111-1-111-1-1-1-1-11-111-11-1-111-1-1-1-11-1
χ10111111111111-1-1111-1-1111111-111-11-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ11111111111111-1-1111-1-111-1-1-1-1-111-1111-1-1-1-1-1-11111-11-111-1-111-1-1-1-111-11
χ12111111111111-1-1111-1-111-1-1-1-1-111-11-1-1-1-111-1-11111-1-1-1-1-11-1111111-1-11-1
χ13111111111111-1-1-1-11-1-1111111-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1111111-1-1-11
χ14111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-11-11111-111-1-1-1-1111-1
χ15111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-11-1-1-1-111111-1
χ16111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111-111111-1-111-1-1-1-1-11
χ172222222-2-2-22-20022200-2-200000-2-202000000002i2i−2i−2i00000002i−2i00000000
χ182222222-2-2-22-20022200-2-200000-2-20200000000−2i−2i2i2i0000000−2i2i00000000
χ192222222-2-2-22-200-2-2200-2-200000220-2000000002i2i−2i−2i0000000−2i2i00000000
χ202222222-2-2-22-200-2-2200-2-200000220-200000000−2i−2i2i2i00000002i−2i00000000
χ21222222-2222-222200-222-2-20000-200-202200220000000-2000-200000000000
χ22222222-2222-222200-222-2-20000-200-20-2-200-2-200000002000200000000000
χ23222222-2222-22-2-200-2-2-2-2-20000200202200-2-20000000-2000200000000000
χ24222222-2222-22-2-200-2-2-2-2-2000020020-2-2002200000002000-200000000000
χ252222-2-222-2-2222222-2-2-22-20000-22-22-2000000000000-20200000000000000
χ262222-2-222-2-22222-2-2-2-2-22-20000-2-222200000000000020-200000000000000
χ272222-2-222-2-222-2-222-2222-2000022-2-2-200000000000020-200000000000000
χ282222-2-222-2-222-2-2-2-2-2222-200002-22-22000000000000-20200000000000000
χ292222-2-22-2222-20022-200-2222220-220-2002200-2-20000000000-20000000000
χ302222-2-22-2222-20022-200-22-2-2-2-20-220-200-2-20022000000000020000000000
χ312222-2-22-2222-200-2-2-200-22222202-20200-2-200-2-2000000000020000000000
χ322222-2-22-2222-200-2-2-200-22-2-2-2-202-202002200220000000000-20000000000
χ332222-2-2-22-2-2-2222002-2-2-220000200-200000000000000002-20000002-20000
χ342222-2-2-22-2-2-2222002-2-2-220000200-20000000000000000-22000000-220000
χ352222-2-2-22-2-2-22-2-200222-220000-200200000000000000002-2000000-220000
χ362222-2-2-22-2-2-22-2-200222-220000-20020000000000000000-220000002-20000
χ3722-2-22-20-22-2022i−2i0002i−2i0022−2−2000002i−2i002-22−2i2−i2i2−i2000000000i2−i2002−200
χ3822-2-22-20-22-2022i−2i0002i−2i0022−2−200000−2i2i00-222−2i2−i2i2−i2000000000−i2i200−2200
χ3922-2-22-20-22-2022i−2i0002i−2i00−2−222000002i−2i002-2−22−i2i2−i2i2000000000−i2i200−2200
χ4022-2-22-20-22-2022i−2i0002i−2i00−2−22200000−2i2i00-22−22−i2i2−i2i2000000000i2−i2002−200
χ4122-2-22-20-22-202−2i2i000−2i2i0022−2−2000002i−2i00-222−2−i2i2−i2i2000000000i2−i200−2200
χ4222-2-22-20-22-202−2i2i000−2i2i0022−2−200000−2i2i002-22−2−i2i2−i2i2000000000−i2i2002−200
χ4322-2-22-20-22-202−2i2i000−2i2i00−2−222000002i−2i00-22−22i2−i2i2−i2000000000−i2i2002−200
χ4422-2-22-20-22-202−2i2i000−2i2i00−2−22200000−2i2i002-2−22i2−i2i2−i2000000000i2−i200−2200
χ45444444-4-4-4-4-4-40000-4004400000000000000000000000000000000000000
χ464444-4-4-4-444-4-400004004-400000000000000000000000000000000000000
χ4744-4-44-404-440-40000000000000000000000000022−22−222200000000000000000
χ4844-4-44-404-440-400000000000000000000000000−222222−2200000000000000000
χ4944-4-4-44044-40-40000000002222−22−2200000000000−2222000000000000000000000
χ5044-4-4-44044-40-4000000000−22−2222220000000000022−22000000000000000000000
χ5144-4-4-440-4-44044i−4i000−4i4i0000000000000000000000000000000000000000
χ5244-4-4-440-4-4404−4i4i0004i−4i0000000000000000000000000000000000000000
χ534-4-44004000-40004i−4i0000022−2222−2200000002i2−2i20000000000000000000000000
χ544-4-44004000-40004i−4i00000−2222−22220000000−2i22i20000000000000000000000000
χ554-4-44004000-4000−4i4i0000022−2222−220000000−2i22i20000000000000000000000000
χ564-4-44004000-4000−4i4i00000−2222−222200000002i2−2i20000000000000000000000000
χ578-88-8000000000000000004-4-440000000000000000000000000000000000
χ588-88-800000000000000000-444-40000000000000000000000000000000000
χ598-8-8800-80008000000000000000000000000000000000000000000000000

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