Finite Group Databasebeta

← Group #337270

Character table — Group #337270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1-1-111-1
χ3111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11
χ51111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ61111111111111111111111-1-111-1-1-1-1111111-1-1-1-1111111-11-1-11111-1-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111111-11
χ11111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-111
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-111111-1-111-11-1
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-11-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-111-1-111-111
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1111-1-111111-1-1
χ172222222222-22-2-2-22-2-22222002200000000-2-200000000-220-200000000000
χ182222222222-22-2-2-22-2-2222200-2-200000000-2-2000000002-20200000000000
χ192222222222-22-2-2-22-2-2-2-2-2-20022000000002200000000-2-20200000000000
χ202222222222-22-2-2-22-2-2-2-2-2-200-2-2000000002200000000220-200000000000
χ2122222222-2-22-2222-2-2-20000220022-2-222-2-2000000000000-2000000000000
χ2222222222-2-22-2222-2-2-200002200-2-2-2-2-2-2220000000000002000000000000
χ2322222222-2-22-2222-2-2-20000-2-2002222-2-222000000000000-2000000000000
χ2422222222-2-22-2222-2-2-20000-2-200-2-22222-2-20000000000002000000000000
χ2522-2-2-222-200-202-2200022−2−22i−2i002-2002i−2i002−2i2i2−i2−i2i2i2−i2−i200000000002−2000
χ2622-2-2-222-200-202-2200022−2−22i−2i00-2200−2i2i002−2i2i2−i2−i2−i2−i2i2i20000000000−22000
χ2722-2-2-222-200-202-2200022−2−2−2i2i002-200−2i2i002−2−i2−i2i2i2−i2−i2i2i200000000002−2000
χ2822-2-2-222-200-202-2200022−2−2−2i2i00-22002i−2i002−2−i2−i2i2i2i2i2−i2−i20000000000−22000
χ2922-2-2-222-200-202-22000−2−2222i−2i002-2002i−2i00−22−i2−i2i2i2−i2−i2i2i20000000000−22000
χ3022-2-2-222-200-202-22000−2−2222i−2i00-2200−2i2i00−22−i2−i2i2i2i2i2−i2−i200000000002−2000
χ3122-2-2-222-200-202-22000−2−222−2i2i002-200−2i2i00−22i2i2−i2−i2i2i2−i2−i20000000000−22000
χ3222-2-2-222-200-202-22000−2−222−2i2i00-22002i−2i00−22i2i2−i2−i2−i2−i2i2i200000000002−2000
χ332-22-22-22-2-2-2-2222-222-20000000000000000002-22-2000000002i−2i002i−2i00000
χ342-22-22-22-2-2-2-2222-222-20000000000000000002-22-200000000−2i2i00−2i2i00000
χ352-22-22-22-2-2-2-2222-222-2000000000000000000-22-22000000002i−2i00−2i2i00000
χ362-22-22-22-2-2-2-2222-222-2000000000000000000-22-2200000000−2i2i002i−2i00000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-4-4-444-404000-4004-44-40000000000000000000000000000000000000
χ39444-4-4-4-444-404000-400-44-440000000000000000000000000000000000000
χ40444-4-4-4-44-440-400040000000000000000000000002i2−2i22i2−2i2000000000000000
χ41444-4-4-4-44-440-40004000000000000000000000000−2i22i2−2i22i2000000000000000
χ4244-444-4-4-4000000000022−22−2222000000000022−220000002-2-22000000000000000
χ4344-444-4-4-4000000000022−22−22220000000000−2222000000-222-2000000000000000
χ4444-444-4-4-40000000000−222222−22000000000022−22000000-222-2000000000000000
χ4544-444-4-4-40000000000−222222−220000000000−22220000002-2-22000000000000000
χ4644-4-4-444-40040-44-40002222−22−22000000000000−222200000000000000000000000
χ4744-4-4-444-40040-44-4000−22−22222200000000000022−2200000000000000000000000
χ484-444-44-4-44-40-40004000000004i−4i000000000000000000000000000000000
χ494-444-44-4-44-40-4000400000000−4i4i000000000000000000000000000000000
χ504-444-44-4-4-4404000-4000000000000000000000000000000000022−220000000
χ514-444-44-4-4-4404000-40000000000000000000000000000000000−22220000000
χ524-44-44-44-4444-4-4-44-44-400000000000000000000000000000000000000000
χ534-44-44-44-444-4-444-4-4-4400000000000000000000000000000000000000000
χ544-44-44-44-4-4-444-4-444-4400000000000000000000000000000000000000000
χ554-4-44-4-44400404-4-40000000000000000000002i2−2i2−2i22i20000000000000000000
χ564-4-44-4-44400404-4-4000000000000000000000−2i22i22i2−2i20000000000000000000
χ574-4-44-4-44400-40-44400000000000004-400000000000000000000000000000
χ584-4-44-4-44400-40-4440000000000000-4400000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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