Finite Group Databasebeta

← Group #315278

Character table — Group #315278

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222222244444488888888888888888816161616161616161616161632323232
order12222222444444444488884444888888888888882444448888882444
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ51111111111111111111111-1-1-1-1111111-1-1-1-11111-111-1111111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-111
χ9111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-111-111-1-1-1-11-11-1
χ10111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-111-11-1-111-1-1-11-11
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-11-1-1-11111-111-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1111-1-1111-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11-111-1-111-11-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-11-1-111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-111-1-11-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1111-1-1-1-1-111-1
χ17222222222-2-22-2-222-2-222220000-2-20000000000000220-2-20000000000
χ18222222222-2-22-2-222-2-222220000-2-20000000000000-2-20220000000000
χ19222222222-2-22-2-222-2-2-2-2-2-200002200000000000002-20-220000000000
χ20222222222-2-22-2-222-2-2-2-2-2-20000220000000000000-2202-20000000000
χ2122222222-222-222-2-2-2-2000022-2-20022-2-200000000200-2000000000000
χ2222222222-222-222-2-2-2-2000022-2-200-2-22200000000-2002000000000000
χ2322222222-222-222-2-2-2-20000-2-2220022-2-200000000-2002000000000000
χ2422222222-222-222-2-2-2-20000-2-22200-2-22200000000200-2000000000000
χ252-222-2-22-22-2-2-2222-2-2200000000002i−2i2i−2i22-2-2000000000000002i−2i0000
χ262-222-2-22-22-2-2-2222-2-2200000000002i−2i2i−2i-2-22200000000000000−2i2i0000
χ272-222-2-22-22-2-2-2222-2-220000000000−2i2i−2i2i22-2-200000000000000−2i2i0000
χ282-222-2-22-22-2-2-2222-2-220000000000−2i2i−2i2i-2-222000000000000002i−2i0000
χ292-222-2-22-2-2222-2-2-22-2222-2-200002-20000000000000000002i−2i2i−2i000000
χ302-222-2-22-2-2222-2-2-22-2222-2-200002-2000000000000000000−2i2i−2i2i000000
χ312-222-2-22-2-2222-2-2-22-22-2-2220000-220000000000000000002i−2i−2i2i000000
χ322-222-2-22-2-2222-2-2-22-22-2-2220000-22000000000000000000−2i2i2i−2i000000
χ332-222-2-22-2-2-2-2222-222-222-2-20000-222i−2i−2i2i00002i2i−2i−2i0000000000000000
χ342-222-2-22-2-2-2-2222-222-222-2-20000-22−2i2i2i−2i0000−2i−2i2i2i0000000000000000
χ352-222-2-22-2-2-2-2222-222-2-2-22200002-22i−2i−2i2i0000−2i−2i2i2i0000000000000000
χ362-222-2-22-2-2-2-2222-222-2-2-22200002-2−2i2i2i−2i00002i2i−2i−2i0000000000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000
χ38444-44-4-4-404-404-400000000000000000022−2222−2200000000000000000000
χ39444-44-4-4-404-404-4000000000000000000−2222−222200000000000000000000
χ40444-44-4-4-40-440-44000000004-400000000000000000000000000000000
χ41444-44-4-4-40-440-4400000000-4400000000000000000000000000000000
χ4244-4-4-4-444400-400-44004-44-40000000000000000000000000000000000
χ4344-4-4-4-444400-400-4400-44-440000000000000000000000000000000000
χ4444-4-4-4-444-4004004-40000000000000000000022−2222−220000000000000000
χ4544-4-4-4-444-4004004-400000000000000000000−2222−22220000000000000000
χ464-444-4-44-4444-4-4-44-44-400000000000000000000000000000000000000
χ474-44-4-44-4404-40-4400000000004-4000000000000000000000000000000
χ484-44-4-44-4404-40-440000000000-44000000000000000000000000000000
χ494-44-4-44-440-4404-400000000000000000022−22−222200000000000000000000
χ504-44-4-44-440-4404-4000000000000000000−222222−2200000000000000000000
χ514-4-4-4444-4400400-4-4000000000000000000002i2−2i2−2i22i20000000000000000
χ524-4-4-4444-4400400-4-400000000000000000000−2i22i22i2−2i20000000000000000
χ534-4-4-4444-4-400-40044004-4-440000000000000000000000000000000000
χ544-4-4-4444-4-400-4004400-444-40000000000000000000000000000000000
χ5588-88-88-8-8000000000000000000000000000000000000000000000000
χ568-8-888-8-88000000000000000000000000000000000000000000000000

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