Finite Group Databasebeta

← Group #271305

Character table — Group #271305

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444444442224444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11-1111111
χ511111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-11-1-1-1-111
χ611111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-111111-1-1
χ711111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ911111111111111111-1-1-1-11-11111-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1111-1-11-1
χ1011111111111111111-1-1-1-11-11111-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-11-1-111-11
χ1111111111111111111-1-1-1-11-111-1-111-1111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-111-11
χ1211111111111111111-1-1-1-11-111-1-111-111-1-1-1-11111-1-1-1-11111-11-1-111-1-111-1-11-1
χ1311111111111111111-1-1-1-11-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111111111-1-11-111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11111-1-11-1-1-1111-1
χ172222222222-2-222-2-2-222-2-2-2-22200002-2-20000000000000000200000-20000000
χ182222222222-2-222-2-2-222-2-2-2-2-2-200002220000000000000000-20000020000000
χ192222222222-2-222-2-2-2-2-222-22220000-2-2-20000000000000000-20000020000000
χ202222222222-2-222-2-2-2-2-222-22-2-20000-2220000000000000000200000-20000000
χ2122222222-2-222-2-222-22222-2-20022-2-2-20000000000000000000200000-2000000
χ2222222222-2-222-2-222-22222-2-200-2-222-20000000000000000000-2000002000000
χ2322222222-2-222-2-222-2-2-2-2-2-2200222220000000000000000000-200000-2000000
χ2422222222-2-222-2-222-2-2-2-2-2-2200-2-2-2-2200000000000000000002000002000000
χ2522222222-2-2-2-2-2-2-2-2222-2-222000000-2000000000000000000002-22-200000000
χ2622222222-2-2-2-2-2-2-2-2222-2-222000000-200000000000000000000-22-2200000000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-20000002000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-2000000200000000000000000000-222-200000000
χ292-2-2-222-222-2222-2-2-220000-202-2000002-22i2i−2i−2i00002i2i−2i−2i000000000000000000
χ302-2-2-222-222-2222-2-2-220000-202-2000002-2−2i−2i2i2i0000−2i−2i2i2i000000000000000000
χ312-2-2-222-222-2222-2-2-220000-20-2200000-222i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ322-2-2-222-222-2222-2-2-220000-20-2200000-22−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ332-2-2-222-222-2-2-22-222-20000202-200000-22000022-2-2000022-2-200000000000000
χ342-2-2-222-222-2-2-22-222-20000202-200000-220000-2-2220000-2-22200000000000000
χ352-2-2-222-222-2-2-22-222-2000020-22000002-2000022-2-20000-2-22200000000000000
χ362-2-2-222-222-2-2-22-222-2000020-22000002-20000-2-222000022-2-200000000000000
χ37444-4-44-4-44-400-4400000000000000000022−2222−2200000000000000000000000000
χ38444-4-44-4-44-400-44000000000000000000−2222−222200000000000000000000000000
χ39444-4-44-4-4-44004-4000000000000000000000022−2222−220000000000000000000000
χ40444-4-44-4-4-44004-40000000000000000000000−2222−22220000000000000000000000
χ4144-444-4-4-40000000004-40000000000000000000002-22-22-22-200000000000000
χ4244-444-4-4-40000000004-4000000000000000000000-22-22-22-2200000000000000
χ4344-444-4-4-4000000000-440000000000000000000002-22-2-22-2200000000000000
χ4444-444-4-4-4000000000-44000000000000000000000-22-222-22-200000000000000
χ4544-4-4-4-444004-4004-400000000000000000000000000000000000000000022−2200
χ4644-4-4-4-444004-4004-4000000000000000000000000000000000000000000−222200
χ4744-4-4-4-44400-4400-44000000000000000000000000000000000000000022−220000
χ4844-4-4-4-44400-4400-440000000000000000000000000000000000000000−22220000
χ494-444-4-4-44004-400-44000000000004i−4i000000000000000000000000000000000
χ504-444-4-4-44004-400-4400000000000−4i4i000000000000000000000000000000000
χ514-444-4-4-4400-44004-40000000004i−4i00000000000000000000000000000000000
χ524-444-4-4-4400-44004-4000000000−4i4i00000000000000000000000000000000000
χ534-44-44-44-4000000000004i−4i00000000000000000002i−2i−2i2i2-2-2200000000000000
χ544-44-44-44-4000000000004i−4i0000000000000000000−2i2i2i−2i-222-200000000000000
χ554-44-44-44-400000000000−4i4i00000000000000000002i−2i−2i2i-222-200000000000000
χ564-44-44-44-400000000000−4i4i0000000000000000000−2i2i2i−2i2-2-2200000000000000
χ574-4-44-444-44400-4-40000000000000000002i2−2i2−2i22i200000000000000000000000000
χ584-4-44-444-44400-4-4000000000000000000−2i22i22i2−2i200000000000000000000000000
χ594-4-44-444-4-4-40044000000000000000000000022−22−22220000000000000000000000
χ604-4-44-444-4-4-400440000000000000000000000−222222−220000000000000000000000
χ614-4-4-444-44-4444-44-4-4-4000040000000000000000000000000000000000000000
χ624-4-4-444-44-44-4-4-444440000-40000000000000000000000000000000000000000

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