Finite Group Databasebeta

← Group #258854

Character table — Group #258854

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122222222444488888888888888888881616161616161616161616161616161616161616
order12222222444444444444444444444448888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1111-1-1111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1
χ5111111111111111111111-1-1111-1-1111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-11111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111
χ91111111111111111-1-111-11111-111-1-1-11111-1-1-1-1-1-1-111111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-11111-111-1-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-111-1-111
χ111111111111111111-1-111-111-1-1-11111-11111-1-1-1-11-1-1-1-1-1-1-11111-1-11111-1-1
χ121111111111111111-1-111-111-1-1-11111-1-1-1-1-111111-1-1-1-1-11111-1-111-1-1-1-111
χ131111111111111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-111-11111-1-1-1-1111-11111-1-1-1-1-1-111-1-111
χ161111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111111-111-1-1-1-11111-1-111-1-1
χ1722222222222-2-2-2-2222-2-2-20022200-2-2-200000000200-20000000000000000
χ1822222222222-2-2-2-2222-2-2-200-2-220022-200000000-20020000000000000000
χ1922222222222-2-2-2-22-2-2-2-220022-20022200000000-200-20000000000000000
χ2022222222222-2-2-2-22-2-2-2-2200-2-2-200-2-220000000020020000000000000000
χ2122222222-2-2-22222-222-2-2-22200-2-2-20020000000002-200000000000000000
χ2222222222-2-2-22222-222-2-2-2-2-200-222002000000000-2200000000000000000
χ2322222222-2-2-22222-2-2-2-2-2222002-2-200-2000000000-2200000000000000000
χ2422222222-2-2-22222-2-2-2-2-22-2-20022200-20000000002-200000000000000000
χ2522222222-2-2-2-2-2-2-2-2222220000-20000-20000000000002-2002-20000000000
χ2622222222-2-2-2-2-2-2-2-2222220000-20000-2000000000000-2200-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-200002000020000000000002-200-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-20000200002000000000000-22002-20000000000
χ292-2-2222-2-222-22-22-2-200-2202i−2i0002i−2i0000000000000000000002i−2i002-20000
χ302-2-2222-2-222-22-22-2-200-2202i−2i0002i−2i000000000000000000000−2i2i00-220000
χ312-2-2222-2-222-22-22-2-200-220−2i2i000−2i2i0000000000000000000002i−2i00-220000
χ322-2-2222-2-222-22-22-2-200-220−2i2i000−2i2i000000000000000000000−2i2i002-20000
χ332-2-2222-2-2-2-222-22-22002-202i−2i000−2i2i000000000000000002-200002i−2i000000
χ342-2-2222-2-2-2-222-22-22002-202i−2i000−2i2i00000000000000000-220000−2i2i000000
χ352-2-2222-2-2-2-222-22-22002-20−2i2i0002i−2i000000000000000002-20000−2i2i000000
χ362-2-2222-2-2-2-222-22-22002-20−2i2i0002i−2i00000000000000000-2200002i−2i000000
χ37444-44-4-4-4000000004-4000000000000022-2-222-2-200000000000000000000
χ38444-44-4-4-4000000004-40000000000000-2-222-2-22200000000000000000000
χ39444-44-4-4-400000000-44000000000000022-2-2-2-22200000000000000000000
χ40444-44-4-4-400000000-440000000000000-2-22222-2-200000000000000000000
χ4144-44-4-4-444-440000-400000000000000022−2222−22000000000000000000000000
χ4244-44-4-4-444-440000-4000000000000000−2222−2222000000000000000000000000
χ4344-44-4-4-44-44-40000400000000000000000002i2−2i22i2−2i200000000000000000000
χ4444-44-4-4-44-44-4000040000000000000000000−2i22i2−2i22i200000000000000000000
χ4544-4-4-444-400044-4-4000000000000000022−22−2222000000000000000000000000
χ4644-4-4-444-400044-4-40000000000000000−222222−22000000000000000000000000
χ4744-4-4-444-4000-4-444000000000000000000002i2−2i2−2i22i200000000000000000000
χ4844-4-4-444-4000-4-44400000000000000000000−2i22i22i2−2i200000000000000000000
χ494-444-4-44-44-4-4000040000000000004i−4i00000000000000000000000000000
χ504-444-4-44-44-4-400004000000000000−4i4i00000000000000000000000000000
χ514-444-4-44-4-4440000-400000004-40000000000000000000000000000000000
χ524-444-4-44-4-4440000-40000000-440000000000000000000000000000000000
χ534-44-4-44-440004-4-4400000000000000000000000000000000000000002i2−2i200
χ544-44-4-44-440004-4-440000000000000000000000000000000000000000−2i22i200
χ554-44-4-44-44000-444-40000000000000000000000000000000000000000002i2−2i2
χ564-44-4-44-44000-444-4000000000000000000000000000000000000000000−2i22i2
χ574-4-4444-4-444-4-44-44-4004-4000000000000000000000000000000000000000
χ584-4-4444-4-4-4-44-44-44400-44000000000000000000000000000000000000000
χ598-8-8-88-888000000000000000000000000000000000000000000000000000

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