Finite Group Databasebeta

← Group #350686

Character table — Group #350686

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244448888888888888888888888888888888888816161616161616163232
order12222222444444444444222224444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-111-111-1-1-11111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-111-111-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-111-111-1-1-1-1-1-1-11111-1-1-1-11111-111-1-11111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-111-111-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-111-1-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-111-1-1-111-11111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-111-1-1-111-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-111-1-1-111-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-222-2-2222-2-2-20000000000000000-2-2-222000000000000000000
χ182222222222-2-222-2-222-2-22-2-222-20000000000000000-222-2-2000000000000000000
χ192222222222-2-222-2-2-2-2-2-2-22222200000000000000002-2-2-2-2000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2-2-2-22000000000000000022222000000000000000000
χ2122222222-2-222-2-22222-2-2-20000222-2-222-2-200000000-20000000000000000000000
χ2222222222-2-222-2-22222-2-2-200002-2-222-2-22200000000-20000000000000000000000
χ2322222222-2-222-2-222-2-2-2-220000-222-2-2-2-2220000000020000000000000000000000
χ2422222222-2-222-2-222-2-2-2-220000-2-2-22222-2-20000000020000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-20000-20000000022-2-222-2-220000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-20000-200000000-2-222-2-22220000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222000020000000022-2-2-2-222-20000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22220000200000000-2-22222-2-2-20000000000000000000000
χ29222-2-2-2-222-22-22-22-2002-20002-2000002i−2i2i−2i2i−2i2i−2i00000002-2000000000000000000
χ30222-2-2-2-222-22-22-22-2002-20002-200000−2i2i−2i2i−2i2i−2i2i00000002-2000000000000000000
χ31222-2-2-2-222-22-22-22-2002-2000-22000002i−2i2i−2i−2i2i−2i2i0000000-22000000000000000000
χ32222-2-2-2-222-22-22-22-2002-2000-2200000−2i2i−2i2i2i−2i2i−2i0000000-22000000000000000000
χ33222-2-2-2-222-2-222-2-2200-220002-202i−2i2i−2i000000002i−2i2i−2i000-22000000000000000000
χ34222-2-2-2-222-2-222-2-2200-220002-20−2i2i−2i2i00000000−2i2i−2i2i000-22000000000000000000
χ35222-2-2-2-222-2-222-2-2200-22000-2202i−2i2i−2i00000000−2i2i−2i2i0002-2000000000000000000
χ36222-2-2-2-222-2-222-2-2200-22000-220−2i2i−2i2i000000002i−2i2i−2i0002-2000000000000000000
χ37222-2-2-2-22-222-2-222-200-2202-200000002i−2i−2i2i00002i−2i−2i2i02-200000000000000000000
χ38222-2-2-2-22-222-2-222-200-2202-20000000−2i2i2i−2i0000−2i2i2i−2i02-200000000000000000000
χ39222-2-2-2-22-222-2-222-200-220-2200000002i−2i−2i2i0000−2i2i2i−2i0-2200000000000000000000
χ40222-2-2-2-22-222-2-222-200-220-220000000−2i2i2i−2i00002i−2i−2i2i0-2200000000000000000000
χ41222-2-2-2-22-22-22-22-22002-202-20002i−2i−2i2i0000−2i2i2i−2i00000-2200000000000000000000
χ42222-2-2-2-22-22-22-22-22002-202-2000−2i2i2i−2i00002i−2i−2i2i00000-2200000000000000000000
χ43222-2-2-2-22-22-22-22-22002-20-220002i−2i−2i2i00002i−2i−2i2i000002-200000000000000000000
χ44222-2-2-2-22-22-22-22-22002-20-22000−2i2i2i−2i0000−2i2i2i−2i000002-200000000000000000000
χ4544-444-4-4-44400-4-40000000000000000000000000000000000000000022−2200000000
χ4644-444-4-4-44400-4-400000000000000000000000000000000000000000−222200000000
χ4744-444-4-4-4-4-4004400000000000000000000000000000000000000000002i2−2i2000000
χ4844-444-4-4-4-4-400440000000000000000000000000000000000000000000−2i22i2000000
χ4944-4-4-444-44-400-4400000000000000000000000000000000000002i22i2−2i2−2i20000000000
χ5044-4-4-444-44-400-440000000000000000000000000000000000000−2i2−2i22i22i20000000000
χ5144-4-4-444-4-44004-40000000000000000000000000000000002i22i2−2i2−2i200000000000000
χ5244-4-4-444-4-44004-4000000000000000000000000000000000−2i2−2i22i22i200000000000000
χ534-44-444-4-4000000004i−4i000000000000000000000000000002-22-22i−2i2i−2i0000000000
χ544-44-444-4-4000000004i−4i00000000000000000000000000000-22-22−2i2i−2i2i0000000000
χ554-44-444-4-400000000−4i4i000000000000000000000000000002-22-2−2i2i−2i2i0000000000
χ564-44-444-4-400000000−4i4i00000000000000000000000000000-22-222i−2i2i−2i0000000000
χ574-4-44-44-44004400-4-400000000000000000000000000000002i2−2i2−2i22i200000000000000
χ584-4-44-44-44004400-4-40000000000000000000000000000000−2i22i22i2−2i200000000000000
χ594-4-44-44-4400-4-400440000000000000000000000000000000000022−22−22220000000000
χ604-4-44-44-4400-4-4004400000000000000000000000000000000000−222222−220000000000
χ614-4-4-44-444004-400-4400000000000000000000000000000000000000000000022−2200
χ624-4-4-44-444004-400-44000000000000000000000000000000000000000000000−222200
χ634-4-4-44-44400-44004-4000000000000000000000000000000000000000000022−220000
χ644-4-4-44-44400-44004-40000000000000000000000000000000000000000000−22220000
χ658-888-8-88-8000000000000000000000000000000000000000000000000000000000

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