Finite Group Databasebeta

← Group #317754

Character table — Group #317754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224444448888888888161616161616161616161616161616161616161616161616
order12222222444444444444444488888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111
χ91111111111111111-1-1-1-111-1-11111-1-1-1-11-11-111-1-1-1-11111-1-111-1-111-1-1
χ101111111111111111-1-1-1-111-1-11111-1-1-1-11-11-1-1-11111-1-1-1-111-1-11111-1-1
χ111111111111111111-1-1-1-111-1-11111-1-1-1-1-11-1111-1-1-1-111-1-111-1-111-1-111
χ121111111111111111-1-1-1-111-1-11111-1-1-1-1-11-11-1-11111-1-111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-111111-11-11111-1-1-1-111-1-1-1-111-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-111111-11-1-1-1-1-11111-1-11111-1-1-1-111
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-11-111111-1-1-1-1-1-11111-1-111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-11111-11-11-1-1-1-1111111-1-1-1-11111-1-1
χ172222222222-2-2-222-22222-2-2-2-20000000022-2-200000000000000000000
χ182222222222-2-2-222-22222-2-2-2-200000000-2-22200000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-222000000002-2-2200000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-22200000000-222-200000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22-222-2-222-2-2000000000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-22-2-2-222-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-222-2-2-2222-2-2-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-222-2-2-22-2-22222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2200000000000000000000000000002i−2i2i−2i
χ2622222222-2-2-2-2-2-2-2-222-2-222-220000000000000000000000000000−2i2i−2i2i
χ2722222222-2-2-2-2-2-2-2-2-2-222222-200000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-222222-20000000000000000000000000000−2i2i2i−2i
χ29222-2-2-2-222-22-2-22-2200002-2002i−2i2i−2i00000000002i−2i2-200000000000000
χ30222-2-2-2-222-22-2-22-2200002-2002i−2i2i−2i0000000000−2i2i-2200000000000000
χ31222-2-2-2-222-22-2-22-2200002-200−2i2i−2i2i00000000002i−2i-2200000000000000
χ32222-2-2-2-222-22-2-22-2200002-200−2i2i−2i2i0000000000−2i2i2-200000000000000
χ33222-2-2-2-22-222-2-2-2220000-22002i−2i−2i2i000000002i−2i00002-2000000000000
χ34222-2-2-2-22-222-2-2-2220000-22002i−2i−2i2i00000000−2i2i0000-22000000000000
χ35222-2-2-2-22-222-2-2-2220000-2200−2i2i2i−2i000000002i−2i0000-22000000000000
χ36222-2-2-2-22-222-2-2-2220000-2200−2i2i2i−2i00000000−2i2i00002-2000000000000
χ37444-4-4-4-444-4-4444-4-40000-440000000000000000000000000000000000
χ38444-4-4-4-44-44-444-44-400004-40000000000000000000000000000000000
χ3944-444-4-4-44-4000-4404-44-4000000000000000000000000000000000000
χ4044-444-4-4-44-4000-440-44-44000000000000000000000000000000000000
χ4144-444-4-4-4-440004-404-4-44000000000000000000000000000000000000
χ4244-444-4-4-4-440004-40-444-4000000000000000000000000000000000000
χ4344-4-4-444-444000-4-4000000000000022−2222−22000000000000000000000000
χ4444-4-4-444-444000-4-40000000000000−2222−2222000000000000000000000000
χ4544-4-4-444-4-4-400044000000000000022−22−2222000000000000000000000000
χ4644-4-4-444-4-4-4000440000000000000−222222−22000000000000000000000000
χ474-444-44-4-40044-400-4000000000000000000000000000022−220000000000
χ484-444-44-4-40044-400-40000000000000000000000000000−22220000000000
χ494-444-44-4-400-4-440040000000000000000000000000000002i2−2i200000000
χ504-444-44-4-400-4-44004000000000000000000000000000000−2i22i200000000
χ514-44-44-44-4004-4400-40000000000000000000000000000000022−22000000
χ524-44-44-44-4004-4400-400000000000000000000000000000000−2222000000
χ534-44-44-44-400-44-400400000000000000000000000000000000002i2−2i20000
χ544-44-44-44-400-44-40040000000000000000000000000000000000−2i22i20000
χ558-8-88-8-888000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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