Finite Group Databasebeta

← Group #317752

Character table — Group #317752

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
χ9111111111111111111-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-1-11111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-11111-1-1-1-11-11-1-1-11111-1-1-1-111-1-11111-1-1
χ11111111111111111111-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1-1-111-1-111-1-111-1-111
χ12111111111111111111-1-1-1-1-1-11111-1-1-1-1-11-11-1-11111-1-111-1-111-1-1-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111111-11-11111-1-1-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111111-11-1-1-1-1-11111-1-11111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-11-111111-1-1-1-1-1-11111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-1111111-1-1-1-11111-1-1
χ172222222222-2-2-222-2-2-22222-2-20000000022-2-200000000000000000000
χ182222222222-2-2-222-2-2-22222-2-200000000-2-22200000000000000000000
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
χ2122222222-2-2222-2-22-2-222-2-22-222-2-222-2-2000000000000000000000000
χ2222222222-2-2222-2-22-2-222-2-22-2-2-222-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-222-2222-2-2-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-22-2-22222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2200000000000000000000000000002i−2i2i−2i
χ2622222222-2-2-2-2-2-2-2-22222-2-2-220000000000000000000000000000−2i2i−2i2i
χ2722222222-2-2-2-2-2-2-2-222-2-2222-200000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-222-2-2222-20000000000000000000000000000−2i2i2i−2i
χ29222-2-2-2-222-22-2-22-222-20000002i−2i2i−2i00000000002i−2i2-200000000000000
χ30222-2-2-2-222-22-2-22-222-20000002i−2i2i−2i0000000000−2i2i-2200000000000000
χ31222-2-2-2-222-22-2-22-222-2000000−2i2i−2i2i00000000002i−2i-2200000000000000
χ32222-2-2-2-222-22-2-22-222-2000000−2i2i−2i2i0000000000−2i2i2-200000000000000
χ33222-2-2-2-22-222-2-2-222-220000002i−2i−2i2i000000002i−2i00002-2000000000000
χ34222-2-2-2-22-222-2-2-222-220000002i−2i−2i2i00000000−2i2i0000-22000000000000
χ35222-2-2-2-22-222-2-2-222-22000000−2i2i2i−2i000000002i−2i0000-22000000000000
χ36222-2-2-2-22-222-2-2-222-22000000−2i2i2i−2i00000000−2i2i00002-2000000000000
χ37444-4-4-4-444-4-4444-4-4-4400000000000000000000000000000000000000
χ38444-4-4-4-44-44-444-44-44-400000000000000000000000000000000000000
χ3944-444-4-4-44-4000-440004-44-40000000000000000000000000000000000
χ4044-444-4-4-44-4000-44000-44-440000000000000000000000000000000000
χ4144-444-4-4-4-440004-40004-4-440000000000000000000000000000000000
χ4244-444-4-4-4-440004-4000-444-40000000000000000000000000000000000
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
χ474-4-44-44-440044-400-400000000000000000000000000000000002i2−2i20000
χ484-4-44-44-440044-400-40000000000000000000000000000000000−2i22i20000
χ494-4-44-44-4400-4-440040000000000000000000000000000000022−22000000
χ504-4-44-44-4400-4-4400400000000000000000000000000000000−2222000000
χ514-4-4-44-444004-4400-40000000000000000000000000000002i2−2i200000000
χ524-4-4-44-444004-4400-4000000000000000000000000000000−2i22i200000000
χ534-4-4-44-44400-44-4004000000000000000000000000000022−220000000000
χ544-4-4-44-44400-44-40040000000000000000000000000000−22220000000000
χ558-888-8-88-8000000000000000000000000000000000000000000000000
χ568-88-888-8-8000000000000000000000000000000000000000000000000

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