Finite Group Databasebeta

← Group #328784

Character table — Group #328784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222444444444444444422444444488888888244444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111111111-1-1-1-11-1-1111-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-11-1-1111-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-11
χ111111111111111111-1-1-1-11-1-1111-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111-11
χ121111111111111111-1-1-1-11-1-1111-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-11111-1-11-1
χ131111111111111111-1-1-1-11-1-11-1-111-111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-11
χ141111111111111111-1-1-1-11-1-11-1-111-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111-1
χ151111111111111111-1-1-1-11-1-11-1-111-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111-1
χ161111111111111111-1-1-1-11-1-11-1-111-111-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1-11
χ1722222222222-2-2-22-222-2-2-222-222-2-2-222-2-200000000000000000000000000
χ1822222222222-2-2-22-222-2-2-222-2-2-222-2-2-22200000000000000000000000000
χ1922222222222-2-2-22-2-2-222-2-2-2-222222-2-2-2-200000000000000000000000000
χ2022222222222-2-2-22-2-2-222-2-2-2-2-2-2-2-22222200000000000000000000000000
χ2122222222-2-2-2222-2222-2-2-2-2-2-2000020000000000002-2-2200000000000000
χ2222222222-2-2-2222-2222-2-2-2-2-2-200002000000000000-222-200000000000000
χ2322222222-2-2-2222-22-2-222-222-20000-20000000000002-22-200000000000000
χ2422222222-2-2-2222-22-2-222-222-20000-2000000000000-22-2200000000000000
χ2522222222-2-2-2-2-2-2-2-222222-2-220000-200000000000000002-22-20000000000
χ2622222222-2-2-2-2-2-2-2-222222-2-220000-20000000000000000-22-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000200000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000020000000000000000-222-20000000000
χ29222-22-2-2-22-2-2000202-20002-20002i−2i0002i−2i22−2−222−2−200000000i2−i2i2−i2000000
χ30222-22-2-2-22-2-2000202-20002-20002i−2i0002i−2i−2−222−2−22200000000−i2i2−i2i2000000
χ31222-22-2-2-22-2-2000202-20002-2000−2i2i000−2i2i22−2−222−2−200000000−i2i2−i2i2000000
χ32222-22-2-2-22-2-2000202-20002-2000−2i2i000−2i2i−2−222−2−22200000000i2−i2i2−i2000000
χ33222-22-2-2-22-2-200020-22000-220002i−2i000−2i2i22−2−2−2−22200000000−i2i2i2−i2000000
χ34222-22-2-2-22-2-200020-22000-220002i−2i000−2i2i−2−22222−2−200000000i2−i2−i2i2000000
χ35222-22-2-2-22-2-200020-22000-22000−2i2i0002i−2i22−2−2−2−22200000000i2−i2−i2i2000000
χ36222-22-2-2-22-2-200020-22000-22000−2i2i0002i−2i−2−22222−2−200000000−i2i2i2−i2000000
χ37444-44-4-4-4-444000-404-4000-44000000000000000000000000000000000000
χ38444-44-4-4-4-444000-40-440004-4000000000000000000000000000000000000
χ3944-44-44-4-444-4000-40000000004-4000000000000000000000000000000000
χ4044-44-44-4-444-4000-4000000000-44000000000000000000000000000000000
χ4144-44-44-4-4-4-440004000000000000004i−4i0000000000000000000000000000
χ4244-44-44-4-4-4-44000400000000000000−4i4i0000000000000000000000000000
χ4344-4-4-4-4444-4444-4-4-40000400-400000000000000000000000000000000000
χ4444-4-4-4-4444-44-4-44-440000-400400000000000000000000000000000000000
χ4544-4-4-4-444-44-444-44-40000-400400000000000000000000000000000000000
χ4644-4-4-4-444-44-4-4-44440000400-400000000000000000000000000000000000
χ474-44-4-44-440004-440-400000000000000000000000000000000000002i2−2i20000
χ484-44-4-44-440004-440-40000000000000000000000000000000000000−2i22i20000
χ494-44-4-44-44000-44-40400000000000000000000000000000000000000022−2200
χ504-44-4-44-44000-44-404000000000000000000000000000000000000000−222200
χ514-4-444-4-440004-4-4040000000000000000022−2222−220000000000000000000000
χ524-4-444-4-440004-4-40400000000000000000−2222−22220000000000000000000000
χ534-4-444-4-44000-4440-40000000000000000000002i2−2i22i2−2i2000000000000000000
χ544-4-444-4-44000-4440-4000000000000000000000−2i22i2−2i22i2000000000000000000
χ554-4-4-4444-400000000004i−4i00000000000002-2-222i−2i−2i2i000000000000000000
χ564-4-4-4444-400000000004i−4i0000000000000-222-2−2i2i2i−2i000000000000000000
χ574-4-4-4444-40000000000−4i4i00000000000002-2-22−2i2i2i−2i000000000000000000
χ584-4-4-4444-40000000000−4i4i0000000000000-222-22i−2i−2i2i000000000000000000
χ598-888-8-88-8000000000000000000000000000000000000000000000000000

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