Finite Group Databasebeta

← Group #327009

Character table — Group #327009

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444224444444444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-111111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-11111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-11
χ111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-11
χ121111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-111-1-1-1-1111111-1-111-1-111-1-1-11
χ1722222222222222-2-222-2-222-2-2-2-22222-2-20000-2-2-200000000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2-2-2220000-22200000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-222-2-222-2-22200002-2-200000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-222-2-2-2-222-2-2000022200000000000000000000000000
χ2122222222-2-2222222-2-222-2-222-2-200000022-2-2-200-2-2220000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2000000-2-222-20022-2-20000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-22200000000002000000000000002-22-20000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2220000000000200000000000000-22-220000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-2-20000002222200-2-2-2-20000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2000000-2-2-2-220022220000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000-2000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000-200000000000000-222-20000000000
χ29222-2-2-2-22002i2i−2i−2i2-2002-2002i−2i00000000002i−2i0002-200i2i2−i2−i222−2−200000000i2−i22−200
χ30222-2-2-2-22002i2i−2i−2i2-2002-2002i−2i00000000002i−2i0002-200−i2−i2i2i2−2−22200000000−i2i2−2200
χ31222-2-2-2-22002i2i−2i−2i2-2002-2002i−2i0000000000−2i2i000-2200i2i2−i2−i222−2−200000000−i2i2−2200
χ32222-2-2-2-22002i2i−2i−2i2-2002-2002i−2i0000000000−2i2i000-2200−i2−i2i2i2−2−22200000000i2−i22−200
χ33222-2-2-2-2200−2i−2i2i2i2-2002-200−2i2i00000000002i−2i000-2200i2i2−i2−i2−2−22200000000−i2i22−200
χ34222-2-2-2-2200−2i−2i2i2i2-2002-200−2i2i00000000002i−2i000-2200−i2−i2i2i222−2−200000000i2−i2−2200
χ35222-2-2-2-2200−2i−2i2i2i2-2002-200−2i2i0000000000−2i2i0002-200i2i2−i2−i2−2−22200000000i2−i2−2200
χ36222-2-2-2-2200−2i−2i2i2i2-2002-200−2i2i0000000000−2i2i0002-200−i2−i2i2i222−2−200000000−i2i22−200
χ372-2222-2-2-2-2-22-22-20022002-2000000002i−2i000002i−2i0000i2−i2i2−i2i2−i2i2−i200002−22−2000000
χ382-2222-2-2-2-2-22-22-20022002-2000000002i−2i000002i−2i0000−i2i2−i2i2−i2i2−i2i20000−22−22000000
χ392-2222-2-2-2-2-22-22-20022002-200000000−2i2i00000−2i2i0000i2−i2i2−i2i2−i2i2−i20000−22−22000000
χ402-2222-2-2-2-2-22-22-20022002-200000000−2i2i00000−2i2i0000−i2i2−i2i2−i2i2−i2i200002−22−2000000
χ412-2222-2-2-2-2-2-22-22002200-22000000002i−2i00000−2i2i0000i2−i2i2−i2−i2i2−i2i20000−222−2000000
χ422-2222-2-2-2-2-2-22-22002200-22000000002i−2i00000−2i2i0000−i2i2−i2i2i2−i2i2−i200002−2−22000000
χ432-2222-2-2-2-2-2-22-22002200-2200000000−2i2i000002i−2i0000i2−i2i2−i2−i2i2−i2i200002−2−22000000
χ442-2222-2-2-2-2-2-22-22002200-2200000000−2i2i000002i−2i0000−i2i2−i2i2i2−i2i2−i20000−222−2000000
χ45444-4-4-4-44004i4i−4i−4i-4400-4400−4i4i00000000000000000000000000000000000000000
χ46444-4-4-4-4400−4i−4i4i4i-4400-44004i−4i00000000000000000000000000000000000000000
χ4744-44-44-4-44-40000004-400000000004-400000000000000000000000000000000000
χ4844-44-44-4-44-40000004-40000000000-4400000000000000000000000000000000000
χ4944-44-44-4-4-44000000-44000000004-40000000000000000000000000000000000000
χ5044-44-44-4-4-44000000-4400000000-440000000000000000000000000000000000000
χ514-4444-4-4-4444-44-400-4-400-440000000000000000000000000000000000000000000
χ524-4444-4-4-444-44-4400-4-4004-40000000000000000000000000000000000000000000
χ534-44-4-444-4004i−4i−4i4i000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ544-44-4-444-4004i−4i−4i4i00000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ554-44-4-444-400−4i4i4i−4i000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ564-44-4-444-400−4i4i4i−4i00000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ574-4-44-4-4444-400004-4-44-4400004-4000000000000000000000000000000000000000
χ584-4-44-4-4444-40000-44-444-40000-44000000000000000000000000000000000000000
χ594-4-44-4-444-4400004-44-4-440000-44000000000000000000000000000000000000000
χ604-4-44-4-444-440000-444-44-400004-4000000000000000000000000000000000000000
χ614-4-4-444-440000004400-4-40000000000004i−4i0000000000000000000000000000000
χ624-4-4-444-440000004400-4-4000000000000−4i4i0000000000000000000000000000000
χ634-4-4-444-44000000-4-400440000000000000000000004-40000000000000000000000
χ644-4-4-444-44000000-4-40044000000000000000000000-440000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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