Finite Group Databasebeta

← Group #329081

Character table — Group #329081

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444444444448888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-11111-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-111-1-1-1-111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111111-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11-1
χ101111111111111-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-11
χ111111111111111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ121111111111111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111-1-1-111-1-1-1-1111111-1-111-1-1-1-1111-1
χ131111111111111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-11
χ141111111111111-1-1-1-11111-1-1-1-11-1-111-1-11111-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-11-1
χ151111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111-1-111-111111111-1-1-1-1-1-111-1-111-1-1111-1
χ161111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111-1-111-11111-1-1-1-11111-1-11111-1-111-1-1-11
χ172222222222-2-2-2222222-2-222-2-2-22200-2-2-2-20000-222000000000000000000000000
χ182222222222-2-2-2222222-2-222-2-2-2-2-20022220000-2-2-2000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-2-222-22200-2-22200002-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-2-222-2-2-20022-2-20000222000000000000000000000000
χ2122222222-2-22222222-2-22-2-2-222-200220000-2-2-2-2-200220000000000000000000000
χ2222222222-2-22222222-2-22-2-2-222-200-2-200002222-200-2-20000000000000000000000
χ2322222222-2-2222-2-2-2-2-2-22-222-2-2-200220000-2-222200-2-20000000000000000000000
χ2422222222-2-2222-2-2-2-2-2-22-222-2-2-200-2-2000022-2-2200220000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-22-2-2-2-2200000000000020000000000002-22-20000000000
χ2622222222-2-2-2-2-22222-2-2-22-2-2-2-220000000000002000000000000-22-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000-20000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000-2000000000000-222-20000000000
χ2922-22-2-22-22-20002i2i−2i−2i2-2002i−2i0002-2000000000002i−2i0022−2−2i2i2−i2−i2000000002−2i2−i200
χ3022-22-2-22-22-20002i2i−2i−2i2-2002i−2i0002-2000000000002i−2i00−2−222−i2−i2i2i200000000−22−i2i200
χ3122-22-2-22-22-20002i2i−2i−2i2-2002i−2i000-2200000000000−2i2i0022−2−2i2i2−i2−i200000000−22−i2i200
χ3222-22-2-22-22-20002i2i−2i−2i2-2002i−2i000-2200000000000−2i2i00−2−222−i2−i2i2i2000000002−2i2−i200
χ3322-22-2-22-22-2000−2i−2i2i2i2-200−2i2i0002-200000000000−2i2i0022−2−2−i2−i2i2i2000000002−2−i2i200
χ3422-22-2-22-22-2000−2i−2i2i2i2-200−2i2i0002-200000000000−2i2i00−2−222i2i2−i2−i200000000−22i2−i200
χ3522-22-2-22-22-2000−2i−2i2i2i2-200−2i2i000-22000000000002i−2i0022−2−2−i2−i2i2i200000000−22i2−i200
χ3622-22-2-22-22-2000−2i−2i2i2i2-200−2i2i000-22000000000002i−2i00−2−222i2i2−i2−i2000000002−2−i2i200
χ372-2-222-2-220022-22-22-200-20002-20000000002-22-200000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2000000
χ382-2-222-2-220022-22-22-200-20002-20000000002-22-200000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2000000
χ392-2-222-2-220022-22-22-200-20002-2000000000-22-2200000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2000000
χ402-2-222-2-220022-22-22-200-20002-2000000000-22-2200000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2000000
χ412-2-222-2-220022-2-22-2200-2000-220000000002-2-2200000i2−i2i2−i2−i2i2−i2i20000i2−i2−i2i2000000
χ422-2-222-2-220022-2-22-2200-2000-220000000002-2-2200000−i2i2−i2i2i2−i2i2−i20000−i2i2i2−i2000000
χ432-2-222-2-220022-2-22-2200-2000-22000000000-222-200000i2−i2i2−i2−i2i2−i2i20000−i2i2i2−i2000000
χ442-2-222-2-220022-2-22-2200-2000-22000000000-222-200000−i2i2−i2i2i2−i2i2−i20000i2−i2−i2i2000000
χ45444-44-4-4-4444-440000-4-4-4-400004000000000000000000000000000000000000000
χ46444-44-4-4-444-44-40000-4-4440000-4000000000000000000000000000000000000000
χ47444-44-4-4-4-4-44-44000044-440000-4000000000000000000000000000000000000000
χ48444-44-4-4-4-4-4-44-40000444-400004000000000000000000000000000000000000000
χ4944-44-4-44-4-440004i4i−4i−4i-4400−4i4i000000000000000000000000000000000000000000
χ5044-44-4-44-4-44000−4i−4i4i4i-44004i−4i000000000000000000000000000000000000000000
χ5144-4-4-44-444-40000000-4400000000000004i−4i0000000000000000000000000000000
χ5244-4-4-44-444-40000000-440000000000000−4i4i0000000000000000000000000000000
χ5344-4-4-44-44-4400000004-4000000000004i−4i000000000000000000000000000000000
χ5444-4-4-44-44-4400000004-400000000000−4i4i000000000000000000000000000000000
χ554-444-44-4-4000004i−4i−4i4i000000000000000000000000002i−2i−2i2i-222-200000000000000
χ564-444-44-4-4000004i−4i−4i4i00000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ574-444-44-4-400000−4i4i4i−4i000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ584-444-44-4-400000−4i4i4i−4i00000000000000000000000000−2i2i2i−2i-222-200000000000000
χ594-4-444-4-4400-4-444-44-4004000-440000000000000000000000000000000000000000
χ604-4-444-4-4400-4-44-44-440040004-40000000000000000000000000000000000000000
χ614-4-4-4444-4004-4-400000040000000000000000000004-40000000000000000000000
χ624-4-4-4444-4004-4-40000004000000000000000000000-440000000000000000000000
χ634-4-4-4444-400-444000000-4000000004i−4i00000000000000000000000000000000000
χ644-4-4-4444-400-444000000-400000000−4i4i00000000000000000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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