Finite Group Databasebeta

← Group #279348

Character table — Group #279348

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888884444488888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11-1
χ9111111111111111111-1-1-1-1111111-1-1-1-111111111-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-11111-1-1
χ12111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ172222222222-22-2-2-22-2-2000022-2-2-2-200002222-2-2-2-200200-2-2000022000000000000000000
χ182222222222-22-2-2-22-2-2000022-2-2-2-20000-2-2-2-2222200200220000-2-2000000000000000000
χ192222222222-22-2-2-22-2-20000-2-2222200002222222200-200-2-20000-2-2000000000000000000
χ202222222222-22-2-2-22-2-20000-2-222220000-2-2-2-2-2-2-2-200-20022000022000000000000000000
χ2122222222-2-22-2222-2-2-222222222-2-2-2-2-2-200000000-2-2-22200000000000000000000000000
χ2222222222-2-22-2222-2-2-22222-2-2-2-222-2-2-2-200000000222-2-200000000000000000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-22222-2-222220000000022-2-2-200000000000000000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2-2-2-2-222222200000000-2-222200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222000022-2-22200000000000000-200002i2i−2i−2i002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222000022-2-22200000000000000-20000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2220000-2-222-2-200000000000000200002i2i−2i−2i00−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2220000-2-222-2-20000000000000020000−2i−2i2i2i002i2i−2i−2i00000000000000
χ29222-2-2-22-2222-22-2-2-22-222-2-200000022-2-20000000000000000000000000002-2002-2000000
χ30222-2-2-22-2222-22-2-2-22-222-2-200000022-2-2000000000000000000000000000-2200-22000000
χ31222-2-2-22-2222-22-2-2-22-2-2-222000000-2-2220000000000000000000000000002-200-22000000
χ32222-2-2-22-2222-22-2-2-22-2-2-222000000-2-222000000000000000000000000000-22002-2000000
χ33222-2-2-22-2-2-2222-2-22-2222-2-2000000-2-22200000000000000000000000002i−2i002i−2i00000000
χ34222-2-2-22-2-2-2222-2-22-2222-2-2000000-2-2220000000000000000000000000−2i2i00−2i2i00000000
χ35222-2-2-22-2-2-2222-2-22-22-2-22200000022-2-200000000000000000000000002i−2i00−2i2i00000000
χ36222-2-2-22-2-2-2222-2-22-22-2-22200000022-2-20000000000000000000000000−2i2i002i−2i00000000
χ372-2-222-22-20020-2-220002i−2i2i−2i2-22-2000000i2i2−i2−i2i2i2−i2−i20002i−2ii2−i22−22−2i2−i22−22−200000000000000
χ382-2-222-22-20020-2-220002i−2i2i−2i2-22-2000000−i2−i2i2i2−i2−i2i2i20002i−2i−i2i2−22−22−i2i2−22−2200000000000000
χ392-2-222-22-20020-2-220002i−2i2i−2i-22-22000000i2i2−i2−i2−i2−i2i2i2000−2i2ii2−i22−22−2−i2i2−22−2200000000000000
χ402-2-222-22-20020-2-220002i−2i2i−2i-22-22000000−i2−i2i2i2i2i2−i2−i2000−2i2i−i2i2−22−22i2−i22−22−200000000000000
χ412-2-222-22-20020-2-22000−2i2i−2i2i2-22-2000000i2i2−i2−i2i2i2−i2−i2000−2i2ii2−i2−22−22i2−i2−22−2200000000000000
χ422-2-222-22-20020-2-22000−2i2i−2i2i2-22-2000000−i2−i2i2i2−i2−i2i2i2000−2i2i−i2i22−22−2−i2i22−22−200000000000000
χ432-2-222-22-20020-2-22000−2i2i−2i2i-22-22000000i2i2−i2−i2−i2−i2i2i20002i−2ii2−i2−22−22−i2i22−22−200000000000000
χ442-2-222-22-20020-2-22000−2i2i−2i2i-22-22000000−i2−i2i2i2i2i2−i2−i20002i−2i−i2i22−22−2i2−i2−22−2200000000000000
χ452-2-222-22-200-2022-200000002-2-22002-22-2i2i2−i2−i2−i2−i2i2i22-2000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000
χ462-2-222-22-200-2022-200000002-2-22002-22-2−i2−i2i2i2i2i2−i2−i22-2000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000
χ472-2-222-22-200-2022-200000002-2-2200-22-22i2i2−i2−i2−i2−i2i2i2-22000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i200000000000000
χ482-2-222-22-200-2022-200000002-2-2200-22-22−i2−i2i2i2i2i2−i2−i2-22000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i200000000000000
χ492-2-222-22-200-2022-20000000-222-2002-22-2i2i2−i2−i2i2i2−i2−i2-22000−i2i2i2−i2−i2i2−i2i2−i2i2i2−i200000000000000
χ502-2-222-22-200-2022-20000000-222-2002-22-2−i2−i2i2i2−i2−i2i2i2-22000i2−i2−i2i2i2−i2i2−i2i2−i2−i2i200000000000000
χ512-2-222-22-200-2022-20000000-222-200-22-22i2i2−i2−i2i2i2−i2−i22-2000−i2i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ522-2-222-22-200-2022-20000000-222-200-22-22−i2−i2i2i2−i2−i2i2i22-2000i2−i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ53444-4-4-44-444-4-4-444-4-4400000000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-4-44-44444-400000000000000000000000000000000000000000000000000000
χ5544-44-4-4-444-404000-4000000000000000000000000000000000000000000000000022−220000
χ5644-44-4-4-444-404000-40000000000000000000000000000000000000000000000000−22220000
χ5744-44-4-4-44-440-400040000000000000000000000000000000000000000000000000002i2−2i200
χ5844-44-4-4-44-440-40004000000000000000000000000000000000000000000000000000−2i22i200
χ5944-4-444-4-44-40-40004000000000000000000004i−4i4i−4i0000000000000000000000000000000
χ6044-4-444-4-44-40-4000400000000000000000000−4i4i−4i4i0000000000000000000000000000000
χ6144-4-444-4-4-4404000-400000000000000004-44-400000000000000000000000000000000000
χ6244-4-444-4-4-4404000-40000000000000000-44-4400000000000000000000000000000000000
χ634-44-44-4-440000000000000000004i−4i00002i2−2i2−2i22i222−22−22220000000000000000000000000000000
χ644-44-44-4-440000000000000000004i−4i0000−2i22i22i2−2i2−222222−220000000000000000000000000000000
χ654-44-44-4-44000000000000000000−4i4i00002i2−2i2−2i22i2−222222−220000000000000000000000000000000
χ664-44-44-4-44000000000000000000−4i4i0000−2i22i22i2−2i222−22−22220000000000000000000000000000000
χ674-4-4-4-44440040-44-40004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ684-4-4-4-44440040-44-4000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ694-4-4-4-444400-404-4400000000000004-4-44000000000000000000000000000000000000000
χ704-4-4-4-444400-404-440000000000000-444-4000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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