Finite Group Databasebeta

← Group #279352

Character table — Group #279352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888884444488888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11-1
χ9111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111111111-1-111-1-111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-11111-1-1-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-111-1-1-1-111111-1
χ172222222222-22-2-2-22-2-2000022220000-2-222222222-20000-2-20000-2-2000000000000000000
χ182222222222-22-2-2-22-2-2000022220000-2-2-2-2-2-2-2-2-2-2-2000022000022000000000000000000
χ192222222222-22-2-2-22-2-20000-2-2-2-20000222222-2-2-2-220000-2-2000022000000000000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-2000022-2-2-2-2222220000220000-2-2000000000000000000
χ2122222222-2-22-2222-2-2-2222222-2-2-2-2-2-22200000000-222-2-200000000000000000000000000
χ2222222222-2-22-2222-2-2-22222-2-222-2-2-2-2-2-2000000002-2-22200000000000000000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-222-2-222222200000000-2-2-22200000000000000000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2-2-2222222-2-200000000222-2-200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222000022-2-20000-2-20000000020000002i2i−2i−2i002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222000022-2-20000-2-2000000002000000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2220000-2-22200002200000000-20000002i2i−2i−2i00−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2220000-2-22200002200000000-2000000−2i−2i2i2i002i2i−2i−2i00000000000000
χ29222-2-2-22-2222-22-2-2-22-222-2-2000022-2-2000000000000000000000000000002-22-200000000
χ30222-2-2-22-2222-22-2-2-22-222-2-2000022-2-200000000000000000000000000000-22-2200000000
χ31222-2-2-22-2222-22-2-2-22-2-2-2220000-2-222000000000000000000000000000002-2-2200000000
χ32222-2-2-22-2222-22-2-2-22-2-2-2220000-2-22200000000000000000000000000000-222-200000000
χ33222-2-2-22-2-2-2222-2-22-2222-2-20000-2-2220000000000000000000000000002i−2i0000002i−2i0000
χ34222-2-2-22-2-2-2222-2-22-2222-2-20000-2-222000000000000000000000000000−2i2i000000−2i2i0000
χ35222-2-2-22-2-2-2222-2-22-22-2-222000022-2-20000000000000000000000000002i−2i000000−2i2i0000
χ36222-2-2-22-2-2-2222-2-22-22-2-222000022-2-2000000000000000000000000000−2i2i0000002i−2i0000
χ372-2-222-22-20020-2-220002i−2i2i−2i2i−2i0000002i−2ii2i2−i2−i222−2−202-200i2−i22−22−22−2i2−i2i2−i200000000000000
χ382-2-222-22-20020-2-220002i−2i2i−2i2i−2i0000002i−2i−i2−i2i2i2−2−22202-200−i2i2−22−22−22−i2i2−i2i200000000000000
χ392-2-222-22-20020-2-220002i−2i2i−2i−2i2i000000−2i2ii2i2−i2−i2−2−2220-2200i2−i22−22−2−22−i2i2−i2i200000000000000
χ402-2-222-22-20020-2-220002i−2i2i−2i−2i2i000000−2i2i−i2−i2i2i222−2−20-2200−i2i2−22−222−2i2−i2i2−i200000000000000
χ412-2-222-22-20020-2-22000−2i2i−2i2i2i−2i0000002i−2ii2i2−i2−i222−2−20-2200i2−i2−22−222−2−i2i2−i2i200000000000000
χ422-2-222-22-20020-2-22000−2i2i−2i2i2i−2i0000002i−2i−i2−i2i2i2−2−2220-2200−i2i22−22−2−22i2−i2i2−i200000000000000
χ432-2-222-22-20020-2-22000−2i2i−2i2i−2i2i000000−2i2ii2i2−i2−i2−2−22202-200i2−i2−22−22−22i2−i2i2−i200000000000000
χ442-2-222-22-20020-2-22000−2i2i−2i2i−2i2i000000−2i2i−i2−i2i2i222−2−202-200−i2i22−22−22−2−i2i2−i2i200000000000000
χ452-2-222-22-200-2022-200000002i−2i002-22-2−2i2ii2i2−i2−i222−2−20002i−2i−i2i2i2−i2−i2i2−22−222−200000000000000
χ462-2-222-22-200-2022-200000002i−2i002-22-2−2i2i−i2−i2i2i2−2−2220002i−2ii2−i2−i2i2i2−i22−22−2−2200000000000000
χ472-2-222-22-200-2022-200000002i−2i00-22-22−2i2ii2i2−i2−i222−2−2000−2i2i−i2i2−i2i2i2−i2−222−2−2200000000000000
χ482-2-222-22-200-2022-200000002i−2i00-22-22−2i2i−i2−i2i2i2−2−222000−2i2ii2−i2i2−i2−i2i22−2−222−200000000000000
χ492-2-222-22-200-2022-20000000−2i2i002-22-22i−2ii2i2−i2−i2−2−222000−2i2i−i2i2i2−i2−i2i22−22−2−2200000000000000
χ502-2-222-22-200-2022-20000000−2i2i002-22-22i−2i−i2−i2i2i222−2−2000−2i2ii2−i2−i2i2i2−i2−22−222−200000000000000
χ512-2-222-22-200-2022-20000000−2i2i00-22-222i−2ii2i2−i2−i2−2−2220002i−2i−i2i2−i2i2i2−i22−2−222−200000000000000
χ522-2-222-22-200-2022-20000000−2i2i00-22-222i−2i−i2−i2i2i222−2−20002i−2ii2−i2i2−i2−i2i2−222−2−2200000000000000
χ53444-4-4-44-444-4-4-444-4-4400000000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-4-44-44444-400000000000000000000000000000000000000000000000000000
χ5544-44-4-4-444-404000-40000000000000000000000000000000000000000000000022−22000000
χ5644-44-4-4-444-404000-400000000000000000000000000000000000000000000000−2222000000
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
χ634-44-44-4-4400000000000000004-40000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000
χ644-44-44-4-4400000000000000004-4000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000
χ654-44-44-4-440000000000000000-440000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ664-44-44-4-440000000000000000-44000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ674-4-4-4-44440040-44-40004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ684-4-4-4-44440040-44-4000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ694-4-4-4-444400-404-44000000000004-4-4400000000000000000000000000000000000000000
χ704-4-4-4-444400-404-4400000000000-444-400000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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