Finite Group Databasebeta

← Group #267151

Character table — Group #267151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888884444488888888888822448888888824
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
χ511111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ91111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-11
χ101111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1
χ111111111111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111-1
χ121111111111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-11
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-11111-1-1-1-11-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-111-1-1-1-11111-11
χ17222222222-2-222-2-2222-2-22222-2-2-2-2-2-2-2-200000000222-2-200000000000000000000000000
χ18222222222-2-222-2-2222-2-2-2-2-2-2-2-2-2-22222000000002-2-22200000000000000000000000000
χ19222222222-2-222-2-22-2-2222222-2-222-2-2-2-200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-222-2-2-2-2-2-222222200000000-222-2-200000000000000000000000000
χ2122222222-222-2-222-222220000-2-2-2-2000022222222-20000-2-2-2-20000000000000000000000
χ2222222222-222-2-222-222220000-2-2-2-20000-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2322222222-222-2-222-2-2-2-2-20000-2-22200002222-2-2-2-220000-2-2220000000000000000000000
χ2422222222-222-2-222-2-2-2-2-20000-2-2220000-2-2-2-222222000022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-200002222000000000000-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-200002222000000000000-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222000022-2-20000000000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222000022-2-2000000000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-22-2200-2-2002002i−2i22-2-2002i−2i0000i2i2−i2−i222−2−20002i−2ii2−i22−2i2−i2i2−i22−22−200000000000000
χ30222-2-2-22-2200-2-2002002i−2i22-2-2002i−2i0000−i2−i2i2i2−2−2220002i−2i−i2i2−22−i2i2−i2i2−22−2200000000000000
χ31222-2-2-22-2200-2-2002002i−2i-2-222002i−2i0000i2i2−i2−i222−2−2000−2i2ii2−i22−2−i2i2−i2i2−22−2200000000000000
χ32222-2-2-22-2200-2-2002002i−2i-2-222002i−2i0000−i2−i2i2i2−2−222000−2i2i−i2i2−22i2−i2i2−i22−22−200000000000000
χ33222-2-2-22-2200-2-200200−2i2i22-2-200−2i2i0000i2i2−i2−i2−2−222000−2i2ii2−i2−22i2−i2i2−i2−22−2200000000000000
χ34222-2-2-22-2200-2-200200−2i2i22-2-200−2i2i0000−i2−i2i2i222−2−2000−2i2i−i2i22−2−i2i2−i2i22−22−200000000000000
χ35222-2-2-22-2200-2-200200−2i2i-2-22200−2i2i0000i2i2−i2−i2−2−2220002i−2ii2−i2−22−i2i2−i2i22−22−200000000000000
χ36222-2-2-22-2200-2-200200−2i2i-2-22200−2i2i0000−i2−i2i2i222−2−20002i−2i−i2i22−2i2−i2i2−i2−22−2200000000000000
χ37222-2-2-22-2-2002200-2002i−2i000000−2i2i2i2i−2i−2ii2i2−i2−i222−2−202-200−i2i2−222−2−22i2−i2−i2i200000000000000
χ38222-2-2-22-2-2002200-2002i−2i000000−2i2i2i2i−2i−2i−i2−i2i2i2−2−22202-200i2−i22−2−222−2−i2i2i2−i200000000000000
χ39222-2-2-22-2-2002200-2002i−2i000000−2i2i−2i−2i2i2ii2i2−i2−i222−2−20-2200−i2i2−22−222−2−i2i2i2−i200000000000000
χ40222-2-2-22-2-2002200-2002i−2i000000−2i2i−2i−2i2i2i−i2−i2i2i2−2−2220-2200i2−i22−22−2−22i2−i2−i2i200000000000000
χ41222-2-2-22-2-2002200-200−2i2i0000002i−2i2i2i−2i−2ii2i2−i2−i2−2−2220-2200−i2i22−22−2−22−i2i2i2−i200000000000000
χ42222-2-2-22-2-2002200-200−2i2i0000002i−2i2i2i−2i−2i−i2−i2i2i222−2−20-2200i2−i2−22−222−2i2−i2−i2i200000000000000
χ43222-2-2-22-2-2002200-200−2i2i0000002i−2i−2i−2i2i2ii2i2−i2−i2−2−22202-200−i2i22−2−222−2i2−i2−i2i200000000000000
χ44222-2-2-22-2-2002200-200−2i2i0000002i−2i−2i−2i2i2i−i2−i2i2i222−2−202-200i2−i2−222−2−22−i2i2i2−i200000000000000
χ452-2-2-22-222-22-22-22-2200002-22-22-2002-22-20000000000000000000000000002-22-200000000
χ462-2-2-22-222-22-22-22-2200002-22-22-2002-22-2000000000000000000000000000-22-2200000000
χ472-2-2-22-222-22-22-22-220000-22-222-200-22-220000000000000000000000000002-2-2200000000
χ482-2-2-22-222-22-22-22-220000-22-222-200-22-22000000000000000000000000000-222-200000000
χ492-2-2-22-222-2-222-2-22200002-22-2-2200-22-2200000000000000000000000002-20000002-20000
χ502-2-2-22-222-2-222-2-22200002-22-2-2200-22-220000000000000000000000000-22000000-220000
χ512-2-2-22-222-2-222-2-2220000-22-22-22002-22-200000000000000000000000002-2000000-220000
χ522-2-2-22-222-2-222-2-2220000-22-22-22002-22-20000000000000000000000000-220000002-20000
χ5344-444-4-4-404400-4-40000000000000000000004-44-40000000000000000000000000000000
χ5444-444-4-4-404400-4-4000000000000000000000-44-440000000000000000000000000000000
χ5544-444-4-4-40-4-40044000000000000000004i−4i4i−4i00000000000000000000000000000000000
χ5644-444-4-4-40-4-4004400000000000000000−4i4i−4i4i00000000000000000000000000000000000
χ5744-4-4-44-44000000004-40000000000000022−22−222222−22−22220000000000000000000000000000000
χ5844-4-4-44-44000000004-400000000000000−222222−22−222222−220000000000000000000000000000000
χ5944-4-4-44-4400000000-440000000000000022−22−2222−222222−220000000000000000000000000000000
χ6044-4-4-44-4400000000-4400000000000000−222222−2222−22−22220000000000000000000000000000000
χ614-44-444-4-404-400-440000000000000000000000000000000000000000000000002i2−2i2000000
χ624-44-444-4-404-400-44000000000000000000000000000000000000000000000000−2i22i2000000
χ634-44-444-4-40-44004-400000000000000000000000000000000000000000000000000002i2−2i200
χ644-44-444-4-40-44004-40000000000000000000000000000000000000000000000000000−2i22i200
χ654-4-44-444-44004-400-40000000000004i−4i−4i4i000000000000000000000000000000000000000
χ664-4-44-444-44004-400-4000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ674-4-44-444-4-400-4400400004-4-4400000000000000000000000000000000000000000000000
χ684-4-44-444-4-400-440040000-444-400000000000000000000000000000000000000000000000
χ694-4-4-44-44444-4-444-4-400000000-44000000000000000000000000000000000000000000000
χ704-4-4-44-4444-44-44-44-4000000004-4000000000000000000000000000000000000000000000
χ718-888-8-8-88000000000000000000000000000000000000000000000000000000000000000

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