Finite Group Databasebeta

← Group #267175

Character table — Group #267175

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442222224444444444888888884444488888888888822228888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-11
χ611111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111-1
χ711111111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1111-1
χ811111111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-11
χ91111111111111111-1-1-1-11111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-11111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ121111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111
χ131111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-11
χ141111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-11-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-111-1-111-1-11-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-111-1-111-1-111-11
χ172222222222-2-22-2-22222222-2-2-2-2-2-222-2-200000000-222-2-200000000000000000000000000
χ182222222222-2-22-2-222222-2-2-2-2-2-2-2-2-2-222000000002-2-22200000000000000000000000000
χ192222222222-2-22-2-22-2-2-2-222-2-2222222-2-200000000-2-2-22200000000000000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-2-2-22222-2-22200000000222-2-200000000000000000000000000
χ2122222222-2-222-222-2000022-2-20000-2-2-2-22222-2-2-2-220000-2-2220000000000000000000000
χ2222222222-2-222-222-2000022-2-20000-2-2-2-2-2-2-2-222222000022-2-20000000000000000000000
χ2322222222-2-222-222-20000-2-2-2-20000222222222222-20000-2-2-2-20000000000000000000000
χ2422222222-2-222-222-20000-2-2-2-200002222-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022220000-2-22200000000-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2000022220000-2-22200000000-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-222000022-2-2000000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-222000022-2-200000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-2-222-2-22200-200-200002-2002i2i−2i−2i2-20022−2−222−2−20002i−2i2−22−2i2−i2i2−i2i2−i2i2−i200000000000000
χ3022-2-222-2-22200-200-200002-2002i2i−2i−2i2-200−2−222−2−2220002i−2i−22−22−i2i2−i2i2−i2i2−i2i200000000000000
χ3122-2-222-2-22200-200-200002-200−2i−2i2i2i2-20022−2−222−2−2000−2i2i2−22−2−i2i2−i2i2−i2i2−i2i200000000000000
χ3222-2-222-2-22200-200-200002-200−2i−2i2i2i2-200−2−222−2−222000−2i2i−22−22i2−i2i2−i2i2−i2i2−i200000000000000
χ3322-2-222-2-22200-200-20000-22002i2i−2i−2i-220022−2−2−2−222000−2i2i2−2−22i2−i2i2−i2−i2i2−i2i200000000000000
χ3422-2-222-2-22200-200-20000-22002i2i−2i−2i-2200−2−22222−2−2000−2i2i−222−2−i2i2−i2i2i2−i2i2−i200000000000000
χ3522-2-222-2-22200-200-20000-2200−2i−2i2i2i-220022−2−2−2−2220002i−2i2−2−22−i2i2−i2i2i2−i2i2−i200000000000000
χ3622-2-222-2-22200-200-20000-2200−2i−2i2i2i-2200−2−22222−2−20002i−2i−222−2i2−i2i2−i2−i2i2−i2i200000000000000
χ3722-2-222-2-2-2-200200222-2-22-2000000-220022−2−2−2−22202-200−222−22−2−222−2−2200000000000000
χ3822-2-222-2-2-2-200200222-2-22-2000000-2200−2−22222−2−202-2002−2−22−222−2−222−200000000000000
χ3922-2-222-2-2-2-200200222-2-2-220000002-20022−2−222−2−20-2200−22−222−2−22−222−200000000000000
χ4022-2-222-2-2-2-200200222-2-2-220000002-200−2−222−2−2220-22002−22−2−222−22−2−2200000000000000
χ4122-2-222-2-2-2-2002002-2-2222-2000000-220022−2−2−2−2220-2200−222−2−222−2−222−200000000000000
χ4222-2-222-2-2-2-2002002-2-2222-2000000-2200−2−22222−2−20-22002−2−222−2−222−2−2200000000000000
χ4322-2-222-2-2-2-2002002-2-222-220000002-20022−2−222−2−202-200−22−22−222−22−2−2200000000000000
χ4422-2-222-2-2-2-2002002-2-222-220000002-200−2−222−2−22202-2002−22−22−2−22−222−200000000000000
χ452-2-2-22-2222-22-2-22-222-22-2002-22-22-200000000000000000000000000000002-200002-20000
χ462-2-2-22-2222-22-2-22-222-22-2002-22-22-20000000000000000000000000000000-220000-220000
χ472-2-2-22-2222-22-2-22-22-22-22002-2-22-2200000000000000000000000000000002-20000-220000
χ482-2-2-22-2222-22-2-22-22-22-22002-2-22-220000000000000000000000000000000-2200002-20000
χ492-2-2-22-2222-2-22-2-2222-22-200-22-22-22000000000000000000000000000002-200002-2000000
χ502-2-2-22-2222-2-22-2-2222-22-200-22-22-2200000000000000000000000000000-220000-22000000
χ512-2-2-22-2222-2-22-2-222-22-2200-222-22-2000000000000000000000000000002-20000-22000000
χ522-2-2-22-2222-2-22-2-222-22-2200-222-22-200000000000000000000000000000-2200002-2000000
χ53444-4-4-44-400440-4-400000000000000000000000000000000000000000000002i2−2i200000000
χ54444-4-4-44-400440-4-40000000000000000000000000000000000000000000000−2i22i200000000
χ55444-4-4-44-400-4-4044000000000000000000000000000000000000000000000000000022−2200
χ56444-4-4-44-400-4-40440000000000000000000000000000000000000000000000000000−222200
χ574-4444-4-4-44-400400-4000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ584-4444-4-4-44-400400-400000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ594-4444-4-4-4-4400-40044-4-44000000000000000000000000000000000000000000000000000
χ604-4444-4-4-4-4400-4004-444-4000000000000000000000000000000000000000000000000000
χ614-44-4-44-4400000000000000000000004-422−2222−2222−2222−220000000000000000000000000000000
χ624-44-4-44-4400000000000000000000004-4−2222−2222−2222−22220000000000000000000000000000000
χ634-44-4-44-440000000000000000000000-4422−2222−22−2222−22220000000000000000000000000000000
χ644-44-4-44-440000000000000000000000-44−2222−222222−2222−220000000000000000000000000000000
χ654-4-44-444-4004-40-440000000000000000000004-4-440000000000000000000000000000000
χ664-4-44-444-4004-40-44000000000000000000000-444-40000000000000000000000000000000
χ674-4-44-444-400-4404-4000000000000000004-4-4400000000000000000000000000000000000
χ684-4-44-444-400-4404-400000000000000000-444-400000000000000000000000000000000000
χ694-4-4-44-444-444-444-4-4000000-4400000000000000000000000000000000000000000000000
χ704-4-4-44-444-44-444-44-40000004-400000000000000000000000000000000000000000000000
χ7188-88-8-8-88000000000000000000000000000000000000000000000000000000000000000

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