Finite Group Databasebeta

← Group #288821

Character table — Group #288821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888822224444444488888888888888888824882244
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1
χ611111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11-11
χ711111111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-11-1
χ9111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-11-1-11
χ17222222222-2-2222-2-2-2-20000000022222222-2-2-2-20000-2-2000000000000000000000000
χ18222222222-2-2222-2-2-2-2000000002222-2-2-2-222220000-2-2000000000000000000000000
χ19222222222-2-2222-2-2-2-200000000-2-2-2-222-2-2-2-222000022000000000000000000000000
χ20222222222-2-2222-2-2-2-200000000-2-2-2-2-2-22222-2-2000022000000000000000000000000
χ2122222222-222-2-2-222-2-22222-2-2-2-200000000000022-2-20000000000000000002-2000000
χ2222222222-222-2-2-222-2-22222-2-2-2-2000000000000-2-222000000000000000000-22000000
χ2322222222-222-2-2-222-2-2-2-2-2-2222200000000000022-2-2000000000000000000-22000000
χ2422222222-222-2-2-222-2-2-2-2-2-22222000000000000-2-2220000000000000000002-2000000
χ25222-22-2-2-2200-2-220000i2i2−i2−i2i2i2−i2−i222-2-200002i−2i2i−2i000000000022−2−222−2−2i2i2−i2−i200000000
χ26222-22-2-2-2200-2-220000i2i2−i2−i2i2i2−i2−i222-2-20000−2i2i−2i2i0000000000−2−222−2−222i2i2−i2−i200000000
χ27222-22-2-2-2200-2-220000i2i2−i2−i2i2i2−i2−i2-2-22200002i−2i−2i2i000000000022−2−2−2−222−i2−i2i2i200000000
χ28222-22-2-2-2200-2-220000i2i2−i2−i2i2i2−i2−i2-2-2220000−2i2i2i−2i0000000000−2−22222−2−2−i2−i2i2i200000000
χ29222-22-2-2-2200-2-220000−i2−i2i2i2−i2−i2i2i222-2-200002i−2i2i−2i0000000000−2−222−2−222−i2−i2i2i200000000
χ30222-22-2-2-2200-2-220000−i2−i2i2i2−i2−i2i2i222-2-20000−2i2i−2i2i000000000022−2−222−2−2−i2−i2i2i200000000
χ31222-22-2-2-2200-2-220000−i2−i2i2i2−i2−i2i2i2-2-22200002i−2i−2i2i0000000000−2−22222−2−2i2i2−i2−i200000000
χ32222-22-2-2-2200-2-220000−i2−i2i2i2−i2−i2i2i2-2-2220000−2i2i2i−2i000000000022−2−2−2−222i2i2−i2−i200000000
χ332-2-2222-2-2222-22-2-2-2-222i−2i2i−2i2i−2i2i−2i00000000000000000022-2-2000000000000002i−2i0000
χ342-2-2222-2-2222-22-2-2-2-222i−2i2i−2i2i−2i2i−2i000000000000000000-2-22200000000000000−2i2i0000
χ352-2-2222-2-2222-22-2-2-2-22−2i2i−2i2i−2i2i−2i2i00000000000000000022-2-200000000000000−2i2i0000
χ362-2-2222-2-2222-22-2-2-2-22−2i2i−2i2i−2i2i−2i2i000000000000000000-2-222000000000000002i−2i0000
χ372-2-2222-2-2-2222-22-2-22-22i−2i2i−2i−2i2i−2i2i2-22-20000000000002-20000000000002i−2i2i−2i00000000
χ382-2-2222-2-2-2222-22-2-22-22i−2i2i−2i−2i2i−2i2i-22-22000000000000-22000000000000−2i2i−2i2i00000000
χ392-2-2222-2-2-2222-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-22-20000000000002-2000000000000−2i2i−2i2i00000000
χ402-2-2222-2-2-2222-22-2-22-2−2i2i−2i2i2i−2i2i−2i-22-22000000000000-220000000000002i−2i2i−2i00000000
χ412-2-2222-2-2-2-2-22-2222-22000000002-22-2000000000000-2200002-22-22-22-2000000000000
χ422-2-2222-2-2-2-2-22-2222-22000000002-22-2000000000000-220000-22-22-22-22000000000000
χ432-2-2222-2-2-2-2-22-2222-2200000000-22-220000000000002-200002-22-2-22-22000000000000
χ442-2-2222-2-2-2-2-22-2222-2200000000-22-220000000000002-20000-22-222-22-2000000000000
χ452-2-2-22-222-200-22200002−2−22−222−22-2-222-22-2000000000000002−2−222−2−222−2−2200000000
χ462-2-2-22-222-200-22200002−2−22−222−22-2-22-22-2200000000000000−222−2−222−22−2−2200000000
χ472-2-2-22-222-200-22200002−2−22−222−2-222-22-2-22000000000000002−2−22−222−2−222−200000000
χ482-2-2-22-222-200-22200002−2−22−222−2-222-2-222-200000000000000−222−22−2−22−222−200000000
χ492-2-2-22-222-200-2220000−222−22−2−222-2-222-22-200000000000000−222−2−222−2−222−200000000
χ502-2-2-22-222-200-2220000−222−22−2−222-2-22-22-22000000000000002−2−222−2−22−222−200000000
χ512-2-2-22-222-200-2220000−222−22−2−22-222-22-2-2200000000000000−222−22−2−222−2−2200000000
χ522-2-2-22-222-200-2220000−222−22−2−22-222-2-222-2000000000000002−2−22−222−22−2−2200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-40044-400002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ55444-44-4-4-4-40044-40000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ5644-4-4-444-404-40004-4000000000000000000000000000022−2222−2200000000000000000000
χ5744-4-4-444-404-40004-40000000000000000000000000000−2222−222200000000000000000000
χ5844-4-4-444-40-44000-440000000000000000000000004-400000000000000000000000000
χ5944-4-4-444-40-44000-44000000000000000000000000-4400000000000000000000000000
χ604-44-4-44-4404-4000-44000000000000000000000000000022−22−222200000000000000000000
χ614-44-4-44-4404-4000-440000000000000000000000000000−222222−2200000000000000000000
χ624-44-4-44-440-440004-400000000000000000000004-40000000000000000000000000000
χ634-44-4-44-440-440004-40000000000000000000000-440000000000000000000000000000
χ644-4-4444-4-44-4-4-44-4444-400000000000000000000000000000000000000000000000000
χ654-4-4-44-4444004-4-4000022−22−222222−22−2222000000000000000000000000000000000000000000
χ664-4-4-44-4444004-4-40000−222222−22−222222−22000000000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-8-88-8000000000000000000000000000000000000000000000000000000000000

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