Finite Group Databasebeta

← Group #315141

Character table — Group #315141

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888844444444444488888888888888888824884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
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
χ511111111111111111111111111-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11-11
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-11-1-11
χ17222222222-2-22-2-222-2-200000000222222-2-2-2-2220000-2-2000000000000000000000000
χ18222222222-2-22-2-222-2-2000000002222-2-22222-2-20000-2-2000000000000000000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-22222-2-2-2-2000022000000000000000000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-2-2-2-2-22222000022000000000000000000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-200000000000022-2-20000000000000000002-2000000
χ2222222222-222-222-2-2-2-22222-2-2-2-2000000000000-2-222000000000000000000-22000000
χ2322222222-222-222-2-2-2-2-2-2-2-2222200000000000022-2-2000000000000000000-22000000
χ2422222222-222-222-2-2-2-2-2-2-2-22222000000000000-2-2220000000000000000002-2000000
χ2522-2-22-2-222-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000022-2-20000002i−2i0000
χ2622-2-22-2-222-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000-2-222000000−2i2i0000
χ2722-2-22-2-222-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000022-2-2000000−2i2i0000
χ2822-2-22-2-222-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000-2-2220000002i−2i0000
χ2922-2-22-2-22-2222-2-2-22-220000000022-2-20000000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000
χ3022-2-22-2-22-2222-2-2-22-220000000022-2-20000000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3122-2-22-2-22-2222-2-2-22-2200000000-2-222000000000000-222i2i−2i−2i−2i−2i2i2i0000000000000000
χ3222-2-22-2-22-2222-2-2-22-2200000000-2-222000000000000-22−2i−2i2i2i2i2i−2i−2i0000000000000000
χ3322-2-22-2-22-2-2-2222-222-22i2i−2i−2i−2i−2i2i2i22-2-2000000000000-220000000000002i2i−2i−2i00000000
χ3422-2-22-2-22-2-2-2222-222-22i2i−2i−2i−2i−2i2i2i-2-2220000000000002-2000000000000−2i−2i2i2i00000000
χ3522-2-22-2-22-2-2-2222-222-2−2i−2i2i2i2i2i−2i−2i22-2-2000000000000-22000000000000−2i−2i2i2i00000000
χ3622-2-22-2-22-2-2-2222-222-2−2i−2i2i2i2i2i−2i−2i-2-2220000000000002-20000000000002i2i−2i−2i00000000
χ372-222-2-2-22-2002002-200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i002-22i−2i000000002−22−2i2−i2i2−i200002−22−200000000
χ382-222-2-2-22-2002002-200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00-22−2i2i00000000−22−22−i2i2−i2i200002−22−200000000
χ392-222-2-2-22-2002002-200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i002-2−2i2i00000000−22−22i2−i2i2−i20000−22−2200000000
χ402-222-2-2-22-2002002-200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00-222i−2i000000002−22−2−i2i2−i2i20000−22−2200000000
χ412-222-2-2-22-2002002-200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i002-22i−2i00000000−22−22−i2i2−i2i20000−22−2200000000
χ422-222-2-2-22-2002002-200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00-22−2i2i000000002−22−2i2−i2i2−i20000−22−2200000000
χ432-222-2-2-22-2002002-200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i002-2−2i2i000000002−22−2−i2i2−i2i200002−22−200000000
χ442-222-2-2-22-2002002-200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00-222i−2i00000000−22−22i2−i2i2−i200002−22−200000000
χ452-2-2-2-2222200200-2-2002−2−22−222−22i−2i−2i2i2i−2i00002-2000000i2−i2−i2i2−222−20000−i2i2i2−i200000000
χ462-2-2-2-2222200200-2-2002−2−22−222−22i−2i−2i2i−2i2i0000-22000000−i2i2i2−i22−2−220000−i2i2i2−i200000000
χ472-2-2-2-2222200200-2-2002−2−22−222−2−2i2i2i−2i2i−2i0000-22000000i2−i2−i2i22−2−220000i2−i2−i2i200000000
χ482-2-2-2-2222200200-2-2002−2−22−222−2−2i2i2i−2i−2i2i00002-2000000−i2i2i2−i2−222−20000i2−i2−i2i200000000
χ492-2-2-2-2222200200-2-200−222−22−2−222i−2i−2i2i2i−2i00002-2000000−i2i2i2−i22−2−220000i2−i2−i2i200000000
χ502-2-2-2-2222200200-2-200−222−22−2−222i−2i−2i2i−2i2i0000-22000000i2−i2−i2i2−222−20000i2−i2−i2i200000000
χ512-2-2-2-2222200200-2-200−222−22−2−22−2i2i2i−2i2i−2i0000-22000000−i2i2i2−i2−222−20000−i2i2i2−i200000000
χ522-2-2-2-2222200200-2-200−222−22−2−22−2i2i2i−2i−2i2i00002-2000000i2−i2−i2i22−2−220000−i2i2i2−i200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5444-4-44-4-44444-4-4-44-44-400000000000000000000000000000000000000000000000000
χ554-444-4-4-44400-400-44002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ564-444-4-4-44400-400-4400−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ574-44-444-4-404-404-4000000000000000000000000004i−4i00000000000000000000000000
χ584-44-444-4-404-404-400000000000000000000000000−4i4i00000000000000000000000000
χ594-44-444-4-40-440-44000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ604-44-444-4-40-440-4400000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ614-4-444-44-404-40-44000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ624-4-444-44-404-40-4400000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ634-4-444-44-40-4404-40000000000000000000000004i−4i0000000000000000000000000000
χ644-4-444-44-40-4404-4000000000000000000000000−4i4i0000000000000000000000000000
χ654-4-4-4-4444-400-400440022−22−222222−22−2222000000000000000000000000000000000000000000
χ664-4-4-4-4444-400-4004400−222222−22−222222−22000000000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ6888-88-88-8-8000000000000000000000000000000000000000000000000000000000000

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