Finite Group Databasebeta

← Group #289726

Character table — Group #289726

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888822444444444488888888888888888844882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-11111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ9111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-11-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111111111-1-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-11-11-1
χ172222222222-22-2-2-22-2-20000222200002222-2-200-2-20000000000-2-20000000000000000
χ182222222222-22-2-2-22-2-2000022220000-2-2-2-22200220000000000-2-20000000000000000
χ192222222222-22-2-2-22-2-20000-2-2-2-2000022-2-22200-2-20000000000220000000000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-20000-2-222-2-200220000000000220000000000000000
χ2122222222-2-22-2222-2-2-222220000-2-2-2-20000002200-2-2000000000000000000-22000000
χ2222222222-2-22-2222-2-2-222220000-2-2-2-2000000-2-200220000000000000000002-2000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2000022220000002200-2-20000000000000000002-2000000
χ2422222222-2-22-2222-2-2-2-2-2-2-200002222000000-2-20022000000000000000000-22000000
χ25222-22-2-2-22-20-200020022−2−22i2i−2i−2i22−2−22-22i−2i00000000i2i2−i2−i222−2−2000000i2i2−i2−i200000000
χ26222-22-2-2-22-20-200020022−2−22i2i−2i−2i22−2−2-22−2i2i00000000−i2−i2i2i2−2−222000000i2i2−i2−i200000000
χ27222-22-2-2-22-20-200020022−2−2−2i−2i2i2i22−2−22-2−2i2i00000000−i2−i2i2i222−2−2000000−i2−i2i2i200000000
χ28222-22-2-2-22-20-200020022−2−2−2i−2i2i2i22−2−2-222i−2i00000000i2i2−i2−i2−2−222000000−i2−i2i2i200000000
χ29222-22-2-2-22-20-2000200−2−2222i2i−2i−2i−2−2222-22i−2i00000000−i2−i2i2i2−2−222000000−i2−i2i2i200000000
χ30222-22-2-2-22-20-2000200−2−2222i2i−2i−2i−2−222-22−2i2i00000000i2i2−i2−i222−2−2000000−i2−i2i2i200000000
χ31222-22-2-2-22-20-2000200−2−222−2i−2i2i2i−2−2222-2−2i2i00000000i2i2−i2−i2−2−222000000i2i2−i2−i200000000
χ32222-22-2-2-22-20-2000200−2−222−2i−2i2i2i−2−222-222i−2i00000000−i2−i2i2i222−2−2000000i2i2−i2−i200000000
χ332-2-222-2-222-202000-2002−22−22-22-22−22−200002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i20000002−22−200000000
χ342-2-222-2-222-202000-2002−22−22-22-22−22−20000−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i20000002−22−200000000
χ352-2-222-2-222-202000-2002−22−2-22-222−22−200002i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i2000000−22−2200000000
χ362-2-222-2-222-202000-2002−22−2-22-222−22−20000−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i2000000−22−2200000000
χ372-2-222-2-222-202000-200−22−222-22-2−22−2200002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2000000−22−2200000000
χ382-2-222-2-222-202000-200−22−222-22-2−22−220000−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i2000000−22−2200000000
χ392-2-222-2-222-202000-200−22−22-22-22−22−2200002i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i20000002−22−200000000
χ402-2-222-2-222-202000-200−22−22-22-22−22−220000−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i20000002−22−200000000
χ412-2-2-2222-2222-2-22-2-2-2200002i−2i−2i2i00000000000000002-2-22−2i2i2i−2i2i−2i0000000000000000
χ422-2-2-2222-2222-2-22-2-2-2200002i−2i−2i2i0000000000000000-222-22i−2i−2i2i2i−2i0000000000000000
χ432-2-2-2222-2222-2-22-2-2-220000−2i2i2i−2i00000000000000002-2-222i−2i−2i2i−2i2i0000000000000000
χ442-2-2-2222-2222-2-22-2-2-220000−2i2i2i−2i0000000000000000-222-2−2i2i2i−2i−2i2i0000000000000000
χ452-2-2-2222-222-2-22-22-22-22-2-222i−2i−2i2i2-2-2200000000000000000000−2i2i00002i−2i−2i2i00000000
χ462-2-2-2222-222-2-22-22-22-22-2-22−2i2i2i−2i2-2-22000000000000000000002i−2i0000−2i2i2i−2i00000000
χ472-2-2-2222-222-2-22-22-22-2-222-22i−2i−2i2i-222-200000000000000000000−2i2i0000−2i2i2i−2i00000000
χ482-2-2-2222-222-2-22-22-22-2-222-2−2i2i2i−2i-222-2000000000000000000002i−2i00002i−2i−2i2i00000000
χ492-2-2-2222-2-2-2-222-222-222-2-220000-222-2000000000000000000000022-2-20000002-20000
χ502-2-2-2222-2-2-2-222-222-222-2-220000-222-20000000000000000000000-2-222000000-220000
χ512-2-2-2222-2-2-2-222-222-22-222-200002-2-22000000000000000000000022-2-2000000-220000
χ522-2-2-2222-2-2-2-222-222-22-222-200002-2-220000000000000000000000-2-2220000002-20000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4404000-4002222−22−220000−22−22222200000000000000000000000000000000000000
χ55444-44-4-4-4-4404000-400−22−22222200002222−22−2200000000000000000000000000000000000000
χ5644-4-4-4-44400404-4-400000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ5744-4-4-4-44400404-4-40000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ5844-4-4-4-44400-40-44400000000000000000000000004-400000000000000000000000000
χ5944-4-4-4-44400-40-4440000000000000000000000000-4400000000000000000000000000
χ604-444-4-44-40040-4-440000000000000000000004i−4i000000000000000000000000000000
χ614-444-4-44-40040-4-44000000000000000000000−4i4i000000000000000000000000000000
χ624-444-4-44-400-4044-400000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ634-444-4-44-400-4044-40000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ644-4-444-4-44-440-400040022−2222−220000−2222−222200000000000000000000000000000000000000
χ654-4-444-4-44-440-4000400−2222−2222000022−2222−2200000000000000000000000000000000000000
χ664-4-4-4444-4-4-444-44-444-400000000000000000000000000000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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