Finite Group Databasebeta

← Group #283963

Character table — Group #283963

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442222448888888822444444448888888888888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111111-1-1-11
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-11111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-11-1-111-1-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-11-1-1-1-111-11
χ172222222222-22-2-2-220000-2-22222-2-2-2-222000000-2-2000000000000000000-2200000000
χ182222222222-22-2-2-220000-2-22222-2-2-2-2-2-2000000220000000000000000002-200000000
χ192222222222-22-2-2-220000-2-2-2-2-2-222222200000022000000000000000000-2-200000000
χ202222222222-22-2-2-220000-2-2-2-2-2-22222-2-2000000-2-20000000000000000002200000000
χ2122222222-2-22-2222-22222-2-20000000000-2-222-2-20022-2-2000000000000000000000000
χ2222222222-2-22-2222-22222-2-20000000000-2-2-2-22200-2-222000000000000000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-200000000002222-2-200-2-222000000000000000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000000000022-2-2220022-2-2000000000000000000000000
χ25222-2-22-2-20020-2-22022-2-200i2i2−i2−i2i2i2−i2−i200002i−2i00002i−2i00i2i2−i2−i222−2−222−2−2000000000000
χ26222-2-22-2-20020-2-22022-2-200i2i2−i2−i2i2i2−i2−i20000−2i2i0000−2i2i00i2i2−i2−i2−2−222−2−222000000000000
χ27222-2-22-2-20020-2-22022-2-200−i2−i2i2i2−i2−i2i2i200002i−2i00002i−2i00−i2−i2i2i2−2−222−2−222000000000000
χ28222-2-22-2-20020-2-22022-2-200−i2−i2i2i2−i2−i2i2i20000−2i2i0000−2i2i00−i2−i2i2i222−2−222−2−2000000000000
χ29222-2-22-2-20020-2-220-2-22200i2i2−i2−i2i2i2−i2−i200002i−2i0000−2i2i00−i2−i2i2i222−2−2−2−222000000000000
χ30222-2-22-2-20020-2-220-2-22200i2i2−i2−i2i2i2−i2−i20000−2i2i00002i−2i00−i2−i2i2i2−2−22222−2−2000000000000
χ31222-2-22-2-20020-2-220-2-22200−i2−i2i2i2−i2−i2i2i200002i−2i0000−2i2i00i2i2−i2−i2−2−22222−2−2000000000000
χ32222-2-22-2-20020-2-220-2-22200−i2−i2i2i2−i2−i2i2i20000−2i2i00002i−2i00i2i2−i2−i222−2−2−2−222000000000000
χ332-2-2222-2-2222-2-22-2-20000-222i−2i2i−2i2i−2i2i−2i000000000000000000000000002-2002i−2i000000
χ342-2-2222-2-2222-2-22-2-20000-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000-2200−2i2i000000
χ352-2-2222-2-2222-2-22-2-20000-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000002-200−2i2i000000
χ362-2-2222-2-2222-2-22-2-20000-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000-22002i−2i000000
χ372-2-2222-2-222-2-22-22-22-22-22-22i−2i2i−2i−2i2i−2i2i002-200000000002i−2i2i−2i00000000000000000000
χ382-2-2222-2-222-2-22-22-22-22-22-2−2i2i−2i2i2i−2i2i−2i002-20000000000−2i2i−2i2i00000000000000000000
χ392-2-2222-2-222-2-22-22-2-22-222-22i−2i2i−2i−2i2i−2i2i00-220000000000−2i2i−2i2i00000000000000000000
χ402-2-2222-2-222-2-22-22-2-22-222-2−2i2i−2i2i2i−2i2i−2i00-2200000000002i−2i2i−2i00000000000000000000
χ412-2-2222-2-2-2-2-222-2222-22-2-220000000000-22000000000000002-22-22-22-2000000000000
χ422-2-2222-2-2-2-2-222-2222-22-2-220000000000-2200000000000000-22-22-22-22000000000000
χ432-2-2222-2-2-2-2-222-222-22-22-2200000000002-2000000000000002-22-2-22-22000000000000
χ442-2-2222-2-2-2-2-222-222-22-22-2200000000002-200000000000000-22-222-22-2000000000000
χ452-2-2-2-222200-20-22202-2-22002−2−22−222−20000002-200002-22−2−222−2−222−2−22000000000000
χ462-2-2-2-222200-20-22202-2-22002−2−22−222−2000000-220000-222−2−22−222−2−222−2000000000000
χ472-2-2-2-222200-20-22202-2-2200−222−22−2−220000002-200002-2−222−2−222−2−222−2000000000000
χ482-2-2-2-222200-20-22202-2-2200−222−22−2−22000000-220000-22−222−22−2−222−2−22000000000000
χ492-2-2-2-222200-20-2220-222-2002−2−22−222−20000002-20000-22−222−22−2−22−222−2000000000000
χ502-2-2-2-222200-20-2220-222-2002−2−22−222−2000000-2200002-2−222−2−222−22−2−22000000000000
χ512-2-2-2-222200-20-2220-222-200−222−22−2−220000002-20000-222−2−22−222−22−2−22000000000000
χ522-2-2-2-222200-20-2220-222-200−222−22−2−22000000-2200002-22−2−222−2−22−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-4-44-4-400-4044-400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ55444-4-44-4-400-4044-40000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-44-4-44-44-404000-400000000000000000000000000000000000000000000002i2−2i20000
χ5744-44-4-44-44-404000-40000000000000000000000000000000000000000000000−2i22i20000
χ5844-44-4-44-4-440-40004000000000000004-4000000000000000000000000000000000000
χ5944-44-4-44-4-440-4000400000000000000-44000000000000000000000000000000000000
χ604-444-4-4-444-40-4000400000000000000000000000000000000000000000000000022−2200
χ614-444-4-4-444-40-40004000000000000000000000000000000000000000000000000−222200
χ624-444-4-4-44-4404000-400000000000000000000004i−4i0000000000000000000000000000
χ634-444-4-4-44-4404000-40000000000000000000000−4i4i0000000000000000000000000000
χ644-4-4444-4-4-4-444-44-4400004-40000000000000000000000000000000000000000000000
χ654-4-4-4-444400404-4-4000000022−22−222222−22−222200000000000000000000000000000000000000
χ664-4-4-4-444400404-4-40000000−222222−22−222222−2200000000000000000000000000000000000000
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-88-88-8000000000000000000000000000000000000000000000000000000000000

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