Finite Group Databasebeta

← Group #137992

Character table — Group #137992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ91111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2222222-2-222-2-222-2-200000000000000000000000000000000
χ21222-2-2-22-22-200002-200002-22i2i−2i−2i002-2002i−2i00i2i2−i2−i222−2−2i2i2−i2−i222−2−20000000000000000
χ22222-2-2-22-22-200002-200002-22i2i−2i−2i002-2002i−2i00−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000000000000000
χ23222-2-2-22-22-200002-200002-2−2i−2i2i2i002-200−2i2i00i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000000000000000
χ24222-2-2-22-22-200002-200002-2−2i−2i2i2i002-200−2i2i00−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000000000
χ25222-2-2-22-22-200002-20000-222i2i−2i−2i00-2200−2i2i0022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ26222-2-2-22-22-200002-20000-222i2i−2i−2i00-2200−2i2i00−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ27222-2-2-22-22-200002-20000-22−2i−2i2i2i00-22002i−2i0022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ28222-2-2-22-22-200002-20000-22−2i−2i2i2i00-22002i−2i00−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ292-2-22-222-22222-2-2-2-22-22i−2i002i−2i2i−2i2i−2i000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ302-2-22-222-22222-2-2-2-22-22i−2i002i−2i2i−2i2i−2i00000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ312-2-22-222-22222-2-2-2-22-2−2i2i00−2i2i−2i2i−2i2i000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ322-2-22-222-22222-2-2-2-22-2−2i2i00−2i2i−2i2i−2i2i00000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ332-2-22-222-222-2-222-2-2-222i−2i00−2i2i−2i2i2i−2i000000000000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ342-2-22-222-222-2-222-2-2-222i−2i00−2i2i−2i2i2i−2i00000000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ352-2-22-222-222-2-222-2-2-22−2i2i002i−2i2i−2i−2i2i000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ362-2-22-222-222-2-222-2-2-22−2i2i002i−2i2i−2i−2i2i00000000000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ372-2-22-222-2-2-222-2-222-220022000000-2-200002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-22-222-2-2-222-2-222-220022000000-2-200002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-22-222-2-2-222-2-222-2200-2-2000000220000-222−22−22−22−2−22−22−22−220000000000000000
χ402-2-22-222-2-2-222-2-222-2200-2-2000000220000-22−22−22−22−222−22−22−22−20000000000000000
χ412-2-22-222-2-2-2-2-222222-20022000000-2-20000-22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-2-22-222-2-2-2-2-222222-20022000000-2-20000-22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-2-22-222-2-2-2-2-222222-200-2-20000002200002-22−22−2−22−22−22−222−22−20000000000000000
χ442-2-22-222-2-2-2-2-222222-200-2-20000002200002-2−22−222−22−22−22−2−22−220000000000000000
χ452-2-2-22-222-2200002-200222-20000-2-2-222-2000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ462-2-2-22-222-2200002-200222-20000-2-2-222-200000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ472-2-2-22-222-2200002-20022-220000-2-22-2-2200002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ482-2-2-22-222-2200002-20022-220000-2-22-2-220000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ492-2-2-22-222-2200002-200-2-22-2000022-22-2200002-2-2200002-2-2200000000000000000000
χ502-2-2-22-222-2200002-200-2-22-2000022-22-220000-222-20000-222-200000000000000000000
χ512-2-2-22-222-2200002-200-2-2-220000222-22-2000000002-2-220000-222-20000000000000000
χ522-2-2-22-222-2200002-200-2-2-220000222-22-200000000-222-200002-2-220000000000000000
χ5344444444-4-44444-4-4-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ55444-4-4-44-4-440000-44004i−4i000000−4i4i0000000000000000000000000000000000000000
χ56444-4-4-44-4-440000-4400−4i4i0000004i−4i0000000000000000000000000000000000000000
χ5744-444-4-4-4004-44-40000000000000000000000000000000000000000002-22-200000000
χ5844-444-4-4-4004-44-4000000000000000000000000000000000000000000-22-2200000000
χ5944-444-4-4-400-44-440000000000000000000000000000000000000000002-2-2200000000
χ6044-444-4-4-400-44-44000000000000000000000000000000000000000000-222-200000000
χ614-444-4-4-44004-4-44000000000000000000000000000000000000002i−2i2i−2i000000000000
χ624-444-4-4-44004-4-4400000000000000000000000000000000000000−2i2i−2i2i000000000000
χ634-444-4-4-4400-444-4000000000000000000000000000000000000002i−2i−2i2i000000000000
χ644-444-4-4-4400-444-400000000000000000000000000000000000000−2i2i2i−2i000000000000
χ654-4-4-44-4444-40000-440000004-4-44000000000000000000000000000000000000000000
χ664-4-4-44-4444-40000-44000000-444-4000000000000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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