Finite Group Databasebeta

← Group #140943

Character table — Group #140943

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882244444488888888
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
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ2122-22-2-22-22-22-22i2i−2i−2i2i−2i0022-2-22i2i−2i−2i000000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ2222-22-2-22-22-22-22i2i−2i−2i2i−2i0022-2-22i2i−2i−2i00000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ2322-22-2-22-22-22-22i2i−2i−2i2i−2i00-2-222−2i−2i2i2i000000000000000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ2422-22-2-22-22-22-22i2i−2i−2i2i−2i00-2-222−2i−2i2i2i00000000000000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ2522-22-2-22-22-22-2−2i−2i2i2i−2i2i0022-2-2−2i−2i2i2i000000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ2622-22-2-22-22-22-2−2i−2i2i2i−2i2i0022-2-2−2i−2i2i2i00000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ2722-22-2-22-22-22-2−2i−2i2i2i−2i2i00-2-2222i2i−2i−2i000000000000000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ2822-22-2-22-22-22-2−2i−2i2i2i−2i2i00-2-2222i2i−2i−2i00000000000000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ2922-22-2-22-2-22-222i2i−2i−2i−2i2i2-2000000002-22i−2i0000i2i2−i2−i222−2−2i2i2−i2−i222−2−20000000000000000
χ3022-22-2-22-2-22-222i2i−2i−2i−2i2i2-2000000002-22i−2i0000−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000000000000000
χ3122-22-2-22-2-22-222i2i−2i−2i−2i2i-2200000000-22−2i2i000022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ3222-22-2-22-2-22-222i2i−2i−2i−2i2i-2200000000-22−2i2i0000−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ3322-22-2-22-2-22-22−2i−2i2i2i2i−2i2-2000000002-2−2i2i0000i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000000000000000
χ3422-22-2-22-2-22-22−2i−2i2i2i2i−2i2-2000000002-2−2i2i0000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000000000
χ3522-22-2-22-2-22-22−2i−2i2i2i2i−2i-2200000000-222i−2i000022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ3622-22-2-22-2-22-22−2i−2i2i2i2i−2i-2200000000-222i−2i0000−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ372-222-2-2-22-2-2220000002200002-22-2-2-200002-200002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ382-222-2-2-22-2-2220000002200002-22-2-2-200002-20000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ392-222-2-2-22-2-222000000220000-22-22-2-20000-222i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ402-222-2-2-22-2-222000000220000-22-22-2-20000-22−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ412-222-2-2-22-2-222000000-2-200002-22-2220000-222-22-20000-22-2200000000000000000000
χ422-222-2-2-22-2-222000000-2-200002-22-2220000-22-22-2200002-22-200000000000000000000
χ432-222-2-2-22-2-222000000-2-20000-22-222200002-200002-22-20000-22-220000000000000000
χ442-222-2-2-22-2-222000000-2-20000-22-222200002-20000-22-2200002-22-20000000000000000
χ452-2-2222-2-22-2-220000002-22i−2i2i−2i0000-22002i−2i002−2−22i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ462-2-2222-2-22-2-220000002-22i−2i2i−2i0000-22002i−2i00−222−2−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ472-2-2222-2-22-2-220000002-2−2i2i−2i2i0000-2200−2i2i002−2−22−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ482-2-2222-2-22-2-220000002-2−2i2i−2i2i0000-2200−2i2i00−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ492-2-2222-2-22-2-22000000-222i−2i2i−2i00002-200−2i2i00i2−i2−i2i22−2−22−i2i2i2−i2−222−20000000000000000
χ502-2-2222-2-22-2-22000000-222i−2i2i−2i00002-200−2i2i00−i2i2i2−i2−222−2i2−i2−i2i22−2−220000000000000000
χ512-2-2222-2-22-2-22000000-22−2i2i−2i2i00002-2002i−2i00i2−i2−i2i2−222−2−i2i2i2−i22−2−220000000000000000
χ522-2-2222-2-22-2-22000000-22−2i2i−2i2i00002-2002i−2i00−i2i2i2−i22−2−22i2−i2−i2i2−222−20000000000000000
χ5344444444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ554-444-4-4-4444-4-4000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ564-444-4-4-4444-4-400000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ574-44-44-44-400004i−4i4i−4i00000000000000000000000000000000000000002i−2i2-200000000
χ584-44-44-44-400004i−4i4i−4i0000000000000000000000000000000000000000−2i2i-2200000000
χ594-44-44-44-40000−4i4i−4i4i00000000000000000000000000000000000000002i−2i-2200000000
χ604-44-44-44-40000−4i4i−4i4i0000000000000000000000000000000000000000−2i2i2-200000000
χ614-4-4444-4-4-444-40000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ624-4-4444-4-4-444-4000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ634-4-4-4-444400004-4-440000000000000000000000000000000000002-22-2000000000000
χ644-4-4-4-444400004-4-44000000000000000000000000000000000000-22-22000000000000
χ654-4-4-4-44440000-444-40000000000000000000000000000000000002-2-22000000000000
χ664-4-4-4-44440000-444-4000000000000000000000000000000000000-222-2000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6888-8-88-8-88000000000000000000000000000000000000000000000000000000000000

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