Finite Group Databasebeta

← Group #149849

Character table — Group #149849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order12222244444444444444448888888888888888444422224488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ9111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-11-11-11-11-1
χ10111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-11-11
χ11111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−ii−i−ii−ii
χ12111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−ii−iii−ii−i
χ13111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-11
χ14111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-1
χ15111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ17222222222222-2-2-2-2-2-2-2-222000000000000000022-2-22-2000000000000
χ18222222222222-2-2-2-2-2-2-2-2220000000000000000-2-222-22000000000000
χ19222222-2-2-2-2-2-2-2-2-2-2222222000000000000000022-2-2-22000000000000
χ20222222-2-2-2-2-2-2-2-2-2-22222220000000000000000-2-2222-2000000000000
χ2122-2-22-200000022-2-200002-2000000002222-2-2-2-22i−2i2i−2i00002i−2i00000000
χ2222-2-22-200000022-2-200002-2000000002222-2-2-2-2−2i2i−2i2i0000−2i2i00000000
χ2322-2-22-200000022-2-200002-200000000-2-2-2-222222i−2i2i−2i0000−2i2i00000000
χ2422-2-22-200000022-2-200002-200000000-2-2-2-22222−2i2i−2i2i00002i−2i00000000
χ2522-2-22-2000000-2-22200002-22i2i2i2i−2i−2i−2i−2i000000002i−2i−2i2i002-20000000000
χ2622-2-22-2000000-2-22200002-22i2i2i2i−2i−2i−2i−2i00000000−2i2i2i−2i00-220000000000
χ2722-2-22-2000000-2-22200002-2−2i−2i−2i−2i2i2i2i2i000000002i−2i−2i2i00-220000000000
χ2822-2-22-2000000-2-22200002-2−2i−2i−2i−2i2i2i2i2i00000000−2i2i2i−2i002-20000000000
χ294444444444-4-400000000-4-40000000000000000000000000000000000
χ30444444-4-4-4-44400000000-4-40000000000000000000000000000000000
χ314444-4-444-4-400000000000022-2-222-2-222-2-222-2-2000000000000000000
χ324444-4-444-4-4000000000000-2-222-2-222-2-222-2-222000000000000000000
χ334444-4-4-4-44400000000000022-2-222-2-2-2-222-2-222000000000000000000
χ344444-4-4-4-444000000000000-2-222-2-22222-2-222-2-2000000000000000000
χ3544-4-44-400000000004i4i−4i−4i-440000000000000000000000000000000000
χ3644-4-44-40000000000−4i−4i4i4i-440000000000000000000000000000000000
χ3744-4-4-4400004i−4i00000000002i2i−2i−2i−2i−2i2i2i22-2-2-2-222000000000000000000
χ3844-4-4-4400004i−4i0000000000−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000000000000000000
χ3944-4-4-440000−4i4i00000000002i2i−2i−2i−2i−2i2i2i-2-22222-2-2000000000000000000
χ4044-4-4-440000−4i4i0000000000−2i−2i2i2i2i2i−2i−2i22-2-2-2-222000000000000000000
χ414-44-400004i−4i002-22-22i−2i2i−2i00002i2−2i2002i2−2i222−220022−2200000000000000000000
χ424-44-400004i−4i002-22-22i−2i2i−2i0000−2i22i200−2i22i2−222200−222200000000000000000000
χ434-44-400004i−4i00-22-22−2i2i−2i2i002i2−2i2002i2−2i2000022−220022−22000000000000000000
χ444-44-400004i−4i00-22-22−2i2i−2i2i00−2i22i200−2i22i20000−222200−2222000000000000000000
χ454-44-40000−4i4i002-22-2−2i2i−2i2i00002i2−2i2002i2−2i2−222200−222200000000000000000000
χ464-44-40000−4i4i002-22-2−2i2i−2i2i0000−2i22i200−2i22i222−220022−2200000000000000000000
χ474-44-40000−4i4i00-22-222i−2i2i−2i002i2−2i2002i2−2i20000−222200−2222000000000000000000
χ484-44-40000−4i4i00-22-222i−2i2i−2i00−2i22i200−2i22i2000022−220022−22000000000000000000
χ494-4-44004-400002-2-222-2-220022−2200−22220022−2200−222200000000000000000000
χ504-4-44004-400002-2-222-2-2200−22220022−2200−22220022−2200000000000000000000
χ514-4-44004-40000-222-2-222-2000022−2200−22220022−2200−2222000000000000000000
χ524-4-44004-40000-222-2-222-20000−22220022−2200−22220022−22000000000000000000
χ534-4-4400-4400002-2-22-222-20022−2200−222200−22220022−2200000000000000000000
χ544-4-4400-4400002-2-22-222-200−22220022−220022−2200−222200000000000000000000
χ554-4-4400-440000-222-22-2-22000022−2200−222200−22220022−22000000000000000000
χ564-4-4400-440000-222-22-2-220000−22220022−220022−2200−2222000000000000000000

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