Finite Group Databasebeta

← Group #137366

Character table — Group #137366

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444422444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ91-1-111-1-111-11-111-1-11-1ii−i−iii−i−i11-1-1ii−i−i1-11-11-11-1i−iii−i−iii−i−i11-1-1
χ101-1-111-1-111-11-111-1-11-1ii−i−iii−i−i11-1-1ii−i−i1-1-111-1-11i−i−i−iii−i−iii-1-111
χ111-1-111-1-111-11-111-1-11-1ii−i−i−i−iii-1-111ii−i−i1-11-1-111-1−iiii−i−i−i−iii-1-111
χ121-1-111-1-111-11-111-1-11-1ii−i−i−i−iii-1-111ii−i−i1-1-11-11-11−ii−i−iiiii−i−i11-1-1
χ131-1-111-1-111-11-111-1-11-1−i−iiiii−i−i-1-111−i−iii1-11-1-111-1i−i−i−iiiii−i−i-1-111
χ141-1-111-1-111-11-111-1-11-1−i−iiiii−i−i-1-111−i−iii1-1-11-11-11i−iii−i−i−i−iii11-1-1
χ151-1-111-1-111-11-111-1-11-1−i−iii−i−iii11-1-1−i−iii1-11-11-11-1−ii−i−iii−i−iii11-1-1
χ161-1-111-1-111-11-111-1-11-1−i−iii−i−iii11-1-1−i−iii1-1-111-1-11−iiii−i−iii−i−i-1-111
χ172222222222222222-2-2222200000000-2-2-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2000000002222-2-200000000000000000000
χ19222222222222-2-2-2-22-20000222200000000-22000000-2-2000000000000
χ20222222222222-2-2-2-22-20000-2-2-2-200000000-2200000022000000000000
χ21222222222222-2-2-2-2-2200000000222200002-200-2-20000000000000000
χ22222222222222-2-2-2-2-2200000000-2-2-2-200002-200220000000000000000
χ2322-2-2-22-22-222-22-22-2000000000000002i−2i2i−2i00000000000000i2−i2i2−i22−22−2
χ2422-2-2-22-22-222-22-22-2000000000000002i−2i2i−2i00000000000000−i2i2−i2i2−22−22
χ2522-2-2-22-22-222-22-22-200000000000000−2i2i−2i2i00000000000000i2−i2i2−i2−22−22
χ2622-2-2-22-22-222-22-22-200000000000000−2i2i−2i2i00000000000000−i2i2−i2i22−22−2
χ272-22-2-2-222-2-2222-2-22000000000000002-2-22000000000000002−2−222−2−22
χ282-22-2-2-222-2-2222-2-22000000000000002-2-2200000000000000−222−2−222−2
χ292-22-2-2-222-2-2222-2-2200000000000000-222-2000000000000002−2−22−222−2
χ302-22-2-2-222-2-2222-2-2200000000000000-222-200000000000000−222−22−2−22
χ312-2-222-2-222-22-222-2-2-222i2i−2i−2i00000000−2i−2i2i2i-2200000000000000000000
χ322-2-222-2-222-22-222-2-2-22−2i−2i2i2i000000002i2i−2i−2i-2200000000000000000000
χ332-2-222-2-222-22-2-2-2222200002i2i−2i−2i00000000-2-2000000−2i2i000000000000
χ342-2-222-2-222-22-2-2-222220000−2i−2i2i2i00000000-2-20000002i−2i000000000000
χ352-2-222-2-222-22-2-2-222-2-20000000022-2-200002200-220000000000000000
χ362-2-222-2-222-22-2-2-222-2-200000000-2-222000022002-20000000000000000
χ3744444444-4-4-4-40000000000000000000000002200-2-200000000000000
χ3844444444-4-4-4-4000000000000000000000000-2-2002200000000000000
χ3944-44-4-44-400000000002i−2i2i−2i2-22-22i−2i2i−2i00000000000000000000000000
χ4044-44-4-44-400000000002i−2i2i−2i-22-22−2i2i−2i2i00000000000000000000000000
χ4144-44-4-44-40000000000−2i2i−2i2i2-22-2−2i2i−2i2i00000000000000000000000000
χ4244-44-4-44-40000000000−2i2i−2i2i-22-222i−2i2i−2i00000000000000000000000000
χ4344-4-4-44-444-4-44000000000000000000000000000000002-22-200000000
χ4444-4-4-44-444-4-4400000000000000000000000000000000-22-2200000000
χ4544-4-4-44-44-444-4-44-440000000000000000000000000000000000000000
χ464-444-44-4-400000000002-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ474-444-44-4-400000000002-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ484-444-44-4-40000000000-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ494-444-44-4-40000000000-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ504-44-4-4-44444-4-4000000000000000000000000000000002i−2i−2i2i00000000
χ514-44-4-4-44444-4-400000000000000000000000000000000−2i2i2i−2i00000000
χ524-44-4-4-444-4-444-444-40000000000000000000000000000000000000000
χ534-4-444-4-44-44-440000000000000000000000002-200-2200000000000000
χ544-4-444-4-44-44-44000000000000000000000000-22002-200000000000000
χ55888-88-8-8-8000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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