Finite Group Databasebeta

← Group #137409

Character table — Group #137409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222222224444444444444444444444444444224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ91-1-111-1-111-11-111-1-1iiii−i−i−i−i-1ii−i−i111-1-111-1-1ii−i−i1-11-11-1i−iii−i−iii−i−i11-1-1
χ101-1-111-1-111-11-111-1-1iiii−i−i−i−i-1ii−i−i111-1-111-1-1ii−i−i1-1-11-11i−i−i−iii−i−iii-1-111
χ111-1-111-1-111-11-111-1-1iiii−i−i−i−i-1−i−iii1-1-111-1-111−i−iii1-11-11-1i−iii−i−i−i−iii-1-111
χ121-1-111-1-111-11-111-1-1iiii−i−i−i−i-1−i−iii1-1-111-1-111−i−iii1-1-11-11i−i−i−iiiii−i−i11-1-1
χ131-1-111-1-111-11-111-1-1−i−i−i−iiiii-1ii−i−i1-1-111-1-111ii−i−i1-11-11-1−ii−i−iiiii−i−i-1-111
χ141-1-111-1-111-11-111-1-1−i−i−i−iiiii-1ii−i−i1-1-111-1-111ii−i−i1-1-11-11−iiii−i−i−i−iii11-1-1
χ151-1-111-1-111-11-111-1-1−i−i−i−iiiii-1−i−iii111-1-111-1-1−i−iii1-11-11-1−ii−i−iii−i−iii11-1-1
χ161-1-111-1-111-11-111-1-1−i−i−i−iiiii-1−i−iii111-1-111-1-1−i−iii1-1-11-11−iiii−i−iii−i−i-1-111
χ17222222222222222222222222-20000-2000000000000-2-20000-2-2000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-20000-2000000000000-2-2000022000000000000
χ19222222222222-2-2-2-20000000020000-22222-2-2-2-200002-2000000000000000000
χ20222222222222-2-2-2-20000000020000-2-2-2-2-2222200002-2000000000000000000
χ21222222222222-2-2-2-200000000-22222200000000-2-2-2-2-22000000000000000000
χ22222222222222-2-2-2-200000000-2-2-2-2-22000000002222-22000000000000000000
χ2322-2-222-2-222-2-22-2-2222-2-222-2-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ2422-2-222-2-222-2-22-2-2222-2-222-2-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ2522-2-222-2-222-2-22-2-22-2-222-2-222000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ2622-2-222-2-222-2-22-2-22-2-222-2-222000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ272-22-22-22-22-2-222-22-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000002−2−22−i2i2i2−i2
χ282-22-22-22-22-2-222-22-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000−222−2i2−i2−i2i2
χ292-22-22-22-22-2-222-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000002−2−22i2−i2−i2i2
χ302-22-22-22-22-2-222-22-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−222−2−i2i2i2−i2
χ312-2-222-2-222-22-222-2-22i2i2i2i−2i−2i−2i−2i20000-2000000000000-220000−2i2i000000000000
χ322-2-222-2-222-22-222-2-2−2i−2i−2i−2i2i2i2i2i20000-2000000000000-2200002i−2i000000000000
χ332-2-222-2-222-22-2-2-2220000000022i2i−2i−2i200000000−2i−2i2i2i-2-2000000000000000000
χ342-2-222-2-222-22-2-2-222000000002−2i−2i2i2i2000000002i2i−2i−2i-2-2000000000000000000
χ352-2-222-2-222-22-2-2-22200000000-20000-222-2-2-2-222000022000000000000000000
χ362-2-222-2-222-22-2-2-22200000000-20000-2-2-22222-2-2000022000000000000000000
χ3744444444-4-4-4-40000000000000000000000000000000022-2-200000000000000
χ3844444444-4-4-4-400000000000000000000000000000000-2-22200000000000000
χ39444-4-4-4-44000000002i−2i2i−2i2i−2i2i−2i02i−2i2i−2i000002-22-2000000000000000000000000
χ40444-4-4-4-44000000002i−2i2i−2i2i−2i2i−2i0−2i2i−2i2i00000-22-22000000000000000000000000
χ41444-4-4-4-4400000000−2i2i−2i2i−2i2i−2i2i02i−2i2i−2i00000-22-22000000000000000000000000
χ42444-4-4-4-4400000000−2i2i−2i2i−2i2i−2i2i0−2i2i−2i2i000002-22-2000000000000000000000000
χ4344-44-4-44-4000000002i−2i−2i2i2i−2i−2i2i0000002i−2i2i−2i00002-22-200000000000000000000
χ4444-44-4-44-4000000002i−2i−2i2i2i−2i−2i2i000000−2i2i−2i2i0000-22-2200000000000000000000
χ4544-44-4-44-400000000−2i2i2i−2i−2i2i2i−2i0000002i−2i2i−2i0000-22-2200000000000000000000
χ4644-44-4-44-400000000−2i2i2i−2i−2i2i2i−2i000000−2i2i−2i2i00002-22-200000000000000000000
χ4744-4-444-4-444-4-4-444-40000000000000000000000000000000000000000000000
χ4844-4-444-4-4-4-444000000000000000000000000000000000000002-22-200000000
χ4944-4-444-4-4-4-44400000000000000000000000000000000000000-22-2200000000
χ504-444-44-4-4000000002-2-22-222-20000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ514-444-44-4-4000000002-2-22-222-2000000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ524-444-44-4-400000000-222-22-2-220000002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ534-444-44-4-400000000-222-22-2-22000000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ544-44-44-44-44-4-44-44-440000000000000000000000000000000000000000000000
χ554-44-44-44-4-444-4000000000000000000000000000000000000002i−2i−2i2i00000000
χ564-44-44-44-4-444-400000000000000000000000000000000000000−2i2i2i−2i00000000
χ574-4-444-4-44-44-44000000000000000000000000000000002-2-2200000000000000
χ584-4-444-4-44-44-4400000000000000000000000000000000-222-200000000000000
χ594-4-4-4-4444000000002-22-2-22-2202-2-22000002-2-22000000000000000000000000
χ604-4-4-4-4444000000002-22-2-22-220-222-200000-222-2000000000000000000000000
χ614-4-4-4-444400000000-22-222-22-202-2-2200000-222-2000000000000000000000000
χ624-4-4-4-444400000000-22-222-22-20-222-2000002-2-22000000000000000000000000

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