Finite Group Databasebeta

← Group #116109

Character table — Group #116109

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222222244442222444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911-11-1-11-11-1-1111-1-11-1-11111-1-1-1ii−i−iii−i−i1111-1-1-1-1i−i1-1i−i1-111-1-1ii−i−iii−i−i
χ1011-11-1-11-11-1-1111-1-11-1-11111-1-1-1ii−i−iii−i−i1111-1-1-1-1−ii-11−ii-11-1-111ii−i−i−i−iii
χ1111-11-1-11-11-1-1111-1-11-1-11111-1-1-1ii−i−iii−i−i-1-1-1-11111i−i-11i−i-1111-1-1−i−iii−i−iii
χ1211-11-1-11-11-1-1111-1-11-1-11111-1-1-1ii−i−iii−i−i-1-1-1-11111−ii1-1−ii1-1-1-111−i−iiiii−i−i
χ1311-11-1-11-11-1-1111-1-11-1-11111-1-1-1−i−iii−i−iii1111-1-1-1-1i−i-11i−i-11-1-111−i−iiiii−i−i
χ1411-11-1-11-11-1-1111-1-11-1-11111-1-1-1−i−iii−i−iii1111-1-1-1-1−ii1-1−ii1-111-1-1−i−iii−i−iii
χ1511-11-1-11-11-1-1111-1-11-1-11111-1-1-1−i−iii−i−iii-1-1-1-11111i−i1-1i−i1-1-1-111ii−i−i−i−iii
χ1611-11-1-11-11-1-1111-1-11-1-11111-1-1-1−i−iii−i−iii-1-1-1-11111−ii-11−ii-1111-1-1ii−i−iii−i−i
χ172222222222222222-2-2-2-22-2-22-2-200000000000000002200-2-200000000000000
χ182222222222222222-2-2-2-22-2-22-2-20000000000000000-2-2002200000000000000
χ19222222222222-2-2-2-22222-2-2-2-2-2-20000000000000000000000002-22-200000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000-22-2200000000
χ21222222222222-2-2-2-2-2-2-2-2-222-2222222-2-2-2-20000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-222-222-2-2-2-222220000000000000000000000000000
χ2322222222-2-2-2-2222222-2-2-22-2-2-220000000000000000002200-2-2000000000000
χ2422222222-2-2-2-2222222-2-2-22-2-2-22000000000000000000-2-20022000000000000
χ2522222222-2-2-2-22222-2-222-2-22-22-200000000000000000000000000002-22-20000
χ2622222222-2-2-2-22222-2-222-2-22-22-20000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-2-2-222-2-22-2222-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22-2222-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-2-22222-22-22000000000000000000000000000000002-22-2
χ3022222222-2-2-2-2-2-2-2-2-2-22222-22-2200000000000000000000000000000000-22-22
χ3122-22-2-22-22-2-2222-2-2-222-22-2-2-22200000000000000002i−2i00−2i2i00000000000000
χ3222-22-2-22-22-2-2222-2-2-222-22-2-2-2220000000000000000−2i2i002i−2i00000000000000
χ3322-22-2-22-22-2-22-2-2222-2-22-2-2-22220000000000000000000000002-2-2200000000
χ3422-22-2-22-22-2-22-2-2222-2-22-2-2-2222000000000000000000000000-222-200000000
χ3522-22-2-22-22-2-22-2-222-222-2-2222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ3622-22-2-22-22-2-22-2-222-222-2-2222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ3722-22-2-22-2-222-222-2-22-22-2-22-222-20000000000000000002-200-22000000000000
χ3822-22-2-22-2-222-222-2-22-22-2-22-222-2000000000000000000-22002-2000000000000
χ3922-22-2-22-2-222-222-2-2-22-22-2-222-2200000000000000000000000000002i−2i−2i2i0000
χ4022-22-2-22-2-222-222-2-2-22-22-2-222-220000000000000000000000000000−2i2i2i−2i0000
χ4122-22-2-22-2-222-2-2-2222-22-22-22-2-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4222-22-2-22-2-222-2-2-2222-22-22-22-2-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4322-22-2-22-2-222-2-2-222-22-2222-2-22-2000000000000000000000000000000002i−2i−2i2i
χ4422-22-2-22-2-222-2-2-222-22-2222-2-22-200000000000000000000000000000000−2i2i2i−2i
χ45444-4-4-4-4444-4-400000000000000000000002-22-22-22-200000000000000000000
χ46444-4-4-4-4444-4-40000000000000000000000-22-22-22-2200000000000000000000
χ47444-4-4-4-44-4-44400000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ48444-4-4-4-44-4-4440000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ4944-4-444-4-44-44-400000000000000000000002-22-2-22-2200000000000000000000
χ5044-4-444-4-44-44-40000000000000000000000-22-222-22-200000000000000000000
χ5144-4-444-4-4-44-4400000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ5244-4-444-4-4-44-440000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ534-44-44-44-400004-44-400000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ544-44-44-44-400004-44-40000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ554-44-44-44-40000-44-4400000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ564-44-44-44-40000-44-440000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ574-4-4-4-444400004-4-4400000000002-2-222-2-220000000000000000000000000000
χ584-4-4-4-444400004-4-440000000000-222-2-222-20000000000000000000000000000
χ594-4-4-4-44440000-444-400000000002-2-22-222-20000000000000000000000000000
χ604-4-4-4-44440000-444-40000000000-222-22-2-220000000000000000000000000000
χ618-888-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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