Finite Group Databasebeta

← Group #136252

Character table — Group #136252

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222244444444444422224444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111
χ5111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ911-111-1-1-11-11-11-1-1iiii−i−i−i−i111-1-11-1ii−i−i11-1-1ii−i−i1-1i−ii−ii−i11-1-1ii−i−i11-1-1
χ1011-111-1-1-11-11-11-1-1iiii−i−i−i−i111-1-11-1ii−i−i11-1-1ii−i−i1-1−iii−i−ii-1-111−i−iii-1-111
χ1111-111-1-1-11-11-11-1-1iiii−i−i−i−i1-1-1111-1−i−iii-1-111−i−iii1-1i−ii−ii−i11-1-1−i−iii-1-111
χ1211-111-1-1-11-11-11-1-1iiii−i−i−i−i1-1-1111-1−i−iii-1-111−i−iii1-1−iii−i−ii-1-111ii−i−i11-1-1
χ1311-111-1-1-11-11-11-1-1−i−i−i−iiiii111-1-11-1−i−iii11-1-1−i−iii1-1i−i−iii−i-1-111ii−i−i-1-111
χ1411-111-1-1-11-11-11-1-1−i−i−i−iiiii111-1-11-1−i−iii11-1-1−i−iii1-1−ii−ii−ii11-1-1−i−iii11-1-1
χ1511-111-1-1-11-11-11-1-1−i−i−i−iiiii1-1-1111-1ii−i−i-1-111ii−i−i1-1i−i−iii−i-1-111−i−iii11-1-1
χ1611-111-1-1-11-11-11-1-1−i−i−i−iiiii1-1-1111-1ii−i−i-1-111ii−i−i1-1−ii−ii−ii11-1-1ii−i−i-1-111
χ172222222222222222222222220000-2-2000000000000-2-200-2-200000000000000
χ18222222222222222-2-2-2-2-2-2-2-220000-2-2000000000000-2-2002200000000000000
χ19222222222222-2-2-200000000-20000-2222220000-2-2-2-22-2000000000000000000
χ20222222222222-2-2-200000000-20000-22-2-2-2-2000022222-2000000000000000000
χ21222222222222-2-2-200000000-222222-20000-2-2-2-20000-22000000000000000000
χ22222222222222-2-2-200000000-2-2-2-2-22-2000022220000-22000000000000000000
χ2322-222-2-2-22-22-22-2-22i2i2i2i−2i−2i−2i−2i20000-22000000000000-2200−2i2i00000000000000
χ2422-222-2-2-22-22-22-2-2−2i−2i−2i−2i2i2i2i2i20000-22000000000000-22002i−2i00000000000000
χ2522-222-2-2-22-22-2-22200000000-20000-2-22i2i−2i−2i0000−2i−2i2i2i22000000000000000000
χ2622-222-2-2-22-22-2-22200000000-20000-2-2−2i−2i2i2i00002i2i−2i−2i22000000000000000000
χ2722-222-2-2-22-22-2-22200000000-222-2-2220000-2-2220000-2-2000000000000000000
χ2822-222-2-2-22-22-2-22200000000-2-2-22222000022-2-20000-2-2000000000000000000
χ292-222-22-2-2-2-22222-222-2-222-2-2-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-222-22-2-2-2-22222-222-2-222-2-2-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-222-22-2-2-2-22222-2-2-222-2-222-2000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-222-22-2-2-2-22222-2-2-222-2-222-2000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-22-2-222-222-22-222i2i−2i−2i−2i−2i2i2i-20000000000000000000000000000002−2−22−i2i2i2−i2
χ342-2-22-2-222-222-22-222i2i−2i−2i−2i−2i2i2i-2000000000000000000000000000000−222−2i2−i2−i2i2
χ352-2-22-2-222-222-22-22−2i−2i2i2i2i2i−2i−2i-20000000000000000000000000000002−2−22i2−i2−i2i2
χ362-2-22-2-222-222-22-22−2i−2i2i2i2i2i−2i−2i-2000000000000000000000000000000−222−2−i2i2i2−i2
χ3744444444-4-4-4-4000000000000000000000000000000002200-2-2000000000000
χ3844444444-4-4-4-400000000000000000000000000000000-2-20022000000000000
χ39444-4-4-4-4400000002i−2i2i−2i2i−2i2i−2i000000000002i−2i2i−2i2-22-200000000000000000000
χ40444-4-4-4-4400000002i−2i2i−2i2i−2i2i−2i00000000000−2i2i−2i2i-22-2200000000000000000000
χ41444-4-4-4-440000000−2i2i−2i2i−2i2i−2i2i000000000002i−2i2i−2i-22-2200000000000000000000
χ42444-4-4-4-440000000−2i2i−2i2i−2i2i−2i2i00000000000−2i2i−2i2i2-22-200000000000000000000
χ4344-444-4-4-4-44-44000000000000000000000000000000002i−2i00−2i2i000000000000
χ4444-444-4-4-4-44-4400000000000000000000000000000000−2i2i002i−2i000000000000
χ4544-4-4-444-400000002-22-2-22-22000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ4644-4-4-444-400000002-22-2-22-2200000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ4744-4-4-444-40000000-22-222-22-2000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ4844-4-4-444-40000000-22-222-22-200000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ494-444-44-4-444-4-4000000000000000000000000000000000000002-22-200000000
χ504-444-44-4-444-4-400000000000000000000000000000000000000-22-2200000000
χ514-444-44-4-4-4-444-4-4400000000400000000000000000000000000000000000000
χ524-44-44-44-400000002i−2i−2i2i2i−2i−2i2i02-22-2002i−2i2i−2i0000000000000000000000000000
χ534-44-44-44-400000002i−2i−2i2i2i−2i−2i2i0-22-2200−2i2i−2i2i0000000000000000000000000000
χ544-44-44-44-40000000−2i2i2i−2i−2i2i2i−2i02-22-200−2i2i−2i2i0000000000000000000000000000
χ554-44-44-44-40000000−2i2i2i−2i−2i2i2i−2i0-22-22002i−2i2i−2i0000000000000000000000000000
χ564-4-44-4-4444-4-44000000000000000000000000000000000000002-2-2200000000
χ574-4-44-4-4444-4-4400000000000000000000000000000000000000-222-200000000
χ584-4-44-4-444-444-4-44-400000000400000000000000000000000000000000000000
χ594-4-4-444-4400000002-2-22-222-202-2-22002-2-220000000000000000000000000000
χ604-4-4-444-4400000002-2-22-222-20-222-200-222-20000000000000000000000000000
χ614-4-4-444-440000000-222-22-2-2202-2-2200-222-20000000000000000000000000000
χ624-4-4-444-440000000-222-22-2-220-222-2002-2-220000000000000000000000000000

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