Finite Group Databasebeta

← Group #136154

Character table — Group #136154

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1
χ911-11-1-11-11-11-11-1-11ii−i−i1-111-1-1ii−i−iii−i−i1-1i−i1-1i−ii−i11-1-1ii−i−i11-1-1
χ1011-11-1-11-11-11-11-1-11ii−i−i1-111-1-1ii−i−iii−i−i1-1−ii1-1i−i−ii-1-111−i−iii-1-111
χ1111-11-1-11-11-11-11-1-11ii−i−i1-1-1-111ii−i−i−i−iii1-1i−i-11−iii−i11-1-1−i−iii-1-111
χ1211-11-1-11-11-11-11-1-11ii−i−i1-1-1-111ii−i−i−i−iii1-1−ii-11−ii−ii-1-111ii−i−i11-1-1
χ1311-11-1-11-11-11-11-1-11−i−iii1-111-1-1−i−iii−i−iii1-1i−i1-1−iii−i-1-111ii−i−i-1-111
χ1411-11-1-11-11-11-11-1-11−i−iii1-111-1-1−i−iii−i−iii1-1−ii1-1−ii−ii11-1-1−i−iii11-1-1
χ1511-11-1-11-11-11-11-1-11−i−iii1-1-1-111−i−iiiii−i−i1-1i−i-11i−ii−i-1-111−i−iii11-1-1
χ1611-11-1-11-11-11-11-1-11−i−iii1-1-1-111−i−iiiii−i−i1-1−ii-11i−i−ii11-1-1ii−i−i-1-111
χ1722222222222222222222-2-20000-2-2-2-20000-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2000022220000-2-200000000000000000000
χ19222222222222-2-2-2-200002-2222200000000-2200-2-20000000000000000
χ20222222222222-2-2-2-200002-2-2-2-2-200000000-2200220000000000000000
χ21222222222222-2-2-2-20000-220000000022222-20000-2-200000000000000
χ22222222222222-2-2-2-20000-2200000000-2-2-2-22-200002200000000000000
χ2322-22-2-22-22-22-22-2-222i2i−2i−2i-220000−2i−2i2i2i0000-2200000000000000000000
χ2422-22-2-22-22-22-22-2-22−2i−2i2i2i-2200002i2i−2i−2i0000-2200000000000000000000
χ2522-22-2-22-22-22-2-222-200002222-2-200000000-2-200-220000000000000000
χ2622-22-2-22-22-22-2-222-2000022-2-22200000000-2-2002-20000000000000000
χ2722-22-2-22-22-22-2-222-20000-2-2000000002i2i−2i−2i220000−2i2i00000000000000
χ2822-22-2-22-22-22-2-222-20000-2-200000000−2i−2i2i2i2200002i−2i00000000000000
χ292-2222-2-2-222-2-222-2-22-22-200000000000000000000000000002−22−22−22−2
χ302-2222-2-2-222-2-222-2-22-22-20000000000000000000000000000−22−22−22−22
χ312-2222-2-2-222-2-222-2-2-22-2200000000000000000000000000002−22−2−22−22
χ322-2222-2-2-222-2-222-2-2-22-220000000000000000000000000000−22−222−22−2
χ332-2-22-22-222-2-222-22-22i−2i−2i2i0000000000000000000000000000i2−i2−i2i22−2−22
χ342-2-22-22-222-2-222-22-22i−2i−2i2i0000000000000000000000000000−i2i2i2−i2−222−2
χ352-2-22-22-222-2-222-22-2−2i2i2i−2i0000000000000000000000000000i2−i2−i2i2−222−2
χ362-2-22-22-222-2-222-22-2−2i2i2i−2i0000000000000000000000000000−i2i2i2−i22−2−22
χ3744444444-4-4-4-4000000000000000000000000220000-2-2000000000000
χ3844444444-4-4-4-4000000000000000000000000-2-2000022000000000000
χ39444-4-44-4-4000000000000002-22-22-22-22-22-20000000000000000000000
χ40444-4-44-4-4000000000000002-22-2-22-22-22-220000000000000000000000
χ41444-4-44-4-400000000000000-22-222-22-2-22-220000000000000000000000
χ42444-4-44-4-400000000000000-22-22-22-222-22-20000000000000000000000
χ4344-44-4-44-4-44-440000000000000000000000002i−2i0000−2i2i000000000000
χ4444-44-4-44-4-44-44000000000000000000000000−2i2i00002i−2i000000000000
χ4544-4-44-4-44000000000000002-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ4644-4-44-4-44000000000000002-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ4744-4-44-4-4400000000000000-222-22i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ4844-4-44-4-4400000000000000-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ494-4444-4-4-444-4-4-4-4440000000000000000000000000000000000000000
χ504-4444-4-4-4-4-444000000000000000000000000000000002i−2i2i−2i00000000
χ514-4444-4-4-4-4-44400000000000000000000000000000000−2i2i−2i2i00000000
χ524-4-44-44-444-4-44-44-440000000000000000000000000000000000000000
χ534-4-44-44-44-444-4000000000000000000000000000000002i−2i−2i2i00000000
χ544-4-44-44-44-444-400000000000000000000000000000000−2i2i2i−2i00000000
χ558-88-8-8-888000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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