Finite Group Databasebeta

← Group #209002

Character table — Group #209002

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444444444444444444222244444444444444444444444488888888888888882244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1711-111-1-1-11-11-1iiii−i−i−i−iii−i−i11-1-1i−iii−i−i11-1-11-11-11-1i−ii−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ1811-111-1-1-11-11-1iiii−i−i−i−iii−i−i11-1-1i−iii−i−i11-1-11-11-11-1i−ii−i11-1-1i−ii−ii−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-11−ii
χ1911-111-1-1-11-11-1iiii−i−i−i−iii−i−i11-1-1i−iii−i−i11-1-11-1-11-11−ii−ii-1-111−iii−i−ii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii1-1i−i
χ2011-111-1-1-11-11-1iiii−i−i−i−iii−i−i11-1-1i−iii−i−i11-1-11-1-11-11−ii−ii-1-111−iii−i−ii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii
χ2111-111-1-1-11-11-1iiii−i−i−i−iii−i−i-1-111i−i−i−iii11-1-1-111-11-1−iii−i-1-111−ii−iii−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ2211-111-1-1-11-11-1iiii−i−i−i−iii−i−i-1-111i−i−i−iii11-1-1-111-11-1−iii−i-1-111−ii−iii−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i1-1i−i
χ2311-111-1-1-11-11-1iiii−i−i−i−iii−i−i-1-111i−i−i−iii11-1-1-11-11-11i−i−ii11-1-1i−i−ii−ii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ2411-111-1-1-11-11-1iiii−i−i−i−iii−i−i-1-111i−i−i−iii11-1-1-11-11-11i−i−ii11-1-1i−i−ii−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i
χ2511-111-1-1-11-11-1−i−i−i−iiiii−i−iii11-1-1−ii−i−iii11-1-11-11-11-1−ii−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ2611-111-1-1-11-11-1−i−i−i−iiiii−i−iii11-1-1−ii−i−iii11-1-11-11-11-1−ii−ii11-1-1−ii−ii−ii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-11i−i
χ2711-111-1-1-11-11-1−i−i−i−iiiii−i−iii11-1-1−ii−i−iii11-1-11-1-11-11i−ii−i-1-111i−i−iii−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ2811-111-1-1-11-11-1−i−i−i−iiiii−i−iii11-1-1−ii−i−iii11-1-11-1-11-11i−ii−i-1-111i−i−iii−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i
χ2911-111-1-1-11-11-1−i−i−i−iiiii−i−iii-1-111−iiii−i−i11-1-1-111-11-1i−i−ii-1-111i−ii−i−ii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i
χ3011-111-1-1-11-11-1−i−i−i−iiiii−i−iii-1-111−iiii−i−i11-1-1-111-11-1i−i−ii-1-111i−ii−i−ii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii1-1−ii
χ3111-111-1-1-11-11-1−i−i−i−iiiii−i−iii-1-111−iiii−i−i11-1-1-11-11-11−iii−i11-1-1−iii−ii−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-11i−i
χ3211-111-1-1-11-11-1−i−i−i−iiiii−i−iii-1-111−iiii−i−i11-1-1-11-11-11−iii−i11-1-1−iii−ii−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii
χ3322222222222222222222-2-2-2-22222-2-22222-2-2-2-2-2-200000000000000-2-2000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000000000000022000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000000000022000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-22200000000000000-2-2000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-222220000-2-200002-22-200000022002-22-2-2-200000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-222220000-2-200002-22-2000000-2-200-22-222200000000000000000000000000000000
χ3922222222-2-2-2-222-2-222-2-2-2-2-2-20000220000-22-220022-2-2002200000000-2-20000000000000000000000000000
χ4022222222-2-2-2-222-2-222-2-2-2-2-2-20000220000-22-2200-2-22200-2-200000000220000000000000000000000000000
χ4122222222-2-2-2-2-2-222-2-22222220000-2-20000-22-220022-2-200-2-200000000220000000000000000000000000000
χ4222222222-2-2-2-2-2-222-2-22222220000-2-20000-22-2200-2-222002200000000-2-20000000000000000000000000000
χ4322222222-2-2-2-2-2-222-2-222-2-2-2-200002200002-22-20000002200-22-22-2-200000000000000000000000000000000
χ4422222222-2-2-2-2-2-222-2-222-2-2-2-200002200002-22-2000000-2-2002-22-22200000000000000000000000000000000
χ45222-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i002-22-200000000000000000000000000000000i2−i2i2−i22−22−22−22−2i2−i2i2−i20000
χ46222-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i002-22-200000000000000000000000000000000−i2i2−i2i2−22−22−22−22−i2i2−i2i20000
χ47222-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i00-22-2200000000000000000000000000000000i2−i2i2−i22−22−2−22−22−i2i2−i2i20000
χ48222-2-2-22-22-2-222i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i00-22-2200000000000000000000000000000000−i2i2−i2i2−22−222−22−2i2−i2i2−i20000
χ49222-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i00-22-2200000000000000000000000000000000i2−i2i2−i2−22−222−22−2−i2i2−i2i20000
χ50222-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i00-22-2200000000000000000000000000000000−i2i2−i2i22−22−2−22−22i2−i2i2−i20000
χ51222-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i002-22-200000000000000000000000000000000i2−i2i2−i2−22−22−22−22i2−i2i2−i20000
χ52222-2-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i002-22-200000000000000000000000000000000−i2i2−i2i22−22−22−22−2−i2i2−i2i20000
χ5322-222-2-2-22-22-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i22-2-2−2i2i2i2i−2i−2i-2-222-2200000000000000−2i2i000000000000000000000000000000
χ5422-222-2-2-22-22-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i-2-222−2i2i−2i−2i2i2i-2-2222-2000000000000002i−2i000000000000000000000000000000
χ5522-222-2-2-22-22-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i22-2-22i−2i−2i−2i2i2i-2-222-22000000000000002i−2i000000000000000000000000000000
χ5622-222-2-2-22-22-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i-2-2222i−2i2i2i−2i−2i-2-2222-200000000000000−2i2i000000000000000000000000000000
χ5722-222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000−2i2i00002-2-220000002i−2i002-2-22−2i2i00000000000000000000000000000000
χ5822-222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000−2i2i00002-2-22000000−2i2i00-222-22i−2i00000000000000000000000000000000
χ5922-222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00002i−2i0000-222-2002-2-22002i−2i00000000−2i2i0000000000000000000000000000
χ6022-222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00002i−2i0000-222-200-222-200−2i2i000000002i−2i0000000000000000000000000000
χ6122-222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000−2i2i0000-222-2002-2-2200−2i2i000000002i−2i0000000000000000000000000000
χ6222-222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000−2i2i0000-222-200-222-2002i−2i00000000−2i2i0000000000000000000000000000
χ6322-222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00002i−2i00002-2-220000002i−2i00-222-2−2i2i00000000000000000000000000000000
χ6422-222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00002i−2i00002-2-22000000−2i2i002-2-222i−2i00000000000000000000000000000000
χ6522-2-2-22-2222-2-22-22-2-22-2200002i−2i−2i2i00−2i2i2i−2i00000000000000000000000000000000i2−i2−i2i2−i2i2i2−i22−2−222−2−220000
χ6622-2-2-22-2222-2-22-22-2-22-2200002i−2i−2i2i00−2i2i2i−2i00000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−222−2−222−20000
χ6722-2-2-22-2222-2-22-22-2-22-220000−2i2i2i−2i002i−2i−2i2i00000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−222−2−222−20000
χ6822-2-2-22-2222-2-22-22-2-22-220000−2i2i2i−2i002i−2i−2i2i00000000000000000000000000000000−i2i2i2−i2i2−i2−i2i22−2−222−2−220000
χ6922-2-2-22-2222-2-2-22-222-22-200002i−2i−2i2i002i−2i−2i2i00000000000000000000000000000000i2−i2−i2i2i2−i2−i2i22−2−22−222−20000
χ7022-2-2-22-2222-2-2-22-222-22-200002i−2i−2i2i002i−2i−2i2i00000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−22−2−220000
χ7122-2-2-22-2222-2-2-22-222-22-20000−2i2i2i−2i00−2i2i2i−2i00000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−222−22−2−220000
χ7222-2-2-22-2222-2-2-22-222-22-20000−2i2i2i−2i00−2i2i2i−2i00000000000000000000000000000000−i2i2i2−i2−i2i2i2−i22−2−22−222−20000
χ73444-4-4-44-4-444-44i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-44-4-444-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-44-4-4444-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-44-44-4-444-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-40000000000004i−4i4i−4i00000000000000000000000000000000002-22-22i−2i2i−2i00000000000000000000
χ784-444-44-4-40000000000004i−4i4i−4i0000000000000000000000000000000000-22-22−2i2i−2i2i00000000000000000000
χ794-444-44-4-4000000000000−4i4i−4i4i00000000000000000000000000000000002-22-2−2i2i−2i2i00000000000000000000
χ804-444-44-4-4000000000000−4i4i−4i4i0000000000000000000000000000000000-22-222i−2i2i−2i00000000000000000000
χ814-4-44-4-4440000000000004-4-4400000000000000000000000000000000002-2-222-2-2200000000000000000000
χ824-4-44-4-4440000000000004-4-440000000000000000000000000000000000-222-2-222-200000000000000000000
χ834-4-44-4-444000000000000-444-400000000000000000000000000000000002-2-22-222-200000000000000000000
χ844-4-44-4-444000000000000-444-40000000000000000000000000000000000-222-22-2-2200000000000000000000
χ858-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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