Finite Group Databasebeta

← Group #211518

Character table — Group #211518

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444488888888888888884444444488888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ1011111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111
χ1111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1111111111111-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1
χ1611111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-111-1-111
χ1711-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i11-1-1ii−i−iiiii−i−i−i−ii−i1-1i−i1-111-1-111-1-11-1i−i11-1-1ii−i−iii−i−i1-1i−ii−i1-1
χ1811-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i11-1-1ii−i−iiiii−i−i−i−ii−i1-1i−i1-1-1-111-1-1111-1i−i11-1-1−i−iii−i−iii-11−ii−ii-11
χ1911-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i11-1-1ii−i−i−i−i−i−iiiii−ii-11−ii-1111-1-111-1-11-1i−i-1-111ii−i−iii−i−i-11−ii−ii-11
χ2011-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i11-1-1ii−i−i−i−i−i−iiiii−ii-11−ii-11-1-111-1-1111-1i−i-1-111−i−iii−i−iii1-1i−ii−i1-1
χ2111-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i-1-111−i−iiiiiii−i−i−i−i−ii-11−ii-1111-1-1-1-111-11−ii11-1-1ii−i−i−i−iii1-1i−i−ii-11
χ2211-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i-1-111−i−iiiiiii−i−i−i−i−ii-11−ii-11-1-11111-1-1-11−ii11-1-1−i−iiiii−i−i-11−iii−i1-1
χ2311-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i-1-111−i−iii−i−i−i−iiiiii−i1-1i−i1-111-1-1-1-111-11−ii-1-111ii−i−i−i−iii-11−iii−i1-1
χ2411-11-1-11-1ii−i−iii−i−i-11-1111-1-11-1i−ii−i-1-111−i−iii−i−i−i−iiiiii−i1-1i−i1-1-1-11111-1-1-11−ii-1-111−i−iiiii−i−i1-1i−i−ii-11
χ2511-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii11-1-1−i−iiiiiii−i−i−i−ii−i-11i−i-1111-1-111-1-11-1−ii-1-111−i−iii−i−iii-11i−ii−i-11
χ2611-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii11-1-1−i−iiiiiii−i−i−i−ii−i-11i−i-11-1-111-1-1111-1−ii-1-111ii−i−iii−i−i1-1−ii−ii1-1
χ2711-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii11-1-1−i−iii−i−i−i−iiiii−ii1-1−ii1-111-1-111-1-11-1−ii11-1-1−i−iii−i−iii1-1−ii−ii1-1
χ2811-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii11-1-1−i−iii−i−i−i−iiiii−ii1-1−ii1-1-1-111-1-1111-1−ii11-1-1ii−i−iii−i−i-11i−ii−i-11
χ2911-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii-1-111ii−i−iiiii−i−i−i−i−ii1-1−ii1-111-1-1-1-111-11i−i-1-111−i−iiiii−i−i-11i−i−ii1-1
χ3011-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii-1-111ii−i−iiiii−i−i−i−i−ii1-1−ii1-1-1-11111-1-1-11i−i-1-111ii−i−i−i−iii1-1−iii−i-11
χ3111-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii-1-111ii−i−i−i−i−i−iiiiii−i-11i−i-1111-1-1-1-111-11i−i11-1-1−i−iiiii−i−i1-1−iii−i-11
χ3211-11-1-11-1−i−iii−i−iii-11-1111-1-11-1−ii−ii-1-111ii−i−i−i−i−i−iiiiii−i-11i−i-11-1-11111-1-1-11i−i11-1-1ii−i−i−i−iii-11i−i−ii1-1
χ332222222222222222-222-2-222-2-2-2-2-2-2-222222222000000000000000000000000-2-2-2-200000000000000000000
χ342222222222222222-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000000000
χ35222222222222-2-2-2-22-2-222-2-22-2-2-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ36222222222222-2-2-2-22-2-222-2-22-2-2-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000002i−2i2i−2i0000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000−2i2i−2i2i0000000000000000
χ3922222222-2-2-2-222222-2-222-2-22-2-222-2-200000000000000002222-2-2-2-200000000000000000000000000000000
χ4022222222-2-2-2-222222-2-222-2-22-2-222-2-20000000000000000-2-2-2-2222200000000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−2i2i−2i2i0000000000000000
χ4222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i000000000000000000002i−2i2i−2i0000000000000000
χ4322222222-2-2-2-2-2-2-2-2-222-2-222-2-2-222222222-2-2-2-2000000000000000000000000-2-22200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-222-2-222-2-2-22222-2-2-2-2222200000000000000000000000022-2-200000000000000000000
χ45222-2-22-2-22-22-22-22-20-2-2002200000002i−2i2i−2i2i−2i2i−2i00000000000000002−22−2i2−i2i2−i2000000002−22−2i2−i2i2−i200000000
χ46222-2-22-2-22-22-22-22-20-2-2002200000002i−2i2i−2i2i−2i2i−2i0000000000000000−22−22−i2i2−i2i200000000−22−22−i2i2−i2i200000000
χ47222-2-22-2-22-22-22-22-20-2-200220000000−2i2i−2i2i−2i2i−2i2i00000000000000002−22−2−i2i2−i2i2000000002−22−2−i2i2−i2i200000000
χ48222-2-22-2-22-22-22-22-20-2-200220000000−2i2i−2i2i−2i2i−2i2i0000000000000000−22−22i2−i2i2−i200000000−22−22i2−i2i2−i200000000
χ49222-2-22-2-2-22-22-22-220-2-2002200000002i−2i2i−2i−2i2i−2i2i00000000000000002−22−2i2−i2i2−i200000000−22−22−i2i2−i2i200000000
χ50222-2-22-2-2-22-22-22-220-2-2002200000002i−2i2i−2i−2i2i−2i2i0000000000000000−22−22−i2i2−i2i2000000002−22−2i2−i2i2−i200000000
χ51222-2-22-2-2-22-22-22-220-2-200220000000−2i2i−2i2i2i−2i2i−2i00000000000000002−22−2−i2i2−i2i200000000−22−22i2−i2i2−i200000000
χ52222-2-22-2-2-22-22-22-220-2-200220000000−2i2i−2i2i2i−2i2i−2i0000000000000000−22−22i2−i2i2−i2000000002−22−2−i2i2−i2i200000000
χ5322-22-2-22-22i2i−2i−2i2i2i−2i−2i22-2-2-22-22-22−2i2i−2i2i22-2-22i2i−2i−2i000000000000000000000000-22−2i2i00000000000000000000
χ5422-22-2-22-22i2i−2i−2i2i2i−2i−2i22-2-2-22-22-22−2i2i−2i2i-2-222−2i−2i2i2i0000000000000000000000002-22i−2i00000000000000000000
χ5522-22-2-22-22i2i−2i−2i−2i−2i2i2i2-22-2-2-2222-22i−2i−2i2i0000000022-2-2-2-22200000000000000000000−2i2i2i−2i0000000000000000
χ5622-22-2-22-22i2i−2i−2i−2i−2i2i2i2-22-2-2-2222-22i−2i−2i2i00000000-2-22222-2-2000000000000000000002i−2i−2i2i0000000000000000
χ5722-22-2-22-22i2i−2i−2i−2i−2i2i2i-2-2222-22-2-22−2i2i2i−2i00000000000000002i−2i-22−2i2i2-200000000000000000000000000000000
χ5822-22-2-22-22i2i−2i−2i−2i−2i2i2i-2-2222-22-2-22−2i2i2i−2i0000000000000000−2i2i2-22i−2i-2200000000000000000000000000000000
χ5922-22-2-22-2−2i−2i2i2i2i2i−2i−2i2-22-2-2-2222-2−2i2i2i−2i0000000022-2-2-2-222000000000000000000002i−2i−2i2i0000000000000000
χ6022-22-2-22-2−2i−2i2i2i2i2i−2i−2i2-22-2-2-2222-2−2i2i2i−2i00000000-2-22222-2-200000000000000000000−2i2i2i−2i0000000000000000
χ6122-22-2-22-2−2i−2i2i2i2i2i−2i−2i-2-2222-22-2-222i−2i−2i2i00000000000000002i−2i2-2−2i2i-2200000000000000000000000000000000
χ6222-22-2-22-2−2i−2i2i2i2i2i−2i−2i-2-2222-22-2-222i−2i−2i2i0000000000000000−2i2i-222i−2i2-200000000000000000000000000000000
χ6322-22-2-22-2−2i−2i2i2i−2i−2i2i2i22-2-2-22-22-222i−2i2i−2i22-2-2−2i−2i2i2i000000000000000000000000-222i−2i00000000000000000000
χ6422-22-2-22-2−2i−2i2i2i−2i−2i2i2i22-2-2-22-22-222i−2i2i−2i-2-2222i2i−2i−2i0000000000000000000000002-2−2i2i00000000000000000000
χ6522-2-22-2-222i−2i−2i2i2i−2i−2i2i0-22002-200000002i−2i−2i2i-222-200000000000000002−2−22i2−i2−i2i200000000i2−i2−i2i2−222−200000000
χ6622-2-22-2-222i−2i−2i2i2i−2i−2i2i0-22002-200000002i−2i−2i2i-222-20000000000000000−222−2−i2i2i2−i200000000−i2i2i2−i22−2−2200000000
χ6722-2-22-2-222i−2i−2i2i2i−2i−2i2i0-22002-20000000−2i2i2i−2i2-2-2200000000000000002−2−22−i2i2i2−i200000000i2−i2−i2i22−2−2200000000
χ6822-2-22-2-222i−2i−2i2i2i−2i−2i2i0-22002-20000000−2i2i2i−2i2-2-220000000000000000−222−2i2−i2−i2i200000000−i2i2i2−i2−222−200000000
χ6922-2-22-2-22−2i2i2i−2i−2i2i2i−2i0-22002-200000002i−2i−2i2i2-2-2200000000000000002−2−22i2−i2−i2i200000000−i2i2i2−i22−2−2200000000
χ7022-2-22-2-22−2i2i2i−2i−2i2i2i−2i0-22002-200000002i−2i−2i2i2-2-220000000000000000−222−2−i2i2i2−i200000000i2−i2−i2i2−222−200000000
χ7122-2-22-2-22−2i2i2i−2i−2i2i2i−2i0-22002-20000000−2i2i2i−2i-222-200000000000000002−2−22−i2i2i2−i200000000−i2i2i2−i2−222−200000000
χ7222-2-22-2-22−2i2i2i−2i−2i2i2i−2i0-22002-20000000−2i2i2i−2i-222-20000000000000000−222−2i2−i2−i2i200000000i2−i2−i2i22−2−2200000000
χ73444-4-44-4-44-44-4-44-4404400-4-4000000000000000000000000000000000000000000000000000000000000000
χ74444-4-44-4-4-44-444-44-404400-4-4000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-444i−4i−4i4i−4i4i4i−4i04-400-44000000000000000000000000000000000000000000000000000000000000000
χ7644-4-44-4-44−4i4i4i−4i4i−4i−4i4i04-400-44000000000000000000000000000000000000000000000000000000000000000
χ774-44-4-4-444000000004004-400-4000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ784-44-4-4-444000000004004-400-400000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ794-44-4-4-44400000000-400-440040000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ804-44-4-4-44400000000-400-4400400000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ814-4-4-4444-400000000400-4400-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ824-4-4-4444-400000000400-4400-400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ834-4-4-4444-400000000-4004-40040000000000000022−2222−22−2222−22220000000000000000000000000000000000000000
χ844-4-4-4444-400000000-4004-400400000000000000−2222−222222−2222−220000000000000000000000000000000000000000
χ858-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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