Finite Group Databasebeta

← Group #210089

Character table — Group #210089

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444444444444442222444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ17111-1-1-1-1111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i11-1-1i−ii−iii−i−i1-11-11-1i−ii−iii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1i−i1-1i−i1-1
χ18111-1-1-1-1111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i11-1-1i−ii−iii−i−i1-11-11-1i−ii−iii−i−i11-1-1−i−iii-1-111−i−iii-1-111−ii-11−ii-11
χ19111-1-1-1-1111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i-1-111i−ii−i−i−iii1-11-1-11i−i−ii−i−iii-1-111ii−i−i11-1-1−i−iii-1-111i−i1-1−ii-11
χ20111-1-1-1-1111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i-1-111i−ii−i−i−iii1-11-1-11i−i−ii−i−iii-1-111−i−iii-1-111ii−i−i11-1-1−ii-11i−i1-1
χ21111-1-1-1-1111-1-1ii−i−iii−i−i11-1-1-1-111−i−iii11-1-1i−ii−iii−i−i1-1-111-1−iii−i−i−iii-1-111ii−i−i11-1-1ii−i−i11-1-1−ii-11−ii-11
χ22111-1-1-1-1111-1-1ii−i−iii−i−i11-1-1-1-111−i−iii11-1-1i−ii−iii−i−i1-1-111-1−iii−i−i−iii-1-111−i−iii-1-111−i−iii-1-111i−i1-1i−i1-1
χ23111-1-1-1-1111-1-1ii−i−iii−i−i11-1-1-1-111−i−iii-1-111i−ii−i−i−iii1-1-11-11−ii−iiii−i−i11-1-1ii−i−i11-1-1−i−iii-1-111−ii-11i−i1-1
χ24111-1-1-1-1111-1-1ii−i−iii−i−i11-1-1-1-111−i−iii-1-111i−ii−i−i−iii1-1-11-11−ii−iiii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1i−i1-1−ii-11
χ25111-1-1-1-1111-1-1−i−iii−i−iii11-1-111-1-1−i−iii11-1-1−ii−ii−i−iii1-11-11-1−ii−ii−i−iii11-1-1ii−i−i-1-111ii−i−i-1-111i−i-11i−i-11
χ26111-1-1-1-1111-1-1−i−iii−i−iii11-1-111-1-1−i−iii11-1-1−ii−ii−i−iii1-11-11-1−ii−ii−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−ii1-1−ii1-1
χ27111-1-1-1-1111-1-1−i−iii−i−iii11-1-111-1-1−i−iii-1-111−ii−iiii−i−i1-11-1-11−iii−iii−i−i-1-111ii−i−i-1-111−i−iii11-1-1i−i-11−ii1-1
χ28111-1-1-1-1111-1-1−i−iii−i−iii11-1-111-1-1−i−iii-1-111−ii−iiii−i−i1-11-1-11−iii−iii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−ii1-1i−i-11
χ29111-1-1-1-1111-1-1−i−iii−i−iii11-1-1-1-111ii−i−i11-1-1−ii−ii−i−iii1-1-111-1i−i−iiii−i−i-1-111ii−i−i-1-111ii−i−i-1-111−ii1-1−ii1-1
χ30111-1-1-1-1111-1-1−i−iii−i−iii11-1-1-1-111ii−i−i11-1-1−ii−ii−i−iii1-1-111-1i−i−iiii−i−i-1-111−i−iii11-1-1−i−iii11-1-1i−i-11i−i-11
χ31111-1-1-1-1111-1-1−i−iii−i−iii11-1-1-1-111ii−i−i-1-111−ii−iiii−i−i1-1-11-11i−ii−i−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1−ii1-1i−i-11
χ32111-1-1-1-1111-1-1−i−iii−i−iii11-1-1-1-111ii−i−i-1-111−ii−iiii−i−i1-1-11-11i−ii−i−i−iii11-1-1−i−iii11-1-1ii−i−i-1-111i−i-11−ii1-1
χ33222222222-22-2222222222-22-2000000002222-2-2-2-22222-2-200-2-200-2-200000000000000000000000000000000
χ34222222222-22-2222222222-22-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-20022002200000000000000000000000000000000
χ35222222222-22-2-2-2-2-2-2-2-2-22-22-20000000022222222-2-2-2-2-2-200-2-2002200000000000000000000000000000000
χ36222222222-22-2-2-2-2-2-2-2-2-22-22-200000000-2-2-2-222222222-2-2002200-2-200000000000000000000000000000000
χ3722222222-22-222222-2-2-2-2-22-222222-2-2-2-2000022-2-20000-2-2-2-200220000000000000000000000000000000000
χ3822222222-22-222222-2-2-2-2-22-22-2-2-2-22222000022-2-20000-2-22200-2-20000000000000000000000000000000000
χ3922222222-22-22-2-2-2-22222-22-22222222220000-2-2220000-2-2-2-200-2-20000000000000000000000000000000000
χ4022222222-22-22-2-2-2-22222-22-22-2-2-2-2-2-2-2-20000-2-2220000-2-22200220000000000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000-2-222000022000000002-22-22-22-2000000000000000000000000
χ4222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000-2-22200002200000000-22-22-22-22000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000022-2-2000022000000002-22-2-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000022-2-200002200000000-22-222-22-2000000000000000000000000
χ45222-2-2-2-222-2-222i2i−2i−2i2i2i−2i−2i2-2-220000000022-2-2−2i2i−2i2i2i2i−2i−2i-2200-2200−2i2i00000000000000000000000000000000
χ46222-2-2-2-222-2-222i2i−2i−2i2i2i−2i−2i2-2-2200000000-2-222−2i2i−2i2i−2i−2i2i2i-22002-2002i−2i00000000000000000000000000000000
χ47222-2-2-2-222-2-22−2i−2i2i2i−2i−2i2i2i2-2-220000000022-2-22i−2i2i−2i−2i−2i2i2i-2200-22002i−2i00000000000000000000000000000000
χ48222-2-2-2-222-2-22−2i−2i2i2i−2i−2i2i2i2-2-2200000000-2-2222i−2i2i−2i2i2i−2i−2i-22002-200−2i2i00000000000000000000000000000000
χ49222-2-2-2-22-222-22i2i−2i−2i−2i−2i2i2i-222-222-2-2−2i−2i2i2i00002i−2i−2i2i0000-22-22002i−2i0000000000000000000000000000000000
χ50222-2-2-2-22-222-22i2i−2i−2i−2i−2i2i2i-222-2-2-2222i2i−2i−2i00002i−2i−2i2i0000-222-200−2i2i0000000000000000000000000000000000
χ51222-2-2-2-22-222-2−2i−2i2i2i2i2i−2i−2i-222-222-2-22i2i−2i−2i0000−2i2i2i−2i0000-22-2200−2i2i0000000000000000000000000000000000
χ52222-2-2-2-22-222-2−2i−2i2i2i2i2i−2i−2i-222-2-2-222−2i−2i2i2i0000−2i2i2i−2i0000-222-2002i−2i0000000000000000000000000000000000
χ53222-2-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i-2-222000000000000−2i2i2i−2i00002-2000000002i−2i−2i2i2-2-22000000000000000000000000
χ54222-2-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i-2-222000000000000−2i2i2i−2i00002-200000000−2i2i2i−2i-222-2000000000000000000000000
χ55222-2-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i-2-2220000000000002i−2i−2i2i00002-2000000002i−2i−2i2i-222-2000000000000000000000000
χ56222-2-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i-2-2220000000000002i−2i−2i2i00002-200000000−2i2i2i−2i2-2-22000000000000000000000000
χ5722-222-2-2-2-20-202-22-22-22-22020000000002i−2i2i−2i00002i−2i2i−2i000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ5822-222-2-2-2-20-202-22-22-22-22020000000002i−2i2i−2i00002i−2i2i−2i000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ5922-222-2-2-2-20-202-22-22-22-2202000000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ6022-222-2-2-2-20-202-22-22-22-2202000000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ6122-222-2-2-2-20-20-22-22-22-222020000000002i−2i2i−2i0000−2i2i−2i2i000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ6222-222-2-2-2-20-20-22-22-22-222020000000002i−2i2i−2i0000−2i2i−2i2i000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ6322-222-2-2-2-20-20-22-22-22-22202000000000−2i2i−2i2i00002i−2i2i−2i000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ6422-222-2-2-2-20-20-22-22-22-22202000000000−2i2i−2i2i00002i−2i2i−2i000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ6522-2-2-222-2-20202i−2i−2i2i2i−2i−2i2i20-20000000002i−2i−2i2i0000-222-20000000000000000002−2−22−i2i2i2−i2−i2i2i2−i2−222−200000000
χ6622-2-2-222-2-20202i−2i−2i2i2i−2i−2i2i20-20000000002i−2i−2i2i0000-222-2000000000000000000−222−2i2−i2−i2i2i2−i2−i2i22−2−2200000000
χ6722-2-2-222-2-20202i−2i−2i2i2i−2i−2i2i20-2000000000−2i2i2i−2i00002-2-220000000000000000002−2−22−i2i2i2−i2i2−i2−i2i22−2−2200000000
χ6822-2-2-222-2-20202i−2i−2i2i2i−2i−2i2i20-2000000000−2i2i2i−2i00002-2-22000000000000000000−222−2i2−i2−i2i2−i2i2i2−i2−222−200000000
χ6922-2-2-222-2-2020−2i2i2i−2i−2i2i2i−2i20-20000000002i−2i−2i2i00002-2-220000000000000000002−2−22i2−i2−i2i2−i2i2i2−i22−2−2200000000
χ7022-2-2-222-2-2020−2i2i2i−2i−2i2i2i−2i20-20000000002i−2i−2i2i00002-2-22000000000000000000−222−2−i2i2i2−i2i2−i2−i2i2−222−200000000
χ7122-2-2-222-2-2020−2i2i2i−2i−2i2i2i−2i20-2000000000−2i2i2i−2i0000-222-20000000000000000002−2−22i2−i2−i2i2i2−i2−i2i2−222−200000000
χ7222-2-2-222-2-2020−2i2i2i−2i−2i2i2i−2i20-2000000000−2i2i2i−2i0000-222-2000000000000000000−222−2−i2i2i2−i2−i2i2i2−i22−2−2200000000
χ7344-444-4-4-440404-44-4-44-44-40-4000000000000000000000000000000000000000000000000000000000000000
χ7444-444-4-4-44040-44-444-44-4-40-4000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-440-404i−4i−4i4i−4i4i4i−4i-404000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-440-40−4i4i4i−4i4i−4i−4i4i-404000000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-40404000000000-40-400004-44-4000000000000000000000000000000000000000000000000000000
χ784-444-44-4-40404000000000-40-40000-44-44000000000000000000000000000000000000000000000000000000
χ794-444-44-4-40-40-40000000004044i−4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ804-444-44-4-40-40-4000000000404−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ814-44-44-44-4040-4000000000-40400004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ824-44-44-44-4040-4000000000-4040000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ834-44-44-44-40-40400000000040-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ844-44-44-44-40-40400000000040-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ858-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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