Finite Group Databasebeta

← Group #210088

Character table — Group #210088

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444444444444442222444444444444888888888888888822448888
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
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ17111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i11-1-1ii−i−i11-1-1i−iii−i−i1-11-11-1i−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i
χ18111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i11-1-1ii−i−i11-1-1i−iii−i−i1-11-11-1i−ii−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-11−ii-11−ii
χ19111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i11-1-1ii−i−i-1-111i−i−i−iii1-11-1-11i−i−ii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii
χ20111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i11-1-1ii−i−i-1-111i−i−i−iii1-11-1-11i−i−ii-1-111−i−iii-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i
χ21111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i-1-111−i−iii11-1-1i−iii−i−i1-1-111-1−iii−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i-11−ii
χ22111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i-1-111−i−iii11-1-1i−iii−i−i1-1-111-1−iii−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-11−ii1-1i−i
χ23111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i-1-111−i−iii-1-111i−i−i−iii1-1-11-11−ii−ii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii1-1i−i
χ24111-11-1-1-111-1-1ii−i−iii−i−i11-1-1i−i-1-111−i−iii-1-111i−i−i−iii1-1-11-11−ii−ii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii
χ25111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii11-1-1−i−iii11-1-1−ii−i−iii1-11-11-1−ii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii
χ26111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii11-1-1−i−iii11-1-1−ii−i−iii1-11-11-1−ii−ii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-11i−i-11i−i
χ27111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii11-1-1−i−iii-1-111−iiii−i−i1-11-1-11−iii−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i
χ28111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii11-1-1−i−iii-1-111−iiii−i−i1-11-1-11−iii−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii
χ29111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii-1-111ii−i−i11-1-1−ii−i−iii1-1-111-1i−i−ii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii-11i−i
χ30111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii-1-111ii−i−i11-1-1−ii−i−iii1-1-111-1i−i−ii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-11i−i1-1−ii
χ31111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii-1-111ii−i−i-1-111−iiii−i−i1-1-11-11i−ii−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i1-1−ii
χ32111-11-1-1-111-1-1−i−iii−i−iii11-1-1−ii-1-111ii−i−i-1-111−iiii−i−i1-1-11-11i−ii−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i
χ33222222222-22-2222222222-22-2-2-2222222220000-2-20000-2-2-2-200-2-20000000000000000000000000000000000
χ34222222222-22-2222222222-22-2-2-2-2-2-2-2-2-2-2-20000-2-20000-2-22200220000000000000000000000000000000000
χ35222222222-22-2-2-2-2-2-2-2-2-22-22-2222222-2-2-2-20000220000-2-2-2-200220000000000000000000000000000000000
χ36222222222-22-2-2-2-2-2-2-2-2-22-22-222-2-2-2-222220000220000-2-22200-2-20000000000000000000000000000000000
χ3722222222-22-222222-2-2-2-2-22-2222000000002222-2-22222-2-200-2-200-2-200000000000000000000000000000000
χ3822222222-22-222222-2-2-2-2-22-222200000000-2-2-2-2-2-2-2-2-2-2-2-20022002200000000000000000000000000000000
χ3922222222-22-22-2-2-2-22222-22-22-2-200000000222222-2-2-2-2-2-200-2-2002200000000000000000000000000000000
χ4022222222-22-22-2-2-2-22222-22-22-2-200000000-2-2-2-2222222-2-2002200-2-200000000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000022000022000000002-22-22-22-2000000000000000000000000
χ4222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000002200002200000000-22-22-22-22000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000-2-2000022000000002-22-2-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000-2-200002200000000-22-222-22-2000000000000000000000000
χ45222-22-2-2-22-2-222i2i−2i−2i2i2i−2i−2i2-2-22−2i2i22-2-22i2i−2i−2i0000−2i2i0000-22-2200−2i2i0000000000000000000000000000000000
χ46222-22-2-2-22-2-222i2i−2i−2i2i2i−2i−2i2-2-22−2i2i-2-222−2i−2i2i2i0000−2i2i0000-222-2002i−2i0000000000000000000000000000000000
χ47222-22-2-2-22-2-22−2i−2i2i2i−2i−2i2i2i2-2-222i−2i22-2-2−2i−2i2i2i00002i−2i0000-22-22002i−2i0000000000000000000000000000000000
χ48222-22-2-2-22-2-22−2i−2i2i2i−2i−2i2i2i2-2-222i−2i-2-2222i2i−2i−2i00002i−2i0000-222-200−2i2i0000000000000000000000000000000000
χ49222-22-2-2-2-222-22i2i−2i−2i−2i−2i2i2i-222-22i−2i0000000022-2-2−2i2i2i2i−2i−2i-2200-2200−2i2i00000000000000000000000000000000
χ50222-22-2-2-2-222-22i2i−2i−2i−2i−2i2i2i-222-22i−2i00000000-2-222−2i2i−2i−2i2i2i-22002-2002i−2i00000000000000000000000000000000
χ51222-22-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i-222-2−2i2i0000000022-2-22i−2i−2i−2i2i2i-2200-22002i−2i00000000000000000000000000000000
χ52222-22-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i-222-2−2i2i00000000-2-2222i−2i2i2i−2i−2i-22002-200−2i2i00000000000000000000000000000000
χ53222-22-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2-222−2i2i0000000000002i−2i00002-2000000002-2-222i−2i−2i2i000000000000000000000000
χ54222-22-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2-222−2i2i0000000000002i−2i00002-200000000-222-2−2i2i2i−2i000000000000000000000000
χ55222-22-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-2-2222i−2i000000000000−2i2i00002-2000000002-2-22−2i2i2i−2i000000000000000000000000
χ56222-22-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-2-2222i−2i000000000000−2i2i00002-200000000-222-22i−2i−2i2i000000000000000000000000
χ5722-22-22-2-220-202i−2i2i−2i2i−2i2i−2i-2020002i−2i2i−2i2-22-200000000000000000000000000002−22−2i2−i2i2−i2i2−i2i2−i22−22−200000000
χ5822-22-22-2-220-202i−2i2i−2i2i−2i2i−2i-2020002i−2i2i−2i2-22-20000000000000000000000000000−22−22−i2i2−i2i2−i2i2−i2i2−22−2200000000
χ5922-22-22-2-220-202i−2i2i−2i2i−2i2i−2i-202000−2i2i−2i2i-22-2200000000000000000000000000002−22−2i2−i2i2−i2−i2i2−i2i2−22−2200000000
χ6022-22-22-2-220-202i−2i2i−2i2i−2i2i−2i-202000−2i2i−2i2i-22-220000000000000000000000000000−22−22−i2i2−i2i2i2−i2i2−i22−22−200000000
χ6122-22-22-2-220-20−2i2i−2i2i−2i2i−2i2i-2020002i−2i2i−2i-22-2200000000000000000000000000002−22−2−i2i2−i2i2i2−i2i2−i2−22−2200000000
χ6222-22-22-2-220-20−2i2i−2i2i−2i2i−2i2i-2020002i−2i2i−2i-22-220000000000000000000000000000−22−22i2−i2i2−i2−i2i2−i2i22−22−200000000
χ6322-22-22-2-220-20−2i2i−2i2i−2i2i−2i2i-202000−2i2i−2i2i2-22-200000000000000000000000000002−22−2−i2i2−i2i2−i2i2−i2i22−22−200000000
χ6422-22-22-2-220-20−2i2i−2i2i−2i2i−2i2i-202000−2i2i−2i2i2-22-20000000000000000000000000000−22−22i2−i2i2−i2i2−i2i2−i2−22−2200000000
χ6522-2-2-2-22220202-2-222-2-22-20-20002i−2i−2i2i−2i2i2i−2i00000000000000000000000000002−2−222−2−22i2−i2−i2i2−i2i2i2−i200000000
χ6622-2-2-2-22220202-2-222-2-22-20-20002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000−222−2−222−2−i2i2i2−i2i2−i2−i2i200000000
χ6722-2-2-2-22220202-2-222-2-22-20-2000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002−2−222−2−22−i2i2i2−i2i2−i2−i2i200000000
χ6822-2-2-2-22220202-2-222-2-22-20-2000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000−222−2−222−2i2−i2−i2i2−i2i2i2−i200000000
χ6922-2-2-2-2222020-222-2-222-2-20-20002i−2i−2i2i2i−2i−2i2i00000000000000000000000000002−2−22−222−2i2−i2−i2i2i2−i2−i2i200000000
χ7022-2-2-2-2222020-222-2-222-2-20-20002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000−222−22−2−22−i2i2i2−i2−i2i2i2−i200000000
χ7122-2-2-2-2222020-222-2-222-2-20-2000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000002−2−22−222−2−i2i2i2−i2−i2i2i2−i200000000
χ7222-2-2-2-2222020-222-2-222-2-20-2000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000−222−22−2−22i2−i2−i2i2i2−i2−i2i200000000
χ7344-44-44-4-4-40404i−4i4i−4i−4i4i−4i4i40-4000000000000000000000000000000000000000000000000000000000000000
χ7444-44-44-4-4-4040−4i4i−4i4i4i−4i4i−4i40-4000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-40-404-4-44-444-4404000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-40-40-444-44-4-44404000000000000000000000000000000000000000000000000000000000000000
χ774-444-4-44-4040-4000000000-40400000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ784-444-4-44-4040-4000000000-4040000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ794-444-4-44-40-40400000000040-400000000000000004i−4i4i−4i000000000000000000000000000000000000000000
χ804-444-4-44-40-40400000000040-40000000000000000−4i4i−4i4i000000000000000000000000000000000000000000
χ814-44-4-44-440404000000000-40-400000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ824-44-4-44-440404000000000-40-40000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ834-44-4-44-440-40-400000000040400000000000000004-4-44000000000000000000000000000000000000000000
χ844-44-4-44-440-40-40000000004040000000000000000-444-4000000000000000000000000000000000000000000
χ858-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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