Finite Group Databasebeta

← Group #376145

Character table — Group #376145

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444444444444444444222222222244444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-1-1-11111-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ141111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ151111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111111111-1-1-1-11111-1-1-1-1-1-111
χ17111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−iii−i−ii−iii−i−i11-1-11-111-1-111-1-1i−i1-1ii−i−iii−i−ii−i11-1-1ii−i−iii−i−i11-1-1i−i1-1
χ18111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−iii−i−ii−iii−i−i11-1-11-1-1-11111-1-1i−i1-1−i−iiiii−i−ii−i-1-111−i−iii−i−iii-1-111−ii-11
χ19111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−iii−i−ii−iii−i−i-1-111-1111-1-111-1-1−ii-11ii−i−i−i−iii−ii-1-111−i−iiiii−i−i11-1-1−ii-11
χ20111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−iii−i−ii−iii−i−i-1-111-11-1-11111-1-1−ii-11−i−iii−i−iii−ii11-1-1ii−i−i−i−iii-1-111i−i1-1
χ21111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−i−i−iiii−i−i−iii11-1-1-1111-1-1-1-111−ii-11ii−i−iii−i−i−ii11-1-1ii−i−i−i−iii-1-111−ii-11
χ22111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−i−i−iiii−i−i−iii11-1-1-11-1-111-1-111−ii-11−i−iiiii−i−i−ii-1-111−i−iiiii−i−i11-1-1i−i1-1
χ23111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−i−i−iiii−i−i−iii-1-1111-111-1-1-1-111i−i1-1ii−i−i−i−iiii−i-1-111−i−iii−i−iii-1-111i−i1-1
χ24111-11-1-1-11-11-111-1-1ii−i−i11-1-1ii−i−i−i−iiii−i−i−iii-1-1111-1-1-111-1-111i−i1-1−i−iii−i−iiii−i11-1-1ii−i−iii−i−i11-1-1−ii-11
χ25111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iiiii−i−i−iiii−i−i11-1-1-1111-1-1-1-111i−i-11−i−iii−i−iiii−i11-1-1−i−iiiii−i−i-1-111i−i-11
χ26111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iiiii−i−i−iiii−i−i11-1-1-11-1-111-1-111i−i-11ii−i−i−i−iiii−i-1-111ii−i−i−i−iii11-1-1−ii1-1
χ27111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iiiii−i−i−iiii−i−i-1-1111-111-1-1-1-111−ii1-1−i−iiiii−i−i−ii-1-111ii−i−iii−i−i-1-111−ii1-1
χ28111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iiiii−i−i−iiii−i−i-1-1111-1-1-111-1-111−ii1-1ii−i−iii−i−i−ii11-1-1−i−iii−i−iii11-1-1i−i-11
χ29111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iii−i−iii−ii−i−iii11-1-11-111-1-111-1-1−ii1-1−i−iii−i−iii−ii11-1-1−i−iii−i−iii11-1-1−ii1-1
χ30111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iii−i−iii−ii−i−iii11-1-11-1-1-11111-1-1−ii1-1ii−i−i−i−iii−ii-1-111ii−i−iii−i−i-1-111i−i-11
χ31111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iii−i−iii−ii−i−iii-1-111-1111-1-111-1-1i−i-11−i−iiiii−i−ii−i-1-111ii−i−i−i−iii11-1-1i−i-11
χ32111-11-1-1-11-11-111-1-1−i−iii11-1-1−i−iii−i−iii−ii−i−iii-1-111-11-1-11111-1-1i−i-11ii−i−iii−i−ii−i11-1-1−i−iiiii−i−i-1-111−ii1-1
χ33222222222222-2-2-2-22222-2-2-2-2-2-2-2-200002200002-22-20000000000000000002-22-20000000000000000000000
χ34222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000220000-22-22000000000000000000-22-220000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000-2-200002-22-2000000000000000000-22-220000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000-2-20000-22-220000000000000000002-22-20000000000000000000000
χ3722222222-2-2-2-22-22-222222-22-22-22-20000-2-2000000002200000000-2-2-2-2000000002200000000000000000000
χ3822222222-2-2-2-22-22-222222-22-22-22-20000-2-200000000-2-200000000222200000000-2-200000000000000000000
χ3922222222-2-2-2-22-22-2-2-2-2-22-22-2-22-2200002200000000220000000022-2-200000000-2-200000000000000000000
χ4022222222-2-2-2-22-22-2-2-2-2-22-22-2-22-2200002200000000-2-200000000-2-222000000002200000000000000000000
χ4122222222-2-2-2-2-22-222222-22-22-22-222222-2-2-2-2-2-200000000002-22-20000000000000000000000000000000000
χ4222222222-2-2-2-2-22-222222-22-22-22-22-2-2-2-2-2-222220000000000-22-220000000000000000000000000000000000
χ4322222222-2-2-2-2-22-22-2-2-2-2-22-222-22-2222222-2-2-2-20000000000-22-220000000000000000000000000000000000
χ4422222222-2-2-2-2-22-22-2-2-2-2-22-222-22-2-2-2-2-222222200000000002-22-20000000000000000000000000000000000
χ45222-22-2-2-22-22-2-2-2222i2i−2i−2i-2-222−2i−2i2i2i00002i−2i00002-2-220000000000000000002i−2i−2i2i0000000000000000000000
χ46222-22-2-2-22-22-2-2-2222i2i−2i−2i-2-222−2i−2i2i2i00002i−2i0000-222-2000000000000000000−2i2i2i−2i0000000000000000000000
χ47222-22-2-2-22-22-2-2-222−2i−2i2i2i-2-2222i2i−2i−2i0000−2i2i00002-2-22000000000000000000−2i2i2i−2i0000000000000000000000
χ48222-22-2-2-22-22-2-2-222−2i−2i2i2i-2-2222i2i−2i−2i0000−2i2i0000-222-20000000000000000002i−2i−2i2i0000000000000000000000
χ49222-22-2-2-2-22-222-2-222i2i−2i−2i2-2-222i−2i−2i2i0000−2i2i000000002-200000000−2i2i-22000000002i−2i00000000000000000000
χ50222-22-2-2-2-22-222-2-222i2i−2i−2i2-2-222i−2i−2i2i0000−2i2i00000000-22000000002i−2i2-200000000−2i2i00000000000000000000
χ51222-22-2-2-2-22-222-2-22−2i−2i2i2i2-2-22−2i2i2i−2i00002i−2i000000002-2000000002i−2i-2200000000−2i2i00000000000000000000
χ52222-22-2-2-2-22-222-2-22−2i−2i2i2i2-2-22−2i2i2i−2i00002i−2i00000000-2200000000−2i2i2-2000000002i−2i00000000000000000000
χ53222-22-2-2-2-22-22-222-22i2i−2i−2i-222-2−2i2i2i−2i2i2i−2i−2i−2i2i−2i−2i2i2i00000000002-2-220000000000000000000000000000000000
χ54222-22-2-2-2-22-22-222-22i2i−2i−2i-222-2−2i2i2i−2i−2i−2i2i2i−2i2i2i2i−2i−2i0000000000-222-20000000000000000000000000000000000
χ55222-22-2-2-2-22-22-222-2−2i−2i2i2i-222-22i−2i−2i2i2i2i−2i−2i2i−2i−2i−2i2i2i0000000000-222-20000000000000000000000000000000000
χ56222-22-2-2-2-22-22-222-2−2i−2i2i2i-222-22i−2i−2i2i−2i−2i2i2i2i−2i2i2i−2i−2i00000000002-2-220000000000000000000000000000000000
χ572-2-222-22-22-2-2222-220000-2-22-200002i−2i2i−2i002i−2i2i−2i0000000000000000002-22-20000000000000000002i−2i2i−2i0000
χ582-2-222-22-22-2-2222-220000-2-22-200002i−2i2i−2i002i−2i2i−2i000000000000000000-22-22000000000000000000−2i2i−2i2i0000
χ592-2-222-22-22-2-2222-220000-2-22-20000−2i2i−2i2i00−2i2i−2i2i0000000000000000002-22-2000000000000000000−2i2i−2i2i0000
χ602-2-222-22-22-2-2222-220000-2-22-20000−2i2i−2i2i00−2i2i−2i2i000000000000000000-22-220000000000000000002i−2i2i−2i0000
χ612-2-222-22-2-222-2-222200002-2-2-200002i−2i2i−2i00−2i2i−2i2i0000002-22-2000000000000000000000000002i−2i2i−2i00000000
χ622-2-222-22-2-222-2-222200002-2-2-200002i−2i2i−2i00−2i2i−2i2i000000-22-2200000000000000000000000000−2i2i−2i2i00000000
χ632-2-222-22-2-222-2-222200002-2-2-20000−2i2i−2i2i002i−2i2i−2i0000002-22-200000000000000000000000000−2i2i−2i2i00000000
χ642-2-222-22-2-222-2-222200002-2-2-20000−2i2i−2i2i002i−2i2i−2i000000-22-22000000000000000000000000002i−2i2i−2i00000000
χ652-2-2-222-2222-2-2222-20000-2-2-2200002-2-22002-2-220000000000000000002i−2i−2i2i000000000000000000−2i2i2i−2i0000
χ662-2-2-222-2222-2-2222-20000-2-2-2200002-2-22002-2-22000000000000000000−2i2i2i−2i0000000000000000002i−2i−2i2i0000
χ672-2-2-222-2222-2-2222-20000-2-2-220000-222-200-222-20000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i0000
χ682-2-2-222-2222-2-2222-20000-2-2-220000-222-200-222-2000000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i0000
χ692-2-2-222-22-2-222-22-2-200002-22200002-2-2200-222-20000002-2-22000000000000000000000000002-2-2200000000
χ702-2-2-222-22-2-222-22-2-200002-22200002-2-2200-222-2000000-222-200000000000000000000000000-222-200000000
χ712-2-2-222-22-2-222-22-2-200002-2220000-222-2002-2-220000002-2-2200000000000000000000000000-222-200000000
χ722-2-2-222-22-2-222-22-2-200002-2220000-222-2002-2-22000000-222-2000000000000000000000000002-2-2200000000
χ7344-44-44-4-4000000004i−4i4i−4i00000000000000000000000000000000000000000000002-22-22i−2i2i−2i000000000000
χ7444-44-44-4-4000000004i−4i4i−4i0000000000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ7544-44-44-4-400000000−4i4i−4i4i00000000000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ7644-44-44-4-400000000−4i4i−4i4i0000000000000000000000000000000000000000000000-22-222i−2i2i−2i000000000000
χ7744-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ7844-4-4-4-444000000004-4-440000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ7944-4-4-4-44400000000-444-400000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ8044-4-4-4-44400000000-444-40000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ814-4-444-44-44-4-44-4-44-4000044-4400000000000000000000000000000000000000000000000000000000000000
χ824-4-444-44-4-444-44-4-4-40000-444400000000000000000000000000000000000000000000000000000000000000
χ834-4-4-444-4444-4-4-4-4-440000444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-444-44-4-4444-4440000-44-4-400000000000000000000000000000000000000000000000000000000000000
χ858-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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