Finite Group Databasebeta

← Group #375866

Character table — Group #375866

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222222222444444444444444444444444444444444444222244444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111
χ17111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i11-1-11-11-1ii−i−iii−i−i11-1-11-1i−ii−i1-1
χ18111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11−i−iii-1-1111-1-11−i−iiiii−i−i11-1-1-11−ii−ii-11
χ19111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1ii−i−i-1-111-111-1−i−iii−i−iii-1-1111-1i−i−ii-11
χ20111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11−i−iii11-1-1-11-11ii−i−i−i−iii-1-111-11−iii−i1-1
χ21111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1ii−i−i11-1-11-11-1ii−i−i−i−iii-1-111-11−ii−ii-11
χ22111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−i−iii-1-1111-1-11−i−iii−i−iii-1-1111-1i−ii−i1-1
χ23111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-111-1ii−i−i-1-111-111-1−i−iiiii−i−i11-1-1-11−iii−i1-1
χ24111-1-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-11−i−iii11-1-1-11-11ii−i−iii−i−i11-1-11-1i−i−ii-11
χ25111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1−i−iii-1-111-111-1ii−i−iii−i−i-1-1111-1−iii−i-11
χ26111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i11-1-1-11-11−i−iiiii−i−i-1-111-11i−i−ii1-1
χ27111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii11-1-11-11-1−i−iii−i−iii11-1-11-1−ii−ii1-1
χ28111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11ii−i−i-1-1111-1-11ii−i−i−i−iii11-1-1-11i−ii−i-11
χ29111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-111-1−i−iii-1-111-111-1ii−i−i−i−iii11-1-1-11i−i−ii1-1
χ30111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-11ii−i−i11-1-1-11-11−i−iii−i−iii11-1-11-1−iii−i-11
χ31111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1−i−iii11-1-11-11-1−i−iiiii−i−i-1-111-11i−ii−i-11
χ32111-1-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-11ii−i−i-1-1111-1-11ii−i−iii−i−i-1-1111-1−ii−ii1-1
χ33222222222-2-22-2-22-2-22-2-222222222-2-2-2-2000000000000000022-2-222-2-2220000000000-2-20000000000000000000000
χ34222222222-2-22-2-22-2-22-2-222222222-2-2-2-20000000000000000-2-222-2-222-2-20000000000220000000000000000000000
χ35222222222-2-22-2-22-2-22-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-2-2-20000000000220000000000000000000000
χ36222222222-2-22-2-22-2-22-2-2-2-2-2-2-2-2-2-222220000000000000000-2-222-2-222220000000000-2-20000000000000000000000
χ3722222222-22-2-22-2-22-2-22-222-2-222-2-22-22-2000000000000000000000000000000002-22-200002-22-20000000000000000
χ3822222222-22-2-22-2-22-2-22-222-2-222-2-22-22-200000000000000000000000000000000-22-220000-22-220000000000000000
χ3922222222-22-2-22-2-22-2-22-2-2-222-2-222-22-22000000000000000000000000000000002-22-20000-22-220000000000000000
χ4022222222-22-2-22-2-22-2-22-2-2-222-2-222-22-2200000000000000000000000000000000-22-2200002-22-20000000000000000
χ4122222222-2-22-2-22-2-22-2-2222-2-222-2-2-22-2200000000000000000000000000222-22-2000000-2-200000000000000000000
χ4222222222-2-22-2-22-2-22-2-2222-2-222-2-2-22-2200000000000000000000000000-2-2-22-220000002200000000000000000000
χ4322222222-2-22-2-22-2-22-2-22-2-222-2-2222-22-20000000000000000000000000022-22-22000000-2-200000000000000000000
χ4422222222-2-22-2-22-2-22-2-22-2-222-2-2222-22-200000000000000000000000000-2-22-22-20000002200000000000000000000
χ45222-2-22-2-22-2-2-2222-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i2i2i00000000000000002i2i−2i−2i−2i−2i2i2i2-20000000000-220000000000000000000000
χ46222-2-22-2-22-2-2-2222-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i2i2i0000000000000000−2i−2i2i2i2i2i−2i−2i-2200000000002-20000000000000000000000
χ47222-2-22-2-22-2-2-2222-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i00000000000000002i2i−2i−2i−2i−2i2i2i-2200000000002-20000000000000000000000
χ48222-2-22-2-22-2-2-2222-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i2-20000000000-220000000000000000000000
χ49222-2-22-2-2-22-22-22-22-22-222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i000000000000000000000000000000002-2-2200002i−2i−2i2i0000000000000000
χ50222-2-22-2-2-22-22-22-22-22-222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i00000000000000000000000000000000-222-20000−2i2i2i−2i0000000000000000
χ51222-2-22-2-2-22-22-22-22-22-22−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i000000000000000000000000000000002-2-220000−2i2i2i−2i0000000000000000
χ52222-2-22-2-2-22-22-22-22-22-22−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i00000000000000000000000000000000-222-200002i−2i−2i2i0000000000000000
χ53222-2-22-2-2-2-2222-2-2-2222-22i2i−2i−2i−2i−2i2i2i−2i2i2i−2i000000000000000000000000002-22i−2i−2i2i000000-2200000000000000000000
χ54222-2-22-2-2-2-2222-2-2-2222-22i2i−2i−2i−2i−2i2i2i−2i2i2i−2i00000000000000000000000000-22−2i2i2i−2i0000002-200000000000000000000
χ55222-2-22-2-2-2-2222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i000000000000000000000000002-2−2i2i2i−2i000000-2200000000000000000000
χ56222-2-22-2-2-2-2222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i00000000000000000000000000-222i−2i−2i2i0000002-200000000000000000000
χ572-2-2222-2-2-22-222-22-22-2-2200000000000022-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000002i−2i2i−2i000000000000
χ582-2-2222-2-2-22-222-22-22-2-2200000000000022-2-222-2-200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000−2i2i−2i2i000000000000
χ592-2-2222-2-2-22-222-22-22-2-22000000000000-2-222-2-222000000002i−2i2i−2i2i−2i2i−2i00000000000000000000−2i2i−2i2i000000000000
χ602-2-2222-2-2-22-222-22-22-2-22000000000000-2-222-2-22200000000−2i2i−2i2i−2i2i−2i2i000000000000000000002i−2i2i−2i000000000000
χ612-2-2222-2-2-2-222-2222-2-22-2000000000000000000002i2i−2i−2i2i2i−2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000002-22-200000000
χ622-2-2222-2-2-2-222-2222-2-22-2000000000000000000002i2i−2i−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000-22-2200000000
χ632-2-2222-2-2-2-222-2222-2-22-200000000000000000000−2i−2i2i2i−2i−2i2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000-22-2200000000
χ642-2-2222-2-2-2-222-2222-2-22-200000000000000000000−2i−2i2i2i−2i−2i2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000002-22-200000000
χ652-2-2-2-2222-22-2-2-222-2222-200000000000022-2-2-2-222000000002-22-2-22-22000000000000000000002-2-22000000000000
χ662-2-2-2-2222-22-2-2-222-2222-200000000000022-2-2-2-22200000000-22-222-22-200000000000000000000-222-2000000000000
χ672-2-2-2-2222-22-2-2-222-2222-2000000000000-2-22222-2-2000000002-22-2-22-2200000000000000000000-222-2000000000000
χ682-2-2-2-2222-22-2-2-222-2222-2000000000000-2-22222-2-200000000-22-222-22-2000000000000000000002-2-22000000000000
χ692-2-2-2-2222-2-22-22-222-22-220000000000000000000022-2-2-2-2222-2-22-222-20000000000000000000000002-2-2200000000
χ702-2-2-2-2222-2-22-22-222-22-220000000000000000000022-2-2-2-222-222-22-2-22000000000000000000000000-222-200000000
χ712-2-2-2-2222-2-22-22-222-22-2200000000000000000000-2-22222-2-22-2-22-222-2000000000000000000000000-222-200000000
χ722-2-2-2-2222-2-22-22-222-22-2200000000000000000000-2-22222-2-2-222-22-2-220000000000000000000000002-2-2200000000
χ7344-44-4-44-4000000000000004-4004-400002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ7444-44-4-44-4000000000000004-4004-40000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ7544-44-4-44-400000000000000-4400-4400002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ7644-44-4-44-400000000000000-4400-440000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ7744-4-44-4-44000000000000004i−4i00−4i4i00002i−2i2i−2i−2i2i−2i2i-22-222-22-200000000000000000000000000000000000000000000
χ7844-4-44-4-44000000000000004i−4i00−4i4i0000−2i2i−2i2i2i−2i2i−2i2-22-2-22-2200000000000000000000000000000000000000000000
χ7944-4-44-4-4400000000000000−4i4i004i−4i00002i−2i2i−2i−2i2i−2i2i2-22-2-22-2200000000000000000000000000000000000000000000
χ8044-4-44-4-4400000000000000−4i4i004i−4i0000−2i2i−2i2i2i−2i2i−2i-22-222-22-200000000000000000000000000000000000000000000
χ814-444-4-4-440000000000004i−4i004i−4i0000002i−2i−2i2i2i−2i−2i2i2-2-222-2-2200000000000000000000000000000000000000000000
χ824-444-4-4-440000000000004i−4i004i−4i000000−2i2i2i−2i−2i2i2i−2i-222-2-222-200000000000000000000000000000000000000000000
χ834-444-4-4-44000000000000−4i4i00−4i4i0000002i−2i−2i2i2i−2i−2i2i-222-2-222-200000000000000000000000000000000000000000000
χ844-444-4-4-44000000000000−4i4i00−4i4i000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-2200000000000000000000000000000000000000000000
χ854-44-44-44-40000000000004-400-440000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000000000
χ864-44-44-44-40000000000004-400-44000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000
χ874-44-44-44-4000000000000-44004-40000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000
χ884-44-44-44-4000000000000-44004-4000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000000000
χ894-4-4444-4-4444-444-4-4-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-44-4-4-4-4-4-444444000000000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-44444444-4-4-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-44444-4-4444-444-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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