Finite Group Databasebeta

← Group #147447

Character table — Group #147447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order122222222222444444444444444488888888444488888888888888888888888888881616161616161616161616161616161622224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ17111-11-1-1-111-1-11-11-1ii−i−iii−i−i1-11-111-1-111-1-1i−ii−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ18111-11-1-1-111-1-11-11-1ii−i−iii−i−i1-11-111-1-111-1-1i−ii−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ19111-11-1-1-111-1-11-11-1ii−i−iii−i−i1-11-111-1-111-1-1i−ii−i11-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ20111-11-1-1-111-1-11-11-1ii−i−iii−i−i1-11-111-1-111-1-1i−ii−i11-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ21111-11-1-1-111-1-11-11-1−i−iii−i−iii1-11-111-1-111-1-1−ii−ii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ22111-11-1-1-111-1-11-11-1−i−iii−i−iii1-11-111-1-111-1-1−ii−ii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ23111-11-1-1-111-1-11-11-1−i−iii−i−iii1-11-111-1-111-1-1−ii−ii11-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ24111-11-1-1-111-1-11-11-1−i−iii−i−iii1-11-111-1-111-1-1−ii−ii11-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ25111-11-1-1-1-1-1111-1-11ii−i−i−i−iii1-1-11-1-111-1-111i−i−ii11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-11-1-11i−i−ii
χ26111-11-1-1-1-1-1111-1-11ii−i−i−i−iii1-1-11-1-111-1-111i−i−ii11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111-111-1−iii−i
χ27111-11-1-1-1-1-1111-1-11ii−i−i−i−iii1-1-11-1-111-1-111i−i−ii11-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-111-1−iii−i
χ28111-11-1-1-1-1-1111-1-11ii−i−i−i−iii1-1-11-1-111-1-111i−i−ii11-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-1111-1-11i−i−ii
χ29111-11-1-1-1-1-1111-1-11−i−iiiii−i−i1-1-11-1-111-1-111−iii−i11-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii11-1-1-1-1111-1-11−iii−i
χ30111-11-1-1-1-1-1111-1-11−i−iiiii−i−i1-1-11-1-111-1-111−iii−i11-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-111-1i−i−ii
χ31111-11-1-1-1-1-1111-1-11−i−iiiii−i−i1-1-11-1-111-1-111−iii−i11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111-111-1i−i−ii
χ32111-11-1-1-1-1-1111-1-11−i−iiiii−i−i1-1-11-1-111-1-111−iii−i11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-11-1-11−iii−i
χ332222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ35222222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-2220000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ36222222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-2220000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ37222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ38222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3922222222-2-2-2-222-2-22222-2-2-2-222-2-22222222222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-2-2-2222222-2-222222222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-22222222222-2-22200000000-2-2-2-200000000000000000000000000002−22−2−22−222−22−2−22−2200000000
χ4222222222-2-2-2-2-2-22222222222-2-22200000000-2-2-2-20000000000000000000000000000−22−222−22−2−22−222−22−200000000
χ4322222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22200000000222200000000000000000000000000002−22−2−22−22−22−222−22−200000000
χ4422222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2220000000022220000000000000000000000000000−22−222−22−22−22−2−22−2200000000
χ45222-22-2-2-222-2-22-22-22i2i−2i−2i2i2i−2i−2i2-22-2-2-222-2-2222i−2i2i−2i-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ46222-22-2-2-222-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-22-2-2-222-2-222−2i2i−2i2i-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ47222-22-2-2-222-2-2-22-222i2i−2i−2i−2i−2i2i2i-22-2200000000−2i2i2i−2i0000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−222−2−222−200000000
χ48222-22-2-2-222-2-2-22-222i2i−2i−2i−2i−2i2i2i-22-2200000000−2i2i2i−2i0000000000000000000000000000−i2i2i2−i2−i2i2i2−i22−2−222−2−2200000000
χ49222-22-2-2-222-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22-22000000002i−2i−2i2i0000000000000000000000000000i2−i2−i2i2i2−i2−i2i22−2−222−2−2200000000
χ50222-22-2-2-222-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22-22000000002i−2i−2i2i0000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−2−222−200000000
χ51222-22-2-2-2-2-2222-2-222i2i−2i−2i−2i−2i2i2i2-2-2222-2-222-2-22i−2i−2i2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ52222-22-2-2-2-2-2222-2-22−2i−2i2i2i2i2i−2i−2i2-2-2222-2-222-2-2−2i2i2i−2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ53222-22-2-2-2-2-222-222-22i2i−2i−2i2i2i−2i−2i-222-200000000−2i2i−2i2i00000000000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ54222-22-2-2-2-2-222-222-22i2i−2i−2i2i2i−2i−2i-222-200000000−2i2i−2i2i0000000000000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ55222-22-2-2-2-2-222-222-2−2i−2i2i2i−2i−2i2i2i-222-2000000002i−2i2i−2i00000000000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ56222-22-2-2-2-2-222-222-2−2i−2i2i2i−2i−2i2i2i-222-2000000002i−2i2i−2i0000000000000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ572-2-222-2-222-22-2-222-2000000002-2-222222-2-2-2-200002-22-2000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ582-2-222-2-222-22-2-222-2000000002-2-222222-2-2-2-200002-22-200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ592-2-222-2-222-22-2-222-2000000002-2-22-2-2-2-222220000-22-2200000000000000002-22-22-22-2000000000000000000000000
χ602-2-222-2-222-22-2-222-2000000002-2-22-2-2-2-222220000-22-220000000000000000-22-22-22-22000000000000000000000000
χ612-2-222-2-22-22-22-22-22000000002-22-22222-2-2-2-20000-22-2200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ622-2-222-2-22-22-22-22-22000000002-22-22222-2-2-2-20000-22-220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ632-2-222-2-22-22-22-22-22000000002-22-2-2-2-2-2222200002-22-2000000002-22-2-22-2200000000000000000000000000000000
χ642-2-222-2-22-22-22-22-22000000002-22-2-2-2-2-2222200002-22-200000000-22-222-22-200000000000000000000000000000000
χ652-2-2-2222-22-2-22-2-2220000000022-2-222-2-2-2-22200002-2-22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ662-2-2-2222-22-2-22-2-2220000000022-2-222-2-2-2-22200002-2-2200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ672-2-2-2222-22-2-22-2-2220000000022-2-2-2-22222-2-20000-222-200000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ682-2-2-2222-22-2-22-2-2220000000022-2-2-2-22222-2-20000-222-20000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ692-2-2-2222-2-222-2-2-2-2-200000000222222-2-2-2-2220000-222-200000000000000002-2-22-222-2000000000000000000000000
χ702-2-2-2222-2-222-2-2-2-2-200000000222222-2-2-2-2220000-222-20000000000000000-222-22-2-22000000000000000000000000
χ712-2-2-2222-2-222-2-2-2-2-2000000002222-2-22222-2-200002-2-22000000002-2-22-222-200000000000000000000000000000000
χ722-2-2-2222-2-222-2-2-2-2-2000000002222-2-22222-2-200002-2-2200000000-222-22-2-2200000000000000000000000000000000
χ7344-44-44-4-40000000000004i−4i4i−4i000022−2222−2222−2222−22000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ7444-44-44-4-40000000000004i−4i4i−4i0000−2222−2222−2222−222200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ7544-44-44-4-4000000000000−4i4i−4i4i000022−2222−2222−2222−2200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ7644-44-44-4-4000000000000−4i4i−4i4i0000−2222−2222−2222−2222000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ7744-4-4-4-4440000000000004-4-44000022−22−222222−22−22220000000022−22−222200000000000000000000000000000000000000000000
χ7844-4-4-4-4440000000000004-4-440000−222222−22−222222−2200000000−222222−2200000000000000000000000000000000000000000000
χ7944-4-4-4-444000000000000-444-4000022−22−222222−22−222200000000−222222−2200000000000000000000000000000000000000000000
χ8044-4-4-4-444000000000000-444-40000−222222−22−222222−220000000022−22−222200000000000000000000000000000000000000000000
χ814-444-4-44-4000000004i−4i4i−4i0000000022−2222−22−2222−22220000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ824-444-4-44-4000000004i−4i4i−4i00000000−2222−222222−2222−22000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ834-444-4-44-400000000−4i4i−4i4i0000000022−2222−22−2222−2222000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ844-444-4-44-400000000−4i4i−4i4i00000000−2222−222222−2222−220000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ854-44-4-44-44000000004-4-440000000022−22−2222−222222−2200000000000022−22−22220000000000000000000000000000000000000000
χ864-44-4-44-44000000004-4-4400000000−222222−2222−22−2222000000000000−222222−220000000000000000000000000000000000000000
χ874-44-4-44-4400000000-444-40000000022−22−2222−222222−22000000000000−222222−220000000000000000000000000000000000000000
χ884-44-4-44-4400000000-444-400000000−222222−2222−22−222200000000000022−22−22220000000000000000000000000000000000000000
χ894-4-444-4-444-44-44-4-4400000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ904-4-444-4-44-44-444-44-400000000-44-440000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4444-44-4-4444-4-400000000-4-4440000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4444-4-444-4444400000000-4-4-4-40000000000000000000000000000000000000000000000000000000000000000

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