Finite Group Databasebeta

← Group #194106

Character table — Group #194106

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222244444444444444444444444444448888888888888888222244444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1
χ1411111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1511111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ17111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1ii−i−iii−i−i-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−iii−i−iii−i−i1-11-111-1-111-1-11-11-1i−ii−i
χ18111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1ii−i−iii−i−i-1iiii−i−i−i−iiiii−i−i−i−i-11-11i−ii−i−i−iii−i−iii-11-1111-1-111-1-1-11-11−ii−ii
χ19111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1ii−i−iii−i−i-1−i−i−i−iiiii−i−i−i−iiiii1-11-1i−ii−iii−i−iii−i−i1-11-1-1-111-1-111-11-11−ii−ii
χ20111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1ii−i−iii−i−i-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i−i−iii−i−iii-11-11-1-111-1-1111-11-1i−ii−i
χ21111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1−i−iii−i−iii-1iiii−i−i−i−iiiii−i−i−i−i1-11-1−ii−ii−i−iii−i−iii1-11-1-1-111-1-111-11-11i−ii−i
χ22111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1−i−iii−i−iii-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−iiii−i−iii−i−i-11-11-1-111-1-1111-11-1−ii−ii
χ23111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1−i−iii−i−iii-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii−i−iii−i−iii1-11-111-1-111-1-11-11-1−ii−ii
χ24111-1-1-1-1111-1-1-1-111-1-111-111-1-111-111-1−i−iii−i−iii-1−i−i−i−iiiii−i−i−i−iiiii-11-11−ii−iiii−i−iii−i−i-11-1111-1-111-1-1-11-11i−ii−i
χ25111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11ii−i−i−i−iii-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−iiii−i−i−i−iii1-1-1111-1-1-1-1111-1-11i−i−ii
χ26111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11ii−i−i−i−iii-1iiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii−i−iiiii−i−i-111-111-1-1-1-111-111-1−iii−i
χ27111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11ii−i−i−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−iiii−i−i−i−iii1-1-11-1-11111-1-1-111-1−iii−i
χ28111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11ii−i−i−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii−i−iiiii−i−i-111-1-1-11111-1-11-1-11i−i−ii
χ29111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11−i−iiiii−i−i-1iiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i−i−iiiii−i−i1-1-11-1-11111-1-1-111-1i−i−ii
χ30111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11−i−iiiii−i−i-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−iii−i−i−i−iii-111-1-1-11111-1-11-1-11−iii−i
χ31111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11−i−iiiii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i−i−iiiii−i−i1-1-1111-1-1-1-1111-1-11−iii−i
χ32111-1-1-1-11-1-111-1-1-1-11111-1-1-11111-11-11−i−iiiii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−iii−i−i−i−iii-111-111-1-1-1-111-111-1i−i−ii
χ3322222222222222-2-2-2-2-2-2-2-2-2-2-222-2-22200000000-2000000000000000022-2-2000000000000-2-2220000000000000000
χ3422222222222222-2-2-2-2-2-2-2-2-2-2-222-2-22200000000-20000000000000000-2-22200000000000022-2-20000000000000000
χ35222222222222-2-22222-2-2-2-2-2-2-2-2-2-22-2-20000000020000000000000000000000002-22-22-22-200000000000000000000
χ36222222222222-2-22222-2-2-2-2-2-2-2-2-2-22-2-2000000002000000000000000000000000-22-22-22-2200000000000000000000
χ37222222222222-2-2-2-2-2-22222222-2-22-2-2-222222222-200000000000000000000-2-2-2-20000000000000000000000000000
χ38222222222222-2-2-2-2-2-22222222-2-22-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000000000000000
χ3922222222-2-2-2-2222222-2-2-2222222-2-2-2-200000000-200000000000000002222000000000000-2-2-2-20000000000000000
χ4022222222-2-2-2-2222222-2-2-2222222-2-2-2-200000000-20000000000000000-2-2-2-200000000000022220000000000000000
χ4122222222-2-2-2-2-2-22222222-2-2-2-2-2-22-2222222-2-2-2-2-200000000000000000000-2-2220000000000000000000000000000
χ4222222222-2-2-2-2-2-22222222-2-2-2-2-2-22-222-2-2-2-22222-20000000000000000000022-2-20000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-22220000000020000000000000000000000002-22-2-22-2200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2222000000002000000000000000000000000-22-222-22-200000000000000000000
χ45222-2-2-2-2222-2-22222-2-2-2-22-2-222-2-222-2200000000-20000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ46222-2-2-2-2222-2-22222-2-2-2-22-2-222-2-222-2200000000-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ47222-2-2-2-2222-2-222-2-22222-222-2-2-2-2-2-2-222i2i−2i−2i2i2i−2i−2i200000000000000000000−2i2i−2i2i0000000000000000000000000000
χ48222-2-2-2-2222-2-222-2-22222-222-2-2-2-2-2-2-22−2i−2i2i2i−2i−2i2i2i2000000000000000000002i−2i2i−2i0000000000000000000000000000
χ49222-2-2-2-2222-2-2-2-2-2-222-2-22-2-222222-22-200000000200000000000000002-2-22000000000000-222-20000000000000000
χ50222-2-2-2-2222-2-2-2-2-2-222-2-22-2-222222-22-20000000020000000000000000-222-20000000000002-2-220000000000000000
χ51222-2-2-2-22-2-2222222-2-222-2-2-222-2-2-2-22-22i2i−2i−2i−2i−2i2i2i200000000000000000000−2i2i2i−2i0000000000000000000000000000
χ52222-2-2-2-22-2-2222222-2-222-2-2-222-2-2-2-22-2−2i−2i2i2i2i2i−2i−2i2000000000000000000002i−2i−2i2i0000000000000000000000000000
χ53222-2-2-2-22-2-22222-2-222-2-2222-2-2-2-2222-200000000-20000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ54222-2-2-2-22-2-22222-2-222-2-2222-2-2-2-2222-200000000-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ55222-2-2-2-22-2-222-2-222-2-2-2-2222-2-2222-2-2200000000200000000000000002-22-2000000000000-22-220000000000000000
χ56222-2-2-2-22-2-222-2-222-2-2-2-2222-2-2222-2-220000000020000000000000000-22-220000000000002-22-20000000000000000
χ572-2-222-2-222-22-20000002-222-22-200-20002i−2i2i−2i2i−2i2i−2i0i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−22−22−200000000
χ582-2-222-2-222-22-20000002-222-22-200-20002i−2i2i−2i2i−2i2i−2i0−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000−22−22−22−2200000000
χ592-2-222-2-222-22-20000002-222-22-200-2000−2i2i−2i2i−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000−22−22−22−2200000000
χ602-2-222-2-222-22-20000002-222-22-200-2000−2i2i−2i2i−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−22−22−200000000
χ612-2-222-2-22-22-220000002-22-22-2200-20002i−2i2i−2i−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−2−22−2200000000
χ622-2-222-2-22-22-220000002-22-22-2200-20002i−2i2i−2i−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000−22−222−22−200000000
χ632-2-222-2-22-22-220000002-22-22-2200-2000−2i2i−2i2i2i−2i2i−2i0i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000−22−222−22−200000000
χ642-2-222-2-22-22-220000002-22-22-2200-2000−2i2i−2i2i2i−2i2i−2i0−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−2−22−2200000000
χ652-2-2-2-22222-2-220000002-2-22-2-220020002-2-222-2-22022−2−2−2−22222−2−2−2−222000000000000000000002−2−222−2−2200000000
χ662-2-2-2-22222-2-220000002-2-22-2-220020002-2-222-2-220−2−22222−2−2−2−22222−2−200000000000000000000−222−2−222−200000000
χ672-2-2-2-22222-2-220000002-2-22-2-22002000-222-2-222-2022−2−2−2−22222−2−2−2−22200000000000000000000−222−2−222−200000000
χ682-2-2-2-22222-2-220000002-2-22-2-22002000-222-2-222-20−2−22222−2−2−2−22222−2−2000000000000000000002−2−222−2−2200000000
χ692-2-2-2-2222-222-20000002-2-2-222-20020002-2-22-222-2022−2−2−2−222−2−22222−2−2000000000000000000002−2−22−222−200000000
χ702-2-2-2-2222-222-20000002-2-2-222-20020002-2-22-222-20−2−22222−2−222−2−2−2−22200000000000000000000−222−22−2−2200000000
χ712-2-2-2-2222-222-20000002-2-2-222-2002000-222-22-2-22022−2−2−2−222−2−22222−2−200000000000000000000−222−22−2−2200000000
χ722-2-2-2-2222-222-20000002-2-2-222-2002000-222-22-2-220−2−22222−2−222−2−2−2−222000000000000000000002−2−22−222−200000000
χ7344-44-44-4-40000004-44-400000000000000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ7444-44-44-4-40000004-44-40000000000000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ7544-44-44-4-4000000-44-4400000000000000000000002-22-22-22-2-22-22-22-22000000000000000000000000000000000000
χ7644-44-44-4-4000000-44-440000000000000000000000-22-22-22-222-22-22-22-2000000000000000000000000000000000000
χ7744-4-44-44-40000004-4-4400000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ7844-4-44-44-40000004-4-440000000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ7944-4-44-44-4000000-444-400000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ8044-4-44-44-4000000-444-40000000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ814-444-4-44-400004-4000000000004-40000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ824-444-4-44-400004-4000000000004-4000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ834-444-4-44-40000-4400000000000-4400000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ844-444-4-44-40000-4400000000000-440000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ854-44-444-4-400004-400000000000-44000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ864-44-444-4-400004-400000000000-440000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ874-44-444-4-40000-44000000000004-400000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ884-44-444-4-40000-44000000000004-4000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ894-4-444-4-444-44-4000000-44-4-44-440040000000000000000000000000000000000000000000000000000000000000000
χ904-4-444-4-44-44-44000000-44-44-44-40040000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-44444-4-44000000-444-444-400-40000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-444-4000000-4444-4-4400-40000000000000000000000000000000000000000000000000000000000000000

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