Finite Group Databasebeta

← Group #194105

Character table — Group #194105

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222244444444444444444444444444448888888888888888224444444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ171-11-1-111-111-1-111-1-1111-1-111-1-1-1-111ii−i−i1-1ii−i−i-1iiii−i−i−i−iiiii−i−i−i−i1-1i−i1-1ii−i−ii−i1-11-1ii−i−i11-1-111-1-11-11-1i−ii−i
χ181-11-1-111-111-1-111-1-1111-1-111-1-1-1-111ii−i−i1-1ii−i−i-1iiii−i−i−i−iiiii−i−i−i−i-11i−i-11−i−iiii−i-11-11−i−iii11-1-111-1-1-11-11−ii−ii
χ191-11-1-111-111-1-111-1-1111-1-111-1-1-1-111ii−i−i1-1ii−i−i-1−i−i−i−iiiii−i−i−i−iiiii1-1i−i1-1ii−i−ii−i1-11-1ii−i−i-1-111-1-111-11-11−ii−ii
χ201-11-1-111-111-1-111-1-1111-1-111-1-1-1-111ii−i−i1-1ii−i−i-1−i−i−i−iiiii−i−i−i−iiiii-11i−i-11−i−iiii−i-11-11−i−iii-1-111-1-1111-11-1i−ii−i
χ211-11-1-111-111-1-111-1-1111-1-111-1-1-1-111−i−iii1-1−i−iii-1iiii−i−i−i−iiiii−i−i−i−i1-1−ii1-1−i−iii−ii1-11-1−i−iii-1-111-1-111-11-11i−ii−i
χ221-11-1-111-111-1-111-1-1111-1-111-1-1-1-111−i−iii1-1−i−iii-1iiii−i−i−i−iiiii−i−i−i−i-11−ii-11ii−i−i−ii-11-11ii−i−i-1-111-1-1111-11-1−ii−ii
χ231-11-1-111-111-1-111-1-1111-1-111-1-1-1-111−i−iii1-1−i−iii-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii1-1−i−iii−ii1-11-1−i−iii11-1-111-1-11-11-1−ii−ii
χ241-11-1-111-111-1-111-1-1111-1-111-1-1-1-111−i−iii1-1−i−iii-1−i−i−i−iiiii−i−i−i−iiiii-11−ii-11ii−i−i−ii-11-11ii−i−i11-1-111-1-1-11-11i−ii−i
χ251-11-1-111-1-1-111-1-111111-1-1-1-111-1-111ii−i−i-11−i−iii-1iiii−i−i−i−i−i−i−i−iiiii1-1−ii-11ii−i−ii−i1-1-11−i−iii11-1-1-1-1111-1-11i−i−ii
χ261-11-1-111-1-1-111-1-111111-1-1-1-111-1-111ii−i−i-11−i−iii-1iiii−i−i−i−i−i−i−i−iiiii-11−ii1-1−i−iiii−i-111-1ii−i−i11-1-1-1-111-111-1−iii−i
χ271-11-1-111-1-1-111-1-111111-1-1-1-111-1-111ii−i−i-11−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i1-1−ii-11ii−i−ii−i1-1-11−i−iii-1-11111-1-1-111-1−iii−i
χ281-11-1-111-1-1-111-1-111111-1-1-1-111-1-111ii−i−i-11−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i-11−ii1-1−i−iiii−i-111-1ii−i−i-1-11111-1-11-1-11i−i−ii
χ291-11-1-111-1-1-111-1-111111-1-1-1-111-1-111−i−iii-11ii−i−i-1iiii−i−i−i−i−i−i−i−iiiii1-1i−i-11−i−iii−ii1-1-11ii−i−i-1-11111-1-1-111-1i−i−ii
χ301-11-1-111-1-1-111-1-111111-1-1-1-111-1-111−i−iii-11ii−i−i-1iiii−i−i−i−i−i−i−i−iiiii-11i−i1-1ii−i−i−ii-111-1−i−iii-1-11111-1-11-1-11−iii−i
χ311-11-1-111-1-1-111-1-111111-1-1-1-111-1-111−i−iii-11ii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i1-1i−i-11−i−iii−ii1-1-11ii−i−i11-1-1-1-1111-1-11−iii−i
χ321-11-1-111-1-1-111-1-111111-1-1-1-111-1-111−i−iii-11ii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i-11i−i1-1ii−i−i−ii-111-1−i−iii11-1-1-1-111-111-1i−i−ii
χ332222222222222222-2-2-2-2-2-2-2-2-2-2-2-220000-2-20000200000000000000000000002-22-20000002-22-20000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-220000-2-2000020000000000000000000000-22-22000000-22-220000000000000000
χ35222222222222-2-2-2-222-2-2-2-2-2-2-222-2-2222222-2-2-2-2-200000000000000000022000000-2-2000000000000000000000000
χ36222222222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2-2-2-2222222-2000000000000000000-2-200000022000000000000000000000000
χ37222222222222-2-2-2-2-2-22222222-2-22-20000-2-20000-20000000000000000220022000000-2-2-2-200000000000000000000
χ38222222222222-2-2-2-2-2-22222222-2-22-20000-2-20000-20000000000000000-2-200-2-2000000222200000000000000000000
χ3922222222-2-2-2-2222222-2-2-2222222-2-22222-2-22222-2000000000000000000-2-2000000-2-2000000000000000000000000
χ4022222222-2-2-2-2222222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000002200000022000000000000000000000000
χ4122222222-2-2-2-22222-2-2222-2-2-2-2-2-22-20000220000-200000000000000002200-2-2000000-2-22200000000000000000000
χ4222222222-2-2-2-22222-2-2222-2-2-2-2-2-22-20000220000-20000000000000000-2-2002200000022-2-200000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-220000220000200000000000000000000002-22-2000000-22-220000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-22000022000020000000000000000000000-22-220000002-22-20000000000000000
χ4522-2-2-22-2200002i−2i2i−2i2-20002i−2i2i−2i2-2002i−2i2i−2i002-22-20i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000002−22−2i2−i2i2−i200000000
χ4622-2-2-22-2200002i−2i2i−2i2-20002i−2i2i−2i2-2002i−2i2i−2i002-22-20−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000000000−22−22−i2i2−i2i200000000
χ4722-2-2-22-2200002i−2i2i−2i2-20002i−2i2i−2i2-200−2i2i−2i2i00-22-220i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000−22−22−i2i2−i2i200000000
χ4822-2-2-22-2200002i−2i2i−2i2-20002i−2i2i−2i2-200−2i2i−2i2i00-22-220−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000002−22−2i2−i2i2−i200000000
χ4922-2-2-22-220000−2i2i−2i2i2-2000−2i2i−2i2i2-2002i−2i2i−2i00-22-220i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000002−22−2−i2i2−i2i200000000
χ5022-2-2-22-220000−2i2i−2i2i2-2000−2i2i−2i2i2-2002i−2i2i−2i00-22-220−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000000000−22−22i2−i2i2−i200000000
χ5122-2-2-22-220000−2i2i−2i2i2-2000−2i2i−2i2i2-200−2i2i−2i2i002-22-20i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000000000−22−22i2−i2i2−i200000000
χ5222-2-2-22-220000−2i2i−2i2i2-2000−2i2i−2i2i2-200−2i2i−2i2i002-22-20−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000002−22−2−i2i2−i2i200000000
χ532-22-2-222-222-2-222-2-2-2-2-222-2-22222-220000-220000-200000000000000000000002i−2i−2i2i0000002i−2i−2i2i0000000000000000
χ542-22-2-222-222-2-222-2-2-2-2-222-2-22222-220000-220000-20000000000000000000000−2i2i2i−2i000000−2i2i2i−2i0000000000000000
χ552-22-2-222-222-2-2-2-22222-222-2-222-2-2-2-22i2i−2i−2i2-2−2i−2i2i2i20000000000000000002i−2i000000−2i2i000000000000000000000000
χ562-22-2-222-222-2-2-2-22222-222-2-222-2-2-2-2−2i−2i2i2i2-22i2i−2i−2i2000000000000000000−2i2i0000002i−2i000000000000000000000000
χ572-22-2-222-222-2-2-2-222-2-22-2-222-2-2222-20000-220000200000000000000002-2002-2000000-22-2200000000000000000000
χ582-22-2-222-222-2-2-2-222-2-22-2-222-2-2222-20000-22000020000000000000000-2200-220000002-22-200000000000000000000
χ592-22-2-222-2-2-22222-2-222-22222-2-2-2-2-2-22i2i−2i−2i-222i2i−2i−2i2000000000000000000−2i2i000000−2i2i000000000000000000000000
χ602-22-2-222-2-2-22222-2-222-22222-2-2-2-2-2-2−2i−2i2i2i-22−2i−2i2i2i20000000000000000002i−2i0000002i−2i000000000000000000000000
χ612-22-2-222-2-2-22222-2-2-2-22-2-2-2-222222-200002-20000200000000000000002-200-22000000-222-200000000000000000000
χ622-22-2-222-2-2-22222-2-2-2-22-2-2-2-222222-200002-2000020000000000000000-22002-20000002-2-2200000000000000000000
χ632-22-2-222-2-2-222-2-222-2-2-22222-2-222-2200002-20000-200000000000000000000002i−2i−2i2i000000−2i2i2i−2i0000000000000000
χ642-22-2-222-2-2-222-2-222-2-2-22222-2-222-2200002-20000-20000000000000000000000−2i2i2i−2i0000002i−2i−2i2i0000000000000000
χ652-2-2222-2-200002i−2i−2i2i2-20002i−2i−2i2i-22002-2-2200−2i2i2i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22i2−i2−i2i200000000
χ662-2-2222-2-200002i−2i−2i2i2-20002i−2i−2i2i-22002-2-2200−2i2i2i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−i2i2i2−i200000000
χ672-2-2222-2-200002i−2i−2i2i2-20002i−2i−2i2i-2200-222-2002i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−i2i2i2−i200000000
χ682-2-2222-2-200002i−2i−2i2i2-20002i−2i−2i2i-2200-222-2002i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22i2−i2−i2i200000000
χ692-2-2222-2-20000−2i2i2i−2i2-2000−2i2i2i−2i-22002-2-22002i−2i−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−i2i2i2−i200000000
χ702-2-2222-2-20000−2i2i2i−2i2-2000−2i2i2i−2i-22002-2-22002i−2i−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2i2−i2−i2i200000000
χ712-2-2222-2-20000−2i2i2i−2i2-2000−2i2i2i−2i-2200-222-200−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2i2−i2−i2i200000000
χ722-2-2222-2-20000−2i2i2i−2i2-2000−2i2i2i−2i-2200-222-200−2i2i2i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−i2i2i2−i200000000
χ734444-4-4-4-44-44-400000000000000000000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ744444-4-4-4-44-44-40000000000000000000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ754444-4-4-4-4-44-4400000000000000000000000000002-22-22-22-2-22-22-22-22000000000000000000000000000000000000
χ764444-4-4-4-4-44-440000000000000000000000000000-22-22-22-222-22-22-22-2000000000000000000000000000000000000
χ7744-4-44-44-4000000000044-4000000-40000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ7844-4-44-44-4000000000044-4000000-400000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ7944-4-44-44-40000000000-4-4400000040000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ8044-4-44-44-40000000000-4-440000004000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ8144-4-4-44-4400004i−4i4i−4i-44000−4i4i−4i4i-4400000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-44-440000−4i4i−4i4i-440004i−4i4i−4i-4400000000000000000000000000000000000000000000000000000000000000000
χ834-44-44-4-444-4-4400000000000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ844-44-44-4-444-4-440000000000000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ854-44-44-4-44-444-400000000000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ864-44-44-4-44-444-40000000000000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ874-4-4444-4-400004i−4i−4i4i-44000−4i4i4i−4i4-400000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-4-40000−4i4i4i−4i-440004i−4i−4i4i4-400000000000000000000000000000000000000000000000000000000000000000
χ894-4-44-4-44400000000004-44000000-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ904-4-44-4-44400000000004-44000000-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ914-4-44-4-4440000000000-44-4000000400000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ924-4-44-4-4440000000000-44-40000004000000000000−222222−2222−22−222200000000000000000000000000000000000000000000

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