Finite Group Databasebeta

← Group #194100

Character table — Group #194100

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222244444444444444444444444444448888888888888888224444444444444444448888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-11-1-1-1-11111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-11-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1411111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1511111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ171-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1ii−i−i1ii−i−i-1iiii−i−i−i−iiiii−i−i−i−i1-1i−i1-11-1ii−i−ii−i1-1ii−i−i11-1-111-1-11-11-1i−ii−i
χ181-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1ii−i−i1ii−i−i-1iiii−i−i−i−iiiii−i−i−i−i-11i−i-11-11−i−iiii−i-11−i−iii11-1-111-1-1-11-11−ii−ii
χ191-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1ii−i−i1ii−i−i-1−i−i−i−iiiii−i−i−i−iiiii1-1i−i1-11-1ii−i−ii−i1-1ii−i−i-1-111-1-111-11-11−ii−ii
χ201-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1ii−i−i1ii−i−i-1−i−i−i−iiiii−i−i−i−iiiii-11i−i-11-11−i−iiii−i-11−i−iii-1-111-1-1111-11-1i−ii−i
χ211-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1−i−iii1−i−iii-1iiii−i−i−i−iiiii−i−i−i−i1-1−ii1-11-1−i−iii−ii1-1−i−iii-1-111-1-111-11-11i−ii−i
χ221-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1−i−iii1−i−iii-1iiii−i−i−i−iiiii−i−i−i−i-11−ii-11-11ii−i−i−ii-11ii−i−i-1-111-1-1111-11-1−ii−ii
χ231-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1−i−iii1−i−iii-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii1-11-1−i−iii−ii1-1−i−iii11-1-111-1-11-11-1−ii−ii
χ241-111-1-11-111-1-1111-1-111-1-111-1-1-1-111-1−i−iii1−i−iii-1−i−i−i−iiiii−i−i−i−iiiii-11−ii-11-11ii−i−i−ii-11ii−i−i11-1-111-1-1-11-11i−ii−i
χ251-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11ii−i−i1−i−iii-1iiii−i−i−i−i−i−i−i−iiiii1-1−ii1-1-11ii−i−ii−i-11−i−iii11-1-1-1-1111-1-11i−i−ii
χ261-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11ii−i−i1−i−iii-1iiii−i−i−i−i−i−i−i−iiiii-11−ii-111-1−i−iiii−i1-1ii−i−i11-1-1-1-111-111-1−iii−i
χ271-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11ii−i−i1−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i1-1−ii1-1-11ii−i−ii−i-11−i−iii-1-11111-1-1-111-1−iii−i
χ281-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11ii−i−i1−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i-11−ii-111-1−i−iiii−i1-1ii−i−i-1-11111-1-11-1-11i−i−ii
χ291-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11−i−iii1ii−i−i-1iiii−i−i−i−i−i−i−i−iiiii1-1i−i1-1-11−i−iii−ii-11ii−i−i-1-11111-1-1-111-1i−i−ii
χ301-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11−i−iii1ii−i−i-1iiii−i−i−i−i−i−i−i−iiiii-11i−i-111-1ii−i−i−ii1-1−i−iii-1-11111-1-11-1-11−iii−i
χ311-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11−i−iii1ii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i1-1i−i1-1-11−i−iii−ii-11ii−i−i11-1-1-1-1111-1-11−iii−i
χ321-111-1-11-1-1-111111-1-1-1-111-1-111-1-11-11−i−iii1ii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i-11i−i-111-1ii−i−i−ii1-1−i−iii11-1-1-1-111-111-1i−i−ii
χ3322222222222222-2-2-2-2-2-2-2-2-2-2-222-2222222-2-2-2-2-2-20000000000000000002200000000-2-20000000000000000000000
χ3422222222222222-2-2-2-2-2-2-2-2-2-2-222-222-2-2-2-2-22222-2000000000000000000-2-200000000220000000000000000000000
χ35222222222222-2-22222222-2-2-2-2-2-22-2-20000-20000-200000000000000002200-2-2-2-20000002200000000000000000000
χ36222222222222-2-22222222-2-2-2-2-2-22-2-20000-20000-20000000000000000-2-2002222000000-2-200000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-200002000020000000000000000000000002-22-200002-22-20000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-20000200002000000000000000000000000-22-220000-22-220000000000000000
χ3922222222-2-2-2-222-2-2-22222222222-2-2-22222-22222-2000000000000000000-2-200000000-2-20000000000000000000000
χ4022222222-2-2-2-222-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000002200000000220000000000000000000000
χ4122222222-2-2-2-2-2-2222-2-2-2-22222-2-22220000-20000-200000000000000002200-2-222000000-2-200000000000000000000
χ4222222222-2-2-2-2-2-2222-2-2-2-22222-2-22220000-20000-20000000000000000-2-20022-2-20000002200000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22200002000020000000000000000000000002-22-20000-22-220000000000000000
χ4422222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2220000200002000000000000000000000000-22-2200002-22-20000000000000000
χ45222-2-2-2-2200002-20002i−2i2i−2i2i−2i2i−2i2-20002i−2i2i−2i02-22-20i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000002−22−2i2−i2i2−i200000000
χ46222-2-2-2-2200002-20002i−2i2i−2i2i−2i2i−2i2-20002i−2i2i−2i02-22-20−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000000000−22−22−i2i2−i2i200000000
χ47222-2-2-2-2200002-20002i−2i2i−2i2i−2i2i−2i2-2000−2i2i−2i2i0-22-220i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000−22−22−i2i2−i2i200000000
χ48222-2-2-2-2200002-20002i−2i2i−2i2i−2i2i−2i2-2000−2i2i−2i2i0-22-220−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000002−22−2i2−i2i2−i200000000
χ49222-2-2-2-2200002-2000−2i2i−2i2i−2i2i−2i2i2-20002i−2i2i−2i0-22-220i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000002−22−2−i2i2−i2i200000000
χ50222-2-2-2-2200002-2000−2i2i−2i2i−2i2i−2i2i2-20002i−2i2i−2i0-22-220−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000000000−22−22i2−i2i2−i200000000
χ51222-2-2-2-2200002-2000−2i2i−2i2i−2i2i−2i2i2-2000−2i2i−2i2i02-22-20i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000000000−22−22i2−i2i2−i200000000
χ52222-2-2-2-2200002-2000−2i2i−2i2i−2i2i−2i2i2-2000−2i2i−2i2i02-22-20−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000002−22−2−i2i2−i2i200000000
χ532-222-2-22-222-2-222-222-2-222-2-222-2-2-22-22i2i−2i−2i-2−2i−2i2i2i20000000000000000002i−2i00000000−2i2i0000000000000000000000
χ542-222-2-22-222-2-222-222-2-222-2-222-2-2-22-2−2i−2i2i2i-22i2i−2i−2i2000000000000000000−2i2i000000002i−2i0000000000000000000000
χ552-222-2-22-222-2-2-2-22-2-222-2-2-2-222222-220000-20000200000000000000002-200-22-220000002-200000000000000000000
χ562-222-2-22-222-2-2-2-22-2-222-2-2-2-222222-220000-2000020000000000000000-22002-22-2000000-2200000000000000000000
χ572-222-2-22-222-2-2-2-2-222-2-22222-2-222-2-22000020000-20000000000000000000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ582-222-2-22-222-2-2-2-2-222-2-22222-2-222-2-22000020000-2000000000000000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ592-222-2-22-2-2-22222-22222-2-222-2-2-2-2-2-222i2i−2i−2i-22i2i−2i−2i2000000000000000000−2i2i00000000−2i2i0000000000000000000000
χ602-222-2-22-2-2-22222-22222-2-222-2-2-2-2-2-22−2i−2i2i2i-2−2i−2i2i2i20000000000000000002i−2i000000002i−2i0000000000000000000000
χ612-222-2-22-2-2-222-2-22-2-2-2-22222-2-22222-20000-20000200000000000000002-200-222-2000000-2200000000000000000000
χ622-222-2-22-2-2-222-2-22-2-2-2-22222-2-22222-20000-2000020000000000000000-22002-2-220000002-200000000000000000000
χ632-222-2-22-2-2-222-2-2-22222-2-2-2-22222-22-2000020000-20000000000000000000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ642-222-2-22-2-2-222-2-2-22222-2-2-2-22222-22-2000020000-2000000000000000000000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ652-22-222-2-200002-20002i−2i−2i2i2i−2i−2i2i-220002-2-220−2i2i2i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22i2−i2−i2i200000000
χ662-22-222-2-200002-20002i−2i−2i2i2i−2i−2i2i-220002-2-220−2i2i2i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−i2i2i2−i200000000
χ672-22-222-2-200002-20002i−2i−2i2i2i−2i−2i2i-22000-222-202i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−i2i2i2−i200000000
χ682-22-222-2-200002-20002i−2i−2i2i2i−2i−2i2i-22000-222-202i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22i2−i2−i2i200000000
χ692-22-222-2-200002-2000−2i2i2i−2i−2i2i2i−2i-220002-2-2202i−2i−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−i2i2i2−i200000000
χ702-22-222-2-200002-2000−2i2i2i−2i−2i2i2i−2i-220002-2-2202i−2i−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2i2−i2−i2i200000000
χ712-22-222-2-200002-2000−2i2i2i−2i−2i2i2i−2i-22000-222-20−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2i2−i2−i2i200000000
χ722-22-222-2-200002-2000−2i2i2i−2i−2i2i2i−2i-22000-222-20−2i2i2i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−i2i2i2−i200000000
χ73444-4-4-4-440000-440004i−4i4i−4i−4i4i−4i4i-4400000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-440000-44000−4i4i−4i4i4i−4i4i−4i-4400000000000000000000000000000000000000000000000000000000000000000
χ7544-444-4-4-400000044-40000000000-400000000000022−2222−2222−2222−2200000000000000000000000000000000000000000000
χ7644-444-4-4-400000044-40000000000-4000000000000−2222−2222−2222−222200000000000000000000000000000000000000000000
χ7744-444-4-4-4000000-4-4400000000004000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ7844-444-4-4-4000000-4-440000000000400000000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ7944-4-4-444-44-44-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ8044-4-4-444-44-44-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ8144-4-4-444-4-44-4400000000000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ8244-4-4-444-4-44-440000000000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ834-44-444-4-40000-440004i−4i−4i4i−4i4i4i−4i4-400000000000000000000000000000000000000000000000000000000000000000
χ844-44-444-4-40000-44000−4i4i4i−4i4i−4i−4i4i4-400000000000000000000000000000000000000000000000000000000000000000
χ854-4-44-44-440000004-440000000000-40000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ864-4-44-44-440000004-440000000000-4000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ874-4-44-44-44000000-44-4000000000040000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000
χ884-4-44-44-44000000-44-40000000000400000000000000000000−2222−222222−2222−22000000000000000000000000000000000000
χ894-4-4-44-4444-4-4400000000000000000000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ904-4-4-44-4444-4-440000000000000000000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ914-4-4-44-444-444-400000000000000000000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000000000
χ924-4-4-44-444-444-40000000000000000000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000000000

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