Finite Group Databasebeta

← Group #194107

Character table — Group #194107

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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1711-1-1-111-111-1-111-1-111-111-1-1-1-111-11ii−i−i1-1ii−i−i-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-11-11-1i−ii−i
χ1811-1-1-111-111-1-111-1-111-111-1-1-1-111-11ii−i−i1-1ii−i−i-1iiii−i−i−i−iiiii−i−i−i−i-11-11i−ii−i-11-11−i−iii−i−iii11-1-111-1-1-11-11−ii−ii
χ1911-1-1-111-111-1-111-1-111-111-1-1-1-111-11ii−i−i1-1ii−i−i-1−i−i−i−iiiii−i−i−i−iiiii1-11-1i−ii−i1-11-1ii−i−iii−i−i-1-111-1-111-11-11−ii−ii
χ2011-1-1-111-111-1-111-1-111-111-1-1-1-111-11ii−i−i1-1ii−i−i-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11-11−i−iii−i−iii-1-111-1-1111-11-1i−ii−i
χ2111-1-1-111-111-1-111-1-111-111-1-1-1-111-11−i−iii1-1−i−iii-1iiii−i−i−i−iiiii−i−i−i−i1-11-1−ii−ii1-11-1−i−iii−i−iii-1-111-1-111-11-11i−ii−i
χ2211-1-1-111-111-1-111-1-111-111-1-1-1-111-11−i−iii1-1−i−iii-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11-11ii−i−iii−i−i-1-111-1-1111-11-1−ii−ii
χ2311-1-1-111-111-1-111-1-111-111-1-1-1-111-11−i−iii1-1−i−iii-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-11-11-1−ii−ii
χ2411-1-1-111-111-1-111-1-111-111-1-1-1-111-11−i−iii1-1−i−iii-1−i−i−i−iiiii−i−i−i−iiiii-11-11−ii−ii-11-11ii−i−iii−i−i11-1-111-1-1-11-11i−ii−i
χ2511-1-1-111-1-1-111-1-11111-1-1-111-1-111-11ii−i−i-11−i−iii-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-1111-1-11i−i−ii
χ2611-1-1-111-1-1-111-1-11111-1-1-111-1-111-11ii−i−i-11−i−iii-1iiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii-111-1−i−iiiii−i−i11-1-1-1-111-111-1−iii−i
χ2711-1-1-111-1-1-111-1-11111-1-1-111-1-111-11ii−i−i-11−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii1-1-11ii−i−i−i−iii-1-11111-1-1-111-1−iii−i
χ2811-1-1-111-1-1-111-1-11111-1-1-111-1-111-11ii−i−i-11−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-111-1−i−iiiii−i−i-1-11111-1-11-1-11i−i−ii
χ2911-1-1-111-1-1-111-1-11111-1-1-111-1-111-11−i−iii-11ii−i−i-1iiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i1-1-11−i−iiiii−i−i-1-11111-1-1-111-1i−i−ii
χ3011-1-1-111-1-1-111-1-11111-1-1-111-1-111-11−i−iii-11ii−i−i-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-111-1ii−i−i−i−iii-1-11111-1-11-1-11−iii−i
χ3111-1-1-111-1-1-111-1-11111-1-1-111-1-111-11−i−iii-11ii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i1-1-11−i−iiiii−i−i11-1-1-1-1111-1-11−iii−i
χ3211-1-1-111-1-1-111-1-11111-1-1-111-1-111-11−i−iii-11ii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i-111-1ii−i−i−i−iii11-1-1-1-111-111-1i−i−ii
χ332222222222222222-2-2-2-2-2-2-2-2-2-2-2-220000-2-20000200000000000000000000000000002-22-22-22-20000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-220000-2-2000020000000000000000000000000000-22-22-22-220000000000000000
χ35222222222222-2-2-2-22222222-2-2-2-22-22222-2-22222-200000000000000000000-2-2-2-20000000000000000000000000000
χ36222222222222-2-2-2-22222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-20000220000-2000000000000000022-2-20000-2-222000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-20000220000-20000000000000000-2-222000022-2-2000000000000000000000000
χ3922222222-2-2-2-22222222-2-2-2-2-2-2-2-22-2222222-2-2-2-2-200000000000000000000-2-2220000000000000000000000000000
χ4022222222-2-2-2-22222222-2-2-2-2-2-2-2-22-2-2-2-2-2222222-20000000000000000000022-2-20000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-222222222-2-20000-2-20000-2000000000000000022220000-2-2-2-2000000000000000000000000
χ4222222222-2-2-2-22222-2-2-222222222-2-20000-2-20000-20000000000000000-2-2-2-200002222000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-220000220000200000000000000000000000000002-22-2-22-220000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-22000022000020000000000000000000000000000-22-222-22-20000000000000000
χ4522-2-2-222-222-2-222-2-2-2-22-2-22222-2-2220000-220000-200000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ4622-2-2-222-222-2-222-2-2-2-22-2-22222-2-2220000-220000-20000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4722-2-2-222-222-2-2-2-22222-222-2-222-2-2-2-22i2i−2i−2i-222i2i−2i−2i200000000000000000000−2i2i−2i2i0000000000000000000000000000
χ4822-2-2-222-222-2-2-2-22222-222-2-222-2-2-2-2−2i−2i2i2i-22−2i−2i2i2i2000000000000000000002i−2i2i−2i0000000000000000000000000000
χ4922-2-2-222-222-2-2-2-222-2-22-2-222-2-2222-200002-20000200000000000000002-2-220000-222-2000000000000000000000000
χ5022-2-2-222-222-2-2-2-222-2-22-2-222-2-2222-200002-2000020000000000000000-222-200002-2-22000000000000000000000000
χ5122-2-2-222-2-2-22222-2-222-2-2-22222-2-2-2-22i2i−2i−2i2-2−2i−2i2i2i200000000000000000000−2i2i2i−2i0000000000000000000000000000
χ5222-2-2-222-2-2-22222-2-222-2-2-22222-2-2-2-2−2i−2i2i2i2-22i2i−2i−2i2000000000000000000002i−2i−2i2i0000000000000000000000000000
χ5322-2-2-222-2-2-22222-2-2-2-2222-2-2-2-2222-20000-220000200000000000000002-22-20000-22-22000000000000000000000000
χ5422-2-2-222-2-2-22222-2-2-2-2222-2-2-2-2222-20000-22000020000000000000000-22-2200002-22-2000000000000000000000000
χ5522-2-2-222-2-2-222-2-222-2-2222-2-222-2-22200002-20000-200000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5622-2-2-222-2-2-222-2-222-2-2222-2-222-2-22200002-20000-20000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ572-222-22-2-22-22-200002-2-22-22-20000202i−2i2i−2i002i−2i2i−2i022−2−222−2−222−2−222−2−200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ582-222-22-2-22-22-200002-2-22-22-20000202i−2i2i−2i002i−2i2i−2i0−2−222−2−222−2−222−2−22200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ592-222-22-2-22-22-200002-2-22-22-2000020−2i2i−2i2i00−2i2i−2i2i022−2−222−2−222−2−222−2−200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ602-222-22-2-22-22-200002-2-22-22-2000020−2i2i−2i2i00−2i2i−2i2i0−2−222−2−222−2−222−2−22200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ612-222-22-2-2-22-2200002-2-2-22-220000202i−2i2i−2i00−2i2i−2i2i022−2−222−2−2−2−222−2−22200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ622-222-22-2-2-22-2200002-2-2-22-220000202i−2i2i−2i00−2i2i−2i2i0−2−222−2−22222−2−222−2−200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ632-222-22-2-2-22-2200002-2-2-22-22000020−2i2i−2i2i002i−2i2i−2i022−2−222−2−2−2−222−2−22200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ642-222-22-2-2-22-2200002-2-2-22-22000020−2i2i−2i2i002i−2i2i−2i0−2−222−2−22222−2−222−2−200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ652-2-2-222-222-2-2200002-222-2-220000-202-2-22002-2-220i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ662-2-2-222-222-2-2200002-222-2-220000-202-2-22002-2-220−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ672-2-2-222-222-2-2200002-222-2-220000-20-222-200-222-20i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ682-2-2-222-222-2-2200002-222-2-220000-20-222-200-222-20−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ692-2-2-222-22-222-200002-22-222-20000-202-2-2200-222-20i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ702-2-2-222-22-222-200002-22-222-20000-202-2-2200-222-20−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ712-2-2-222-22-222-200002-22-222-20000-20-222-2002-2-220i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ722-2-2-222-22-222-200002-22-222-20000-20-222-2002-2-220−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ73444-44-4-4-400004-44-40000000000000000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ74444-44-4-4-400004-44-4000000000000000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ75444-44-4-4-40000-44-440000000000000000000000002-22-22-22-2-22-22-22-22000000000000000000000000000000000000
χ76444-44-4-4-40000-44-44000000000000000000000000-22-22-22-222-22-22-22-2000000000000000000000000000000000000
χ7744-44-4-4-4400004-4-440000000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ7844-44-4-4-4400004-4-44000000000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ7944-44-4-4-440000-444-40000000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ8044-44-4-4-440000-444-4000000000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ814-444-44-4-44-44-40000-444-44-440000-40000000000000000000000000000000000000000000000000000000000000000
χ824-444-44-4-4-44-440000-4444-44-40000-40000000000000000000000000000000000000000000000000000000000000000
χ834-44-4-4-4440000000000000004-44-400000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ844-44-4-4-4440000000000000004-44-4000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ854-44-4-4-444000000000000000-44-44000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ864-44-4-4-444000000000000000-44-440000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ874-4-444-44-40000000000000004-4-4400000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ884-4-444-44-40000000000000004-4-440000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ894-4-444-44-4000000000000000-444-40000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ904-4-444-44-4000000000000000-444-4000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ914-4-4-444-444-4-440000-44-4-444-4000040000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44-444-40000-44-44-4-44000040000000000000000000000000000000000000000000000000000000000000000

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