Finite Group Databasebeta

← Group #205200

Character table — Group #205200

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444448888888844448888888888884444444488888888888888888888888844444444
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-11-1-1-1-111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-1-1-111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-11-1-1-1-111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-1-1-111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171-1-11-1-11111-1-1-111-1-11111-1-111-1-1-11111-1-1-1-11-11-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181-1-11-1-11111-1-1-111-1-11111-1-111-1-1-11111-1-1-1-11-11-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ191-1-11-1-11111-1-1-111-1-11111-1-111-1-1-11111-1-1-1-11-11-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ201-1-11-1-11111-1-1-111-1-11111-1-111-1-1-11111-1-1-1-11-11-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211-1-11-1-11111-1-1-111-1-11111-1-111-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ221-1-11-1-11111-1-1-111-1-11111-1-111-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ231-1-11-1-11111-1-1-111-1-11111-1-111-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ241-1-11-1-11111-1-1-111-1-11111-1-111-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ251-1-11-1-111-1-111-1-1-11111-1-11111-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ261-1-11-1-111-1-111-1-1-11111-1-11111-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ271-1-11-1-111-1-111-1-1-11111-1-11111-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ281-1-11-1-111-1-111-1-1-11111-1-11111-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ291-1-11-1-111-1-111-1-1-11111-1-11111-1-1-1-1-1-1-111111-1-11-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ301-1-11-1-111-1-111-1-1-11111-1-11111-1-1-1-1-1-1-111111-1-11-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ311-1-11-1-111-1-111-1-1-11111-1-11111-1-1-1-1-1-1-111111-1-11-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ321-1-11-1-111-1-111-1-1-11111-1-11111-1-1-1-1-1-1-111111-1-11-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ3322222222222222222-2-2-2-2-2-2222-2-222222222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ3422222222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2222222-2-2-22200000000-2-2-2-20000000000002-22-22-22-200000000000000000000000000000000
χ36222222222222-2-2-2-2-2222222-2-2-22200000000-2-2-2-2000000000000-22-22-22-2200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ3922222222-2-2-2-22-2-2-2-2-2-22222222-2-222222222-2-222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000
χ4022222222-2-2-2-22-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2222222-2-2-2-2-2-2-22200000000-2-2220000000000002-22-2-22-2200000000000000000000000000000000
χ4222222222-2-2-2-2-2222222-2-2-2-2-2-2-22200000000-2-222000000000000-22-222-22-200000000000000000000000000000000
χ4322222222-2-2-2-2-22222-2-22222-2-2-2-2-20000000022-2-2000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4422222222-2-2-2-2-22222-2-22222-2-2-2-2-20000000022-2-200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ452222-2-2-2-22-22-222-22-20000002-2-20022-2-222-2-2000000002-2002-20000000000000000002−22−22−22−22−22−22−22−200000000
χ462222-2-2-2-22-22-222-22-20000002-2-20022-2-222-2-2000000002-2002-2000000000000000000−22−22−22−22−22−22−22−2200000000
χ472222-2-2-2-22-22-222-22-20000002-2-200-2-222-2-22200000000-2200-220000000000000000002−22−22−22−2−22−22−22−2200000000
χ482222-2-2-2-22-22-222-22-20000002-2-200-2-222-2-22200000000-2200-22000000000000000000−22−22−22−222−22−22−22−200000000
χ492222-2-2-2-2-22-222-22-220000002-2-20022-2-222-2-200000000-2200-220000000000000000002−22−2−22−222−22−2−22−2200000000
χ502222-2-2-2-2-22-222-22-220000002-2-20022-2-222-2-200000000-2200-22000000000000000000−22−222−22−2−22−222−22−200000000
χ512222-2-2-2-2-22-222-22-220000002-2-200-2-222-2-222000000002-2002-20000000000000000002−22−2−22−22−22−222−22−200000000
χ522222-2-2-2-2-22-222-22-220000002-2-200-2-222-2-222000000002-2002-2000000000000000000−22−222−22−22−22−2−22−2200000000
χ532-2-2222-2-22-2-22-22-2-220000002-220022-2-2-2-222000000002-200-22000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ542-2-2222-2-22-2-22-22-2-220000002-220022-2-2-2-222000000002-200-22000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ552-2-2222-2-22-2-22-22-2-220000002-2200-2-22222-2-200000000-22002-2000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ562-2-2222-2-22-2-22-22-2-220000002-2200-2-22222-2-200000000-22002-2000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ572-2-2222-2-2-222-2-2-222-20000002-220022-2-2-2-22200000000-22002-2000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ582-2-2222-2-2-222-2-2-222-20000002-220022-2-2-2-22200000000-22002-2000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ592-2-2222-2-2-222-2-2-222-20000002-2200-2-22222-2-2000000002-200-22000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ602-2-2222-2-2-222-2-2-222-20000002-2200-2-22222-2-2000000002-200-22000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ612-2-22-2-22222-2-22-2-2222222-2-2-2-22-2-200000000-22-220000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ622-2-22-2-22222-2-22-2-2222222-2-2-2-22-2-200000000-22-22000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ632-2-22-2-22222-2-22-2-222-2-2-2-222-2-2222000000002-22-2000000000000000000002-2-222-2-22000000000000000000000000
χ642-2-22-2-22222-2-22-2-222-2-2-2-222-2-2222000000002-22-200000000000000000000-222-2-222-2000000000000000000000000
χ652-2-22-2-22222-2-2-222-2-2-2-2-2-22222-2222222-2-2-2-2-22-22-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ662-2-22-2-22222-2-2-222-2-2-2-2-2-22222-222-2-2-2-22222-22-2222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ672-2-22-2-222-2-222222-2-222-2-222-2-22-2-200000000-222-20000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ682-2-22-2-222-2-222222-2-222-2-222-2-22-2-200000000-222-2000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ692-2-22-2-222-2-222222-2-2-2-222-2-2-2-2222000000002-2-22000000000000000000002-2-22-222-2000000000000000000000000
χ702-2-22-2-222-2-222222-2-2-2-222-2-2-2-2222000000002-2-2200000000000000000000-222-22-2-22000000000000000000000000
χ712-2-22-2-222-2-222-2-2-222-2-222-2-222-2222222-2-2-2-2-222-2-2-222-2-22222-2-20000000000000000000000000000000000000000
χ722-2-22-2-222-2-222-2-2-222-2-222-2-222-222-2-2-2-22222-222-222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ734444-4-4-4-44-44-4-4-44-44000000-444000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-44-44-44-44-4000000-444000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-44-4000000000004i−4i4i−4i000002i2−2i22i2−2i22i2−2i22i2−2i2000000000022−220022−220000000000000000000000000000000000000000
χ7644-4-44-44-4000000000004i−4i4i−4i00000−2i22i2−2i22i2−2i22i2−2i22i20000000000−222200−22220000000000000000000000000000000000000000
χ7744-4-44-44-400000000000−4i4i−4i4i000002i2−2i22i2−2i22i2−2i22i2−2i20000000000−222200−22220000000000000000000000000000000000000000
χ7844-4-44-44-400000000000−4i4i−4i4i00000−2i22i2−2i22i2−2i22i2−2i22i2000000000022−220022−220000000000000000000000000000000000000000
χ7944-4-4-44-440000000004-400000004-42i2−2i2−2i22i22i2−2i2−2i22i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ8044-4-4-44-440000000004-400000004-4−2i22i22i2−2i2−2i22i22i2−2i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ8144-4-4-44-44000000000-440000000-442i2−2i2−2i22i22i2−2i2−2i22i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ8244-4-4-44-44000000000-440000000-44−2i22i22i2−2i2−2i22i22i2−2i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ834-44-44-4-440000000004-40000000-442i2−2i2−2i22i2−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ844-44-44-4-440000000004-40000000-44−2i22i22i2−2i22i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ854-44-44-4-44000000000-4400000004-42i2−2i2−2i22i2−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ864-44-44-4-44000000000-4400000004-4−2i22i22i2−2i22i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ874-44-4-444-4000000000004i−4i−4i4i000002i2−2i22i2−2i2−2i22i2−2i22i2000000000022−2200−22220000000000000000000000000000000000000000
χ884-44-4-444-4000000000004i−4i−4i4i00000−2i22i2−2i22i22i2−2i22i2−2i20000000000−22220022−220000000000000000000000000000000000000000
χ894-44-4-444-400000000000−4i4i4i−4i000002i2−2i22i2−2i2−2i22i2−2i22i20000000000−22220022−220000000000000000000000000000000000000000
χ904-44-4-444-400000000000−4i4i4i−4i00000−2i22i2−2i22i22i2−2i22i2−2i2000000000022−2200−22220000000000000000000000000000000000000000
χ914-4-4444-4-44-4-444-444-4000000-44-4000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-4-4-444-444-4-44000000-44-4000000000000000000000000000000000000000000000000000000000000000000

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