Finite Group Databasebeta

← Group #368781

Character table — Group #368781

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444448888888822448888888888882244444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ12111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ13111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ14111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ15111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ171-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i1-11-11-11-1ii−i−iii−i−iii−i−i11-1-111-1-1ii−i−ii−ii−i1-11-1
χ181-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i1-11-11-11-1ii−i−i−i−iii−i−iii-1-111-1-111ii−i−i−ii−ii-11-11
χ191-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i-11-11-11-11−i−iiiii−i−iii−i−i11-1-111-1-1−i−iii−ii−ii-11-11
χ201-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i-11-11-11-11−i−iii−i−iii−i−iii-1-111-1-111−i−iiii−ii−i1-11-1
χ211-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii1-11-11-11-1−i−iiiii−i−iii−i−i-1-111-1-111−i−iiii−ii−i-11-11
χ221-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii1-11-11-11-1−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−ii−ii1-11-1
χ231-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii-11-11-11-11ii−i−iii−i−iii−i−i-1-111-1-111ii−i−i−ii−ii1-11-1
χ241-1-11-1-11111-1-111-1-1111-111-1-1-11-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii-11-11-11-11ii−i−i−i−iii−i−iii11-1-111-1-1ii−i−ii−ii−i-11-11
χ251-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1iiii−i−i−i−i-11-11ii−i−i−i−i−i−iiiii1-1-11-111-1−i−iiiii−i−i−i−iii11-1-1-1-111ii−i−ii−i−ii1-1-11
χ261-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1iiii−i−i−i−i-11-11ii−i−i−i−i−i−iiiii1-1-11-111-1−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i−iii−i-111-1
χ271-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1iiii−i−i−i−i-11-11ii−i−i−i−i−i−iiiii-111-11-1-11ii−i−iii−i−i−i−iii11-1-1-1-111−i−iii−iii−i-111-1
χ281-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1iiii−i−i−i−i-11-11ii−i−i−i−i−i−iiiii-111-11-1-11ii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiii−i−ii1-1-11
χ291-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1−i−i−i−iiiii-11-11−i−iiiiiii−i−i−i−i1-1-11-111-1ii−i−iii−i−i−i−iii-1-11111-1-1−i−iiii−i−ii-111-1
χ301-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1−i−i−i−iiiii-11-11−i−iiiiiii−i−i−i−i1-1-11-111-1ii−i−i−i−iiiii−i−i11-1-1-1-111−i−iii−iii−i1-1-11
χ311-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1−i−i−i−iiiii-11-11−i−iiiiiii−i−i−i−i-111-11-1-11−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−iii−i1-1-11
χ321-1-11-1-11111-1-1-1-111111-1-1-111-11-1-1−i−i−i−iiiii-11-11−i−iiiiiii−i−i−i−i-111-11-1-11−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−ii−i−ii-111-1
χ332222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2000000000000000000002i−2i2i−2i00000000000000002i−2i2i−2i00000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-200000000000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i00000000
χ35222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-222000000000000000000002i−2i2i−2i0000000000000000−2i2i−2i2i00000000
χ36222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-22200000000000000000000−2i2i−2i2i00000000000000002i−2i2i−2i00000000
χ3722222222-2-2-2-2222222-2-2-2-2-2-22-2-2222222222-2-222-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ3822222222-2-2-2-2222222-2-2-2-2-2-22-2-22-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2220000000000000000000000000000000000000000
χ3922222222-2-2-2-22222-2-2222222-222-200000000-2-2-2-20000000000002222-2-2-2-200000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2222222-222-200000000-2-2-2-2000000000000-2-2-2-2222200000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222-2-222222-2-222222222222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-222-2-222222-2-22-2-2-2-2-2-2-2-222-2-2222222-2-222-2-20000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-222-200000000222200000000000022-2-222-2-200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-222-2000000002222000000000000-2-222-2-22200000000000000000000000000000000
χ4522-2-22-2-222-22-200002-2220000-2-2-2222-2-222-2-200002-22-2000000000000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ4622-2-22-2-222-22-200002-2220000-2-2-2222-2-222-2-200002-22-200000000000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ4722-2-22-2-222-22-200002-2220000-2-2-22-2-222-2-2220000-22-22000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ4822-2-22-2-222-22-200002-2220000-2-2-22-2-222-2-2220000-22-2200000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ4922-2-22-2-22-22-2200002-2-2-20000-222222-2-222-2-20000-22-220000000000000000000000002-22-200002-22-2000000000000
χ5022-2-22-2-22-22-2200002-2-2-20000-222222-2-222-2-20000-22-22000000000000000000000000-22-220000-22-22000000000000
χ5122-2-22-2-22-22-2200002-2-2-20000-2222-2-222-2-22200002-22-20000000000000000000000002-22-20000-22-22000000000000
χ5222-2-22-2-22-22-2200002-2-2-20000-2222-2-222-2-22200002-22-2000000000000000000000000-22-2200002-22-2000000000000
χ532-22-2-22-222-2-2200002-22-200002-22-22i2i−2i−2i−2i−2i2i2i00002i−2i−2i2i000000000000000000002-2-220000−2i2i2i−2i0000000000000000
χ542-22-2-22-222-2-2200002-22-200002-22-22i2i−2i−2i−2i−2i2i2i00002i−2i−2i2i00000000000000000000-222-200002i−2i−2i2i0000000000000000
χ552-22-2-22-222-2-2200002-22-200002-22-2−2i−2i2i2i2i2i−2i−2i0000−2i2i2i−2i000000000000000000002-2-2200002i−2i−2i2i0000000000000000
χ562-22-2-22-222-2-2200002-22-200002-22-2−2i−2i2i2i2i2i−2i−2i0000−2i2i2i−2i00000000000000000000-222-20000−2i2i2i−2i0000000000000000
χ572-22-2-22-22-222-200002-2-22000022-2-22i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i0000000000000000000000002i−2i−2i2i00002-2-22000000000000
χ582-22-2-22-22-222-200002-2-22000022-2-22i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i000000000000000000000000−2i2i2i−2i0000-222-2000000000000
χ592-22-2-22-22-222-200002-2-22000022-2-2−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i0000000000000000000000002i−2i−2i2i0000-222-2000000000000
χ602-22-2-22-22-222-200002-2-22000022-2-2−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i000000000000000000000000−2i2i2i−2i00002-2-22000000000000
χ612-2-22-2-22222-2-222-2-2-2-2-22-2-2222-222000000002-2-22000000000000000000002-2-2200000000000000002-2-2200000000
χ622-2-22-2-22222-2-222-2-2-2-2-22-2-2222-222000000002-2-2200000000000000000000-222-20000000000000000-222-200000000
χ632-2-22-2-22222-2-2-2-222-2-2-2222-2-22-22200000000-222-2000000000000000000002-2-220000000000000000-222-200000000
χ642-2-22-2-22222-2-2-2-222-2-2-2222-2-22-22200000000-222-200000000000000000000-222-200000000000000002-2-2200000000
χ652-2-22-2-222-2-22222-2-222-22-2-222-2-22-22i2i2i2i−2i−2i−2i−2i-222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ662-2-22-2-222-2-22222-2-222-22-2-222-2-22-2−2i−2i−2i−2i2i2i2i2i-222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ672-2-22-2-222-2-22222-2-2-2-22-222-2-222-2200000000-22-220000000000002-22-2-22-2200000000000000000000000000000000
χ682-2-22-2-222-2-22222-2-2-2-22-222-2-222-2200000000-22-22000000000000-22-222-22-200000000000000000000000000000000
χ692-2-22-2-222-2-222-2-22222-2222-2-2-2-22-22i2i2i2i−2i−2i−2i−2i2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ702-2-22-2-222-2-222-2-22222-2222-2-2-2-22-2−2i−2i−2i−2i2i2i2i2i2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ712-2-22-2-222-2-222-2-222-2-22-2-2-22222-22000000002-22-20000000000002-2-222-2-2200000000000000000000000000000000
χ722-2-22-2-222-2-222-2-222-2-22-2-2-22222-22000000002-22-2000000000000-222-2-222-200000000000000000000000000000000
χ734444-4-4-4-400004-44-400000000000022−2222−2222−2222−220000000022−220022−22000000000000000000000000000000000000000000
χ744444-4-4-4-400004-44-4000000000000−2222−2222−2222−222200000000−222200−2222000000000000000000000000000000000000000000
χ754444-4-4-4-40000-44-4400000000000022−2222−2222−2222−2200000000−222200−2222000000000000000000000000000000000000000000
χ764444-4-4-4-40000-44-44000000000000−2222−2222−2222−22220000000022−220022−22000000000000000000000000000000000000000000
χ7744-4-44-4-444-44-40000-44-4-40000444-40000000000000000000000000000000000000000000000000000000000000000
χ7844-4-44-4-44-44-440000-444400004-4-4-40000000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-444-40000000000004i−4i4i−4i000022−22−222222−22−222200000000002i2−2i2002i2−2i20000000000000000000000000000000000000000
χ8044-4-4-444-40000000000004i−4i4i−4i0000−222222−22−222222−220000000000−2i22i200−2i22i20000000000000000000000000000000000000000
χ8144-4-4-444-4000000000000−4i4i−4i4i000022−22−222222−22−22220000000000−2i22i200−2i22i20000000000000000000000000000000000000000
χ8244-4-4-444-4000000000000−4i4i−4i4i0000−222222−22−222222−2200000000002i2−2i2002i2−2i20000000000000000000000000000000000000000
χ834-44-44-44-40000000000004i−4i−4i4i00002i2−2i2−2i22i2−2i22i22i2−2i20000000000−22220022−220000000000000000000000000000000000000000
χ844-44-44-44-40000000000004i−4i−4i4i0000−2i22i22i2−2i22i2−2i2−2i22i2000000000022−2200−22220000000000000000000000000000000000000000
χ854-44-44-44-4000000000000−4i4i4i−4i00002i2−2i2−2i22i2−2i22i22i2−2i2000000000022−2200−22220000000000000000000000000000000000000000
χ864-44-44-44-4000000000000−4i4i4i−4i0000−2i22i22i2−2i22i2−2i2−2i22i20000000000−22220022−220000000000000000000000000000000000000000
χ874-44-4-44-444-4-440000-44-440000-44-440000000000000000000000000000000000000000000000000000000000000000
χ884-44-4-44-44-444-40000-444-40000-4-4440000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-4-400004-4-440000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000002i2−2i200−2i22i2000000000000000000000000000000000000000000
χ904-4-4444-4-400004-4-44000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000−2i22i2002i2−2i2000000000000000000000000000000000000000000
χ914-4-4444-4-40000-444-40000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000−2i22i2002i2−2i2000000000000000000000000000000000000000000
χ924-4-4444-4-40000-444-4000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000002i2−2i200−2i22i2000000000000000000000000000000000000000000

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