Finite Group Databasebeta

← Group #209784

Character table — Group #209784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444444444444444448888888888888888224444444444444444448888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ171-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1i−iii−i−i1-11111-1-1-1-1iiii−i−i−i−i1-1i−i1-11-111-1-1ii−i−ii−ii−i11-1-1ii−i−i1-1i−i1-1i−i
χ181-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1i−iii−i−i1-11111-1-1-1-1iiii−i−i−i−i-11−ii1-1-11-1-111−i−iiii−i−ii11-1-1ii−i−i-11−ii-11−ii
χ191-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1i−iii−i−i1-1-1-1-1-11111−i−i−i−iiiii1-1i−i1-11-111-1-1ii−i−ii−ii−i-1-111−i−iii-11−ii-11−ii
χ201-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1i−iii−i−i1-1-1-1-1-11111−i−i−i−iiiii-11−ii1-1-11-1-111−i−iiii−i−ii-1-111−i−iii1-1i−i1-1i−i
χ211-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1-1-111i−i−i−iii1-11111-1-1-1-1iiii−i−i−i−i1-1i−i-111-1-1-111−i−iii−iii−i-1-111−i−iii-11−ii1-1i−i
χ221-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1-1-111i−i−i−iii1-11111-1-1-1-1iiii−i−i−i−i-11−ii-11-1111-1-1ii−i−i−ii−ii-1-111−i−iii1-1i−i-11−ii
χ231-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1-1-111i−i−i−iii1-1-1-1-1-11111−i−i−i−iiiii1-1i−i-111-1-1-111−i−iii−iii−i11-1-1ii−i−i1-1i−i-11−ii
χ241-11-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1-1-111i−i−i−iii1-1-1-1-1-11111−i−i−i−iiiii-11−ii-11-1111-1-1ii−i−i−ii−ii11-1-1ii−i−i-11−ii1-1i−i
χ251-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-111-1-1−ii−i−iii1-11111-1-1-1-1−i−i−i−iiiii1-1−ii1-11-111-1-1−i−iii−ii−ii11-1-1−i−iii1-1−ii1-1−ii
χ261-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-111-1-1−ii−i−iii1-11111-1-1-1-1−i−i−i−iiiii-11i−i1-1-11-1-111ii−i−i−iii−i11-1-1−i−iii-11i−i-11i−i
χ271-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-111-1-1−ii−i−iii1-1-1-1-1-11111iiii−i−i−i−i1-1−ii1-11-111-1-1−i−iii−ii−ii-1-111ii−i−i-11i−i-11i−i
χ281-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-111-1-1−ii−i−iii1-1-1-1-1-11111iiii−i−i−i−i-11i−i1-1-11-1-111ii−i−i−iii−i-1-111ii−i−i1-1−ii1-1−ii
χ291-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-1-1-111−iiii−i−i1-11111-1-1-1-1−i−i−i−iiiii1-1−ii-111-1-1-111ii−i−ii−i−ii-1-111ii−i−i-11i−i1-1−ii
χ301-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-1-1-111−iiii−i−i1-11111-1-1-1-1−i−i−i−iiiii-11i−i-11-1111-1-1−i−iiii−ii−i-1-111ii−i−i1-1−ii-11i−i
χ311-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-1-1-111−iiii−i−i1-1-1-1-1-11111iiii−i−i−i−i1-1−ii-111-1-1-111ii−i−ii−i−ii11-1-1−i−iii1-1−ii-11i−i
χ321-11-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-1-1-111−iiii−i−i1-1-1-1-1-11111iiii−i−i−i−i-11i−i-11-1111-1-1−i−iiii−ii−i11-1-1−i−iii-11i−i1-1−ii
χ3322222222222222222-22-2-2-2-2-22-22-20000-2-20000-2-2000000000000000022-2-200-2-20000000000220000000000000000
χ3422222222222222222-22-2-2-2-2-22-22-20000-2-20000-2-20000000000000000-2-22200220000000000-2-20000000000000000
χ35222222222222-2-2-2-2-22-22-2-2-2-2-22-22222222-2-2-2-2-2-200000000000000000000-2-2000000000022000000000000000000
χ36222222222222-2-2-2-2-22-22-2-2-2-2-22-22-2-2-2-2222222-2-200000000000000000000220000000000-2-2000000000000000000
χ37222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000-2-20000220000000000000000000000002-22-22-22-200000000000000000000
χ38222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000-2-2000022000000000000000000000000-22-22-22-2200000000000000000000
χ3922222222-2-2-2-22222-22-222222-22-222222-2-22222-2-200000000000000000000-2-20000000000-2-2000000000000000000
χ4022222222-2-2-2-22222-22-222222-22-22-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022000000000022000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000220000220000000000000000000000002-22-2-22-2200000000000000000000
χ4222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000022000022000000000000000000000000-22-222-22-200000000000000000000
χ4322222222-2-2-2-2-2-2-2-22-22-222222-22-20000220000-2-20000000000000000222200-2-20000000000-2-20000000000000000
χ4422222222-2-2-2-2-2-2-2-22-22-222222-22-20000220000-2-20000000000000000-2-2-2-200220000000000220000000000000000
χ4522-2-22-22-200002i−2i2i−2i020-22i−2i2i−2i0-2022i−2i2i−2i002-22-200i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000002−22−2i2−i2i2−i200000000
χ4622-2-22-22-200002i−2i2i−2i020-22i−2i2i−2i0-2022i−2i2i−2i002-22-200−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000000000−22−22−i2i2−i2i200000000
χ4722-2-22-22-200002i−2i2i−2i020-22i−2i2i−2i0-202−2i2i−2i2i00-22-2200i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000−22−22−i2i2−i2i200000000
χ4822-2-22-22-200002i−2i2i−2i020-22i−2i2i−2i0-202−2i2i−2i2i00-22-2200−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000002−22−2i2−i2i2−i200000000
χ4922-2-22-22-20000−2i2i−2i2i020-2−2i2i−2i2i0-2022i−2i2i−2i00-22-2200i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000002−22−2−i2i2−i2i200000000
χ5022-2-22-22-20000−2i2i−2i2i020-2−2i2i−2i2i0-2022i−2i2i−2i00-22-2200−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000000000−22−22i2−i2i2−i200000000
χ5122-2-22-22-20000−2i2i−2i2i020-2−2i2i−2i2i0-202−2i2i−2i2i002-22-200i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000000000−22−22i2−i2i2−i200000000
χ5222-2-22-22-20000−2i2i−2i2i020-2−2i2i−2i2i0-202−2i2i−2i2i002-22-200−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000002−22−2−i2i2−i2i200000000
χ532-22-222-2-22i2i−2i−2i2i2i−2i−2i2-2-22−2i−2i2i2i2-2-220000−2i2i0000-2200000000000000002-2−2i2i00-2200000000002i−2i0000000000000000
χ542-22-222-2-22i2i−2i−2i2i2i−2i−2i2-2-22−2i−2i2i2i2-2-220000−2i2i0000-220000000000000000-222i−2i002-20000000000−2i2i0000000000000000
χ552-22-222-2-22i2i−2i−2i−2i−2i2i2i-222-2−2i−2i2i2i-222-222-2-22i−2i−2i−2i2i2i-2200000000000000000000-2200000000002i−2i000000000000000000
χ562-22-222-2-22i2i−2i−2i−2i−2i2i2i-222-2−2i−2i2i2i-222-2-2-2222i−2i2i2i−2i−2i-22000000000000000000002-20000000000−2i2i000000000000000000
χ572-22-222-2-22i2i−2i−2i−2i−2i2i2i-2-2222i2i−2i−2i-2-2220000−2i2i00002-20000000000000000000000002-2-222i−2i−2i2i00000000000000000000
χ582-22-222-2-22i2i−2i−2i−2i−2i2i2i-2-2222i2i−2i−2i-2-2220000−2i2i00002-2000000000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ592-22-222-2-2−2i−2i2i2i2i2i−2i−2i-222-22i2i−2i−2i-222-222-2-2−2i2i2i2i−2i−2i-2200000000000000000000-220000000000−2i2i000000000000000000
χ602-22-222-2-2−2i−2i2i2i2i2i−2i−2i-222-22i2i−2i−2i-222-2-2-222−2i2i−2i−2i2i2i-22000000000000000000002-200000000002i−2i000000000000000000
χ612-22-222-2-2−2i−2i2i2i2i2i−2i−2i-2-222−2i−2i2i2i-2-22200002i−2i00002-20000000000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ622-22-222-2-2−2i−2i2i2i2i2i−2i−2i-2-222−2i−2i2i2i-2-22200002i−2i00002-2000000000000000000000000-222-22i−2i−2i2i00000000000000000000
χ632-22-222-2-2−2i−2i2i2i−2i−2i2i2i2-2-222i2i−2i−2i2-2-2200002i−2i0000-2200000000000000002-22i−2i00-220000000000−2i2i0000000000000000
χ642-22-222-2-2−2i−2i2i2i−2i−2i2i2i2-2-222i2i−2i−2i2-2-2200002i−2i0000-220000000000000000-22−2i2i002-200000000002i−2i0000000000000000
χ652-2-222-2-2200002-2-2202022-2-220-20-22i−2i−2i2i00−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−222−2−2200000000
χ662-2-222-2-2200002-2-2202022-2-220-20-22i−2i−2i2i00−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−222−200000000
χ672-2-222-2-2200002-2-2202022-2-220-20-2−2i2i2i−2i002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−222−200000000
χ682-2-222-2-2200002-2-2202022-2-220-20-2−2i2i2i−2i002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−222−2−2200000000
χ692-2-222-2-220000-222-20202-222-20-20-22i−2i−2i2i002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−222−200000000
χ702-2-222-2-220000-222-20202-222-20-20-22i−2i−2i2i002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−22−2−2200000000
χ712-2-222-2-220000-222-20202-222-20-20-2−2i2i2i−2i00−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−22−2−2200000000
χ722-2-222-2-220000-222-20202-222-20-20-2−2i2i2i−2i00−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−222−200000000
χ73444-4-4-4-444-44-400000000000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ74444-4-4-4-444-44-40000000000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ75444-4-4-4-44-44-4400000000000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ76444-4-4-4-44-44-440000000000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ7744-44-44-4-40000000040400000-40-4000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ7844-44-44-4-40000000040400000-40-40000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ7944-44-44-4-400000000-40-4000004040000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ8044-44-44-4-400000000-40-400000404000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ8144-4-44-44-400004i−4i4i−4i0-404−4i4i−4i4i040-40000000000000000000000000000000000000000000000000000000000000000
χ8244-4-44-44-40000−4i4i−4i4i0-4044i−4i4i−4i040-40000000000000000000000000000000000000000000000000000000000000000
χ834-444-4-44-44i−4i−4i4i00000000000000000000000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000000000000000
χ844-444-4-44-44i−4i−4i4i0000000000000000000000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000000000000000
χ854-444-4-44-4−4i4i4i−4i00000000000000000000000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000000000000000
χ864-444-4-44-4−4i4i4i−4i0000000000000000000000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000000000000000
χ874-4-444-4-4400004-4-440-40-4-444-404040000000000000000000000000000000000000000000000000000000000000000
χ884-4-444-4-440000-444-40-40-44-4-4404040000000000000000000000000000000000000000000000000000000000000000
χ894-4-4-4-44440000000040-400000-404000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ904-4-4-4-44440000000040-400000-4040000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ914-4-4-4-444400000000-4040000040-400000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ924-4-4-4-444400000000-4040000040-4000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000

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