Finite Group Databasebeta

← Group #186571

Character table — Group #186571

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444222244444444444444442224444444444444444444444444222444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-111-1-111-1-1-1-11111111111111111-111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-11-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-111-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-111-11-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ171111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-11-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-11-11-111-1-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ181111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-11-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1-11-11-1-111-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ191111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-11-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-11-11-111-1-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ201111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-11-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1-11-11-1-111-1-111−i−iii−i−iiii−ii−ii−ii−i
χ211111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11-11-111-11-1-1-111-1-111−i−iii−i−iii−ii−iii−ii−i
χ221111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-11-11-1111-1-111-1-1−i−iii−i−iiii−ii−i−ii−ii
χ231111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11-11-111-11-1-1-111-1-111ii−i−iii−i−ii−ii−i−ii−ii
χ241111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-11-11-1111-1-111-1-1ii−i−iii−i−i−ii−iii−ii−i
χ251111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-11-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1111-1-11-11-1-1111-1-1-1-111ii−i−i−i−iiii−i−iii−i−ii
χ261111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-11-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-11111-1-111-1-1-11111-1-1ii−i−i−i−iii−iii−i−iii−i
χ271111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-11-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1111-1-11-11-1-1111-1-1-1-111−i−iiiii−i−i−iii−i−iii−i
χ281111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-11-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-11111-1-111-1-1-11111-1-1−i−iiiii−i−ii−i−iii−i−ii
χ291111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1111-1111-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-1-1-111-1-11-1-11111-1-1−i−iiiii−i−i−iii−ii−i−ii
χ301111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1111-1111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-111-11-111-111-1-1-1-111−i−iiiii−i−ii−i−ii−iii−i
χ311111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1111-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1-111-1-11-1-11111-1-1ii−i−i−i−iiii−i−ii−iii−i
χ321111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1111-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111-11-111-111-1-1-1-111ii−i−i−i−iii−iii−ii−i−ii
χ332222222222222222-2-2-2-2-2-2-2-2-2-2-2-2002200-2-2000000000000000000000000000000002-22-22-22-20000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2002200-2-200000000000000000000000000000000-22-22-22-220000000000000000
χ352222222222-2-2-2-22222-2-2222222-2-200-2-200-2-20000000000000000000002202200-2-2-2-2000000000000000000000000
χ362222222222-2-2-2-22222-2-2222222-2-200-2-200-2-2000000000000000000000-2-20-2-2002222000000000000000000000000
χ372222222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-22222-2-2-2-20000000000000000200200-2-20000000000000000000000000000
χ382222222222-2-2-2-222-2-222-2-2-2-2-2-222-2-2-2-2-2-22222220000000000000000-200-200220000000000000000000000000000
χ3922222222-2-22222-2-222-2-2-2-2-2-222-2-200-2-200220000000000000000000002-202-200-2-222000000000000000000000000
χ4022222222-2-22222-2-222-2-2-2-2-2-222-2-200-2-20022000000000000000000000-220-220022-2-2000000000000000000000000
χ4122222222-2-22222-2-2-2-2222222-2-22222-2-222-2-222220000000000000000-200-200-2-20000000000000000000000000000
χ4222222222-2-22222-2-2-2-2222222-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000200200220000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200220022000000000000000000000000000000002-22-2-22-220000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20022002200000000000000000000000000000000-22-222-22-20000000000000000
χ452222-2-2-2-22222-2-2-2-222-2-222-2-2-2-222002-200-220000000000000000000002-20-2200-22-22000000000000000000000000
χ462222-2-2-2-22222-2-2-2-222-2-222-2-2-2-222002-200-22000000000000000000000-2202-2002-22-2000000000000000000000000
χ472222-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2222-2-2-22-2-2-2220000000000000000200-200-220000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2-2-22-2222-222-2-20000000000000000-2002002-20000000000000000000000000000
χ492222-2-2-2-222-2-222-2-2-2-2-2-2-2-222222200-2200-22000000000000000000000000000000002-2-222-2-220000000000000000
χ502222-2-2-2-222-2-222-2-2-2-2-2-2-2-222222200-2200-2200000000000000000000000000000000-222-2-222-20000000000000000
χ512222-2-2-2-2-2-222-2-222-2-2-2-222-2-2222200-22002-2000000000000000000000000000000002-2-22-222-20000000000000000
χ522222-2-2-2-2-2-222-2-222-2-2-2-222-2-2222200-22002-200000000000000000000000000000000-222-22-2-220000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222002-2002-2000000000000000000000220-2-200-222-2000000000000000000000000
χ542222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222002-2002-2000000000000000000000-2-2022002-2-22000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2222-2-2-2-2222-2-20000000000000000-200200-220000000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2-2-22-222-22-2-2220000000000000000200-2002-20000000000000000000000000000
χ572-22-22i−2i2i−2i002-22i−2i00002-22i−2i2-2002i−2i2-2002i−2i002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ582-22-22i−2i2i−2i002-22i−2i00002-22i−2i2-2002i−2i2-2002i−2i002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ592-22-22i−2i2i−2i002-22i−2i00002-22i−2i2-2002i−2i-2200−2i2i00−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ602-22-22i−2i2i−2i002-22i−2i00002-22i−2i2-2002i−2i-2200−2i2i00−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ612-22-22i−2i2i−2i00-22−2i2i00002-2−2i2i-22002i−2i2-2002i−2i00−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ622-22-22i−2i2i−2i00-22−2i2i00002-2−2i2i-22002i−2i2-2002i−2i00−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ632-22-22i−2i2i−2i00-22−2i2i00002-2−2i2i-22002i−2i-2200−2i2i002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ642-22-22i−2i2i−2i00-22−2i2i00002-2−2i2i-22002i−2i-2200−2i2i002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ652-22-2−2i2i−2i2i002-2−2i2i00002-2−2i2i2-200−2i2i2-200−2i2i00−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ662-22-2−2i2i−2i2i002-2−2i2i00002-2−2i2i2-200−2i2i2-200−2i2i00−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ672-22-2−2i2i−2i2i002-2−2i2i00002-2−2i2i2-200−2i2i-22002i−2i002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ682-22-2−2i2i−2i2i002-2−2i2i00002-2−2i2i2-200−2i2i-22002i−2i002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ692-22-2−2i2i−2i2i00-222i−2i00002-22i−2i-2200−2i2i2-200−2i2i002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ702-22-2−2i2i−2i2i00-222i−2i00002-22i−2i-2200−2i2i2-200−2i2i002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ712-22-2−2i2i−2i2i00-222i−2i00002-22i−2i-2200−2i2i-22002i−2i00−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ722-22-2−2i2i−2i2i00-222i−2i00002-22i−2i-2200−2i2i-22002i−2i00−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ7344-4-444-4-44-400004-40000000000000000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ7444-4-444-4-44-400004-4000000000000000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ7544-4-444-4-4-440000-440000000000000000000000002-22-22-22-2-22-22-22-22000000000000000000000000000000000000
χ7644-4-444-4-4-440000-44000000000000000000000000-22-22-22-222-22-22-22-2000000000000000000000000000000000000
χ7744-4-4-4-4444-40000-440000000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ7844-4-4-4-4444-40000-44000000000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ7944-4-4-4-444-4400004-40000000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ8044-4-4-4-444-4400004-4000000000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ814-44-44i−4i4i−4i004-44i−4i0000-44−4i4i-4400−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ824-44-44i−4i4i−4i00-44−4i4i0000-444i−4i4-400−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i004-4−4i4i0000-444i−4i-44004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i00-444i−4i0000-44−4i4i4-4004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ854-4-444i−4i−4i4i000000004-40000004i−4i00000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000
χ864-4-444i−4i−4i4i000000004-40000004i−4i0000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000
χ874-4-444i−4i−4i4i00000000-44000000−4i4i000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000000000
χ884-4-444i−4i−4i4i00000000-44000000−4i4i00000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i000000004-4000000−4i4i00000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i000000004-4000000−4i4i0000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i00000000-440000004i−4i000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i00000000-440000004i−4i00000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000000000

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