Finite Group Databasebeta

← Group #108654

Character table — Group #108654

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444448888888822448888888888884444444488888888888888888888888888888888
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
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ171111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−ii−ii−i1-11-1
χ181111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1-1-111-1-111−i−iii−i−iii−ii−ii-11-11
χ191111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-11111-1-111-1-1ii−i−iii−i−i−ii−ii-11-11
χ201111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111-1-111-1-111−i−iii−i−iiii−ii−i1-11-1
χ211111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-11111-1-111-1-1−i−iii−i−iiii−ii−i-11-11
χ221111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111-1-111-1-111ii−i−iii−i−i−ii−ii1-11-1
χ231111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii1-11-1
χ241111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1-1-111-1-111ii−i−iii−i−ii−ii−i-11-11
χ251111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i-111-1ii−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-111-1i−i−ii
χ261111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i-111-1ii−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i11-1-1-1-1111-1-11−iii−i
χ271111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i-111-1ii−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii-1-11111-1-11-1-11−iii−i
χ281111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i-111-1ii−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i11-1-1-1-111-111-1i−i−ii
χ291111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii-111-1−i−iiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii11-1-1-1-111-111-1−iii−i
χ301111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii-111-1−i−iiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-1-11111-1-11-1-11i−i−ii
χ311111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii-111-1−i−iiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii11-1-1-1-1111-1-11i−i−ii
χ321111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii-111-1−i−iiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-111-1−iii−i
χ332222222222222222-2-2-2-222-2-222-2-200000000-2-2-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ342222222222222222-2-2-2-222-2-222-2-200000000-2-2-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-222-2-2220000000022-2-2000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-222-2-2220000000022-2-200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ3722222222-2-2-2-222222222-2-222-2-22222222222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ3822222222-2-2-2-222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ3922222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000002-22-22-22-200000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000-22-22-22-2200000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2222222-2-222-2-22222222222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-222-2-20000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000-2-2220000000000002-22-2-22-2200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000-2-222000000000000-22-222-22-200000000000000000000000000000000
χ452222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22200000000-22-22000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ462222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22200000000-22-2200000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ472222-2-2-2-222-2-2-2-222-2-222-2-22222-2-2000000002-2-22000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ482222-2-2-2-222-2-2-2-222-2-222-2-22222-2-2000000002-2-2200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ492222-2-2-2-2-2-22222-2-222-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ502222-2-2-2-2-2-22222-2-222-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ512222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222000000002-22-20000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ522222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222000000002-22-2000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ532222-2-2-2-2-2-222-2-22222-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ542222-2-2-2-2-2-222-2-22222-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ552222-2-2-2-2-2-222-2-222-2-2222222-2-2-2-200000000-222-20000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ562222-2-2-2-2-2-222-2-222-2-2222222-2-2-2-200000000-222-2000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ5722-2-222-2-200002i−2i2i−2i2-22-2002i−2i002i−2i22-2-222-2-2000000002i−2i002i−2i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ5822-2-222-2-200002i−2i2i−2i2-22-2002i−2i002i−2i22-2-222-2-2000000002i−2i002i−2i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ5922-2-222-2-200002i−2i2i−2i2-22-2002i−2i002i−2i-2-222-2-22200000000−2i2i00−2i2i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ6022-2-222-2-200002i−2i2i−2i2-22-2002i−2i002i−2i-2-222-2-22200000000−2i2i00−2i2i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ6122-2-222-2-20000−2i2i−2i2i2-22-200−2i2i00−2i2i22-2-222-2-200000000−2i2i00−2i2i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ6222-2-222-2-20000−2i2i−2i2i2-22-200−2i2i00−2i2i22-2-222-2-200000000−2i2i00−2i2i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ6322-2-222-2-20000−2i2i−2i2i2-22-200−2i2i00−2i2i-2-222-2-222000000002i−2i002i−2i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ6422-2-222-2-20000−2i2i−2i2i2-22-200−2i2i00−2i2i-2-222-2-222000000002i−2i002i−2i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ6522-2-2-2-22200002i−2i−2i2i2-2-22002i−2i00−2i2i2i2i−2i−2i−2i−2i2i2i00000000-22002-20000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ6622-2-2-2-22200002i−2i−2i2i2-2-22002i−2i00−2i2i2i2i−2i−2i−2i−2i2i2i00000000-22002-2000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ6722-2-2-2-22200002i−2i−2i2i2-2-22002i−2i00−2i2i−2i−2i2i2i2i2i−2i−2i000000002-200-220000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ6822-2-2-2-22200002i−2i−2i2i2-2-22002i−2i00−2i2i−2i−2i2i2i2i2i−2i−2i000000002-200-22000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ6922-2-2-2-2220000−2i2i2i−2i2-2-2200−2i2i002i−2i2i2i−2i−2i−2i−2i2i2i000000002-200-220000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ7022-2-2-2-2220000−2i2i2i−2i2-2-2200−2i2i002i−2i2i2i−2i−2i−2i−2i2i2i000000002-200-22000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ7122-2-2-2-2220000−2i2i2i−2i2-2-2200−2i2i002i−2i−2i−2i2i2i2i2i−2i−2i00000000-22002-20000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ7222-2-2-2-2220000−2i2i2i−2i2-2-2200−2i2i002i−2i−2i−2i2i2i2i2i−2i−2i00000000-22002-2000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ7344-4-444-4-400004i−4i4i−4i-44-4400−4i4i00−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ7444-4-444-4-40000−4i4i−4i4i-44-44004i−4i004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-44400004i−4i−4i4i-444-400−4i4i004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-4440000−4i4i4i−4i-444-4004i−4i00−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ774-44-44-44-40000000000004i−4i004i−4i002i2−2i22i2−2i22i2−2i22i2−2i2000000000022−220022−220000000000000000000000000000000000000000
χ784-44-44-44-40000000000004i−4i004i−4i00−2i22i2−2i22i2−2i22i2−2i22i20000000000−222200−22220000000000000000000000000000000000000000
χ794-44-44-44-4000000000000−4i4i00−4i4i002i2−2i22i2−2i22i2−2i22i2−2i20000000000−222200−22220000000000000000000000000000000000000000
χ804-44-44-44-4000000000000−4i4i00−4i4i00−2i22i2−2i22i2−2i22i2−2i22i2000000000022−220022−220000000000000000000000000000000000000000
χ814-44-4-44-440000000000004i−4i00−4i4i0022−2222−22−2222−22220000000000−2i22i2002i2−2i20000000000000000000000000000000000000000
χ824-44-4-44-440000000000004i−4i00−4i4i00−2222−222222−2222−2200000000002i2−2i200−2i22i20000000000000000000000000000000000000000
χ834-44-4-44-44000000000000−4i4i004i−4i0022−2222−22−2222−222200000000002i2−2i200−2i22i20000000000000000000000000000000000000000
χ844-44-4-44-44000000000000−4i4i004i−4i00−2222−222222−2222−220000000000−2i22i2002i2−2i20000000000000000000000000000000000000000
χ854-4-444-4-444i−4i4i−4i00000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000022−2222−22000000000000000000000000000000000000000000000000
χ864-4-444-4-444i−4i4i−4i0000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000−2222−2222000000000000000000000000000000000000000000000000
χ874-4-444-4-44−4i4i−4i4i00000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000−2222−2222000000000000000000000000000000000000000000000000
χ884-4-444-4-44−4i4i−4i4i0000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000022−2222−22000000000000000000000000000000000000000000000000
χ894-4-44-444-44i−4i−4i4i000000000000000022−22−2222−222222−220000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ904-4-44-444-44i−4i−4i4i0000000000000000−222222−2222−22−222200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ914-4-44-444-4−4i4i4i−4i000000000000000022−22−2222−222222−2200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ924-4-44-444-4−4i4i4i−4i0000000000000000−222222−2222−22−22220000−2i22i22i2−2i2000000000000000000000000000000000000000000000000

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