Finite Group Databasebeta

← Group #141120

Character table — Group #141120

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order1222222244444488888888888824444444448888888888444444448888888816161616161616162444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ14111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ15111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ16111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ19222222-2-22222-2-22222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ20222222-2-22222-2-2-2-2-2-222222222-2-22222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000
χ212222-2-2222-22-222222222220000-2-200000000000000-2-2-2-200000000000000002−22−22−22−20000
χ222222-2-2222-22-222222222220000-2-200000000000000-2-2-2-20000000000000000−22−22−22−220000
χ232222-2-2222-22-222-2-2-2-2-2-2-2-20000-2-200000000000000222200000000000000002−22−2−22−220000
χ242222-2-2222-22-222-2-2-2-2-2-2-2-20000-2-20000000000000022220000000000000000−22−222−22−20000
χ252222-2-222-22-22-2-2000000002222-220000000022-2-2-2-2000022-2-222-2-200000000000000000000
χ262222-2-222-22-22-2-2000000002222-220000000022-2-2-2-20000-2-222-2-22200000000000000000000
χ272222-2-222-22-22-2-200000000-2-2-2-2-2200000000-2-222220000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ282222-2-222-22-22-2-200000000-2-2-2-2-2200000000-2-22222000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ292222-2-2-2-22-22-2-2-22222-2-2-2-200002200000000000000-2-2220000000000000000i2−i2−i2i2i2−i2−i2i20000
χ302222-2-2-2-22-22-2-2-22222-2-2-2-200002200000000000000-2-2220000000000000000−i2i2i2−i2−i2i2i2−i20000
χ312222-2-2-2-22-22-2-2-2-2-2-2-222220000220000000000000022-2-20000000000000000i2−i2−i2i2−i2i2i2−i20000
χ322222-2-2-2-22-22-2-2-2-2-2-2-222220000220000000000000022-2-20000000000000000−i2i2i2−i2i2−i2−i2i20000
χ332222-2-2-2-2-22-22220000000022222-200000000-2-222-2-200000000000022-2-2-2-222000000000000
χ342222-2-2-2-2-22-22220000000022222-200000000-2-222-2-2000000000000-2-22222-2-2000000000000
χ352222-2-2-2-2-22-222200000000-2-2-2-22-20000000022-2-22200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ362222-2-2-2-2-22-222200000000-2-2-2-22-20000000022-2-2220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ372-2-222-200-222-200000022-2-22i2i−2i−2i002i2i−2i−2i000000002i−2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ382-2-222-200-222-200000022-2-22i2i−2i−2i002i2i−2i−2i000000002i−2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ392-2-222-200-222-200000022-2-2−2i−2i2i2i00−2i−2i2i2i00000000−2i2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ402-2-222-200-222-200000022-2-2−2i−2i2i2i00−2i−2i2i2i00000000−2i2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ412-2-222-200-222-2000000-2-2222i2i−2i−2i00−2i−2i2i2i000000002i−2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ422-2-222-200-222-2000000-2-2222i2i−2i−2i00−2i−2i2i2i000000002i−2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ432-2-222-200-222-2000000-2-222−2i−2i2i2i002i2i−2i−2i00000000−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ442-2-222-200-222-2000000-2-222−2i−2i2i2i002i2i−2i−2i00000000−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ452-2-22-220022-2-2002i2i−2i−2i00002i2i−2i−2i00000022-2-20000−2i2i2i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ462-2-22-220022-2-2002i2i−2i−2i00002i2i−2i−2i00000022-2-20000−2i2i2i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ472-2-22-220022-2-2002i2i−2i−2i0000−2i−2i2i2i000000-2-22200002i−2i2i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ482-2-22-220022-2-2002i2i−2i−2i0000−2i−2i2i2i000000-2-22200002i−2i2i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ492-2-22-220022-2-200−2i−2i2i2i00002i2i−2i−2i000000-2-2220000−2i2i−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ502-2-22-220022-2-200−2i−2i2i2i00002i2i−2i−2i000000-2-2220000−2i2i−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ512-2-22-220022-2-200−2i−2i2i2i0000−2i−2i2i2i00000022-2-200002i−2i−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ522-2-22-220022-2-200−2i−2i2i2i0000−2i−2i2i2i00000022-2-200002i−2i−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ5344444444-4-4-4-4-4-40000000000004-40000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-444000000000000-440000000000000000000000000000000000000000000000
χ5544-4-4000000004i−4i22−2222−222i2−2i22i2−2i22i2−2i22i2−2i2002-22-22i−2i2i−2i0022−220000000000000000000000000000000000
χ5644-4-4000000004i−4i22−2222−222i2−2i22i2−2i2−2i22i2−2i22i200-22-22−2i2i−2i2i00−22220000000000000000000000000000000000
χ5744-4-4000000004i−4i−2222−2222−2i22i2−2i22i22i2−2i22i2−2i200-22-22−2i2i−2i2i0022−220000000000000000000000000000000000
χ5844-4-4000000004i−4i−2222−2222−2i22i2−2i22i2−2i22i2−2i22i2002-22-22i−2i2i−2i00−22220000000000000000000000000000000000
χ5944-4-400000000−4i4i22−2222−22−2i22i2−2i22i22i2−2i22i2−2i200-22-222i−2i2i−2i00−22220000000000000000000000000000000000
χ6044-4-400000000−4i4i22−2222−22−2i22i2−2i22i2−2i22i2−2i22i2002-22-2−2i2i−2i2i0022−220000000000000000000000000000000000
χ6144-4-400000000−4i4i−2222−22222i2−2i22i2−2i22i2−2i22i2−2i2002-22-2−2i2i−2i2i00−22220000000000000000000000000000000000
χ6244-4-400000000−4i4i−2222−22222i2−2i22i2−2i2−2i22i2−2i22i200-22-222i−2i2i−2i0022−220000000000000000000000000000000000
χ634-44-4004-40000002i2−2i2−2i22i22i2−2i2−2i22i222−22−222200−2i2i2i−2i−2i2i2i−2i22−22000000000000000000000000000000000000
χ644-44-4004-40000002i2−2i2−2i22i22i2−2i2−2i22i2−222222−22002i−2i−2i2i2i−2i−2i2i−2222000000000000000000000000000000000000
χ654-44-4004-4000000−2i22i22i2−2i2−2i22i22i2−2i222−22−2222002i−2i−2i2i2i−2i−2i2i22−22000000000000000000000000000000000000
χ664-44-4004-4000000−2i22i22i2−2i2−2i22i22i2−2i2−222222−2200−2i2i2i−2i−2i2i2i−2i−2222000000000000000000000000000000000000
χ674-44-400-440000002i2−2i2−2i22i2−2i22i22i2−2i222−22−2222002i−2i−2i2i−2i2i2i−2i−2222000000000000000000000000000000000000
χ684-44-400-440000002i2−2i2−2i22i2−2i22i22i2−2i2−222222−2200−2i2i2i−2i2i−2i−2i2i22−22000000000000000000000000000000000000
χ694-44-400-44000000−2i22i22i2−2i22i2−2i2−2i22i222−22−222200−2i2i2i−2i2i−2i−2i2i−2222000000000000000000000000000000000000
χ704-44-400-44000000−2i22i22i2−2i22i2−2i2−2i22i2−222222−22002i−2i−2i2i−2i2i2i−2i22−22000000000000000000000000000000000000
χ714-4-444-4004-4-44004i4i−4i−4i000000000000000000000000−4i4i000000000000000000000000000000
χ724-4-444-4004-4-4400−4i−4i4i4i0000000000000000000000004i−4i000000000000000000000000000000
χ734-4-44-4400-4-44400000044-4-40000000000000000000000-440000000000000000000000000000
χ744-4-44-4400-4-444000000-4-44400000000000000000000004-40000000000000000000000000000

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