Finite Group Databasebeta

← Group #483085

Character table — Group #483085

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222224444444488888888888888881616161611112222222222222244444444888888888888888816161616
order122244444444448888248888888888888816161616161616164444222244444444448888248888888888888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91111-1-1-1-11111-1-1-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i1-11-11111-1-1-1-11111-1-1-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111-1-1-1-11111-1-1-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-111111-1-1-1-11111-1-1-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111-1-1-1-11111-1-1-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-111111-1-1-1-11111-1-1-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111-1-1-1-11111-1-1-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii1-11-11111-1-1-1-11111-1-1-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-111111-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-11
χ141111-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-111-1-11111-1-1-111-11111-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-111-1-11111-1-1-111-1
χ151111-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111-1-111-1-1-1-111-111-11111-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111-1-111-1-1-1-111-111-1
χ161111-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111111-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-11
χ1722222222222222-2-2-2-222-2-2-2-2-2-20000000000000000000022222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000
χ1822222222-2-222-2-22222-2-2-2-2-2-2220000000000000000000022222222-2-222-2-22222-2-2-2-2-2-22200000000000000000000
χ19222222-2-222-2-2-2-20000-2200000000000000i2−i2i2−i2i2−i2i2−i20000222222-2-222-2-2-2-20000-2200000000000000i2−i2i2−i2i2−i2i2−i20000
χ20222222-2-222-2-2-2-20000-2200000000000000−i2i2−i2i2−i2i2−i2i20000222222-2-222-2-2-2-20000-2200000000000000−i2i2−i2i2−i2i2−i2i20000
χ21222222-2-2-2-2-2-22200002-2000000000000002−22−2−22−220000222222-2-2-2-2-2-22200002-2000000000000002−22−2−22−220000
χ22222222-2-2-2-2-2-22200002-200000000000000−22−222−22−20000222222-2-2-2-2-2-22200002-200000000000000−22−222−22−20000
χ232222-2-22222-2-2220000-2-2000000000000002−2−222−2−2200002222-2-22222-2-2220000-2-2000000000000002−2−222−2−220000
χ242222-2-22222-2-2220000-2-200000000000000−222−2−222−200002222-2-22222-2-2220000-2-200000000000000−222−2−222−20000
χ252222-2-222-2-2-2-2-2-200002200000000000000i2−i2−i2i2−i2i2i2−i200002222-2-222-2-2-2-2-2-200002200000000000000i2−i2−i2i2−i2i2i2−i20000
χ262222-2-222-2-2-2-2-2-200002200000000000000−i2i2i2−i2i2−i2−i2i200002222-2-222-2-2-2-2-2-200002200000000000000−i2i2i2−i2i2−i2−i2i20000
χ272222-2-2-2-22222-2-222222-2-2-222-2-2000000000000000000002222-2-2-2-22222-2-222222-2-2-222-2-200000000000000000000
χ282222-2-2-2-2-2-22222-2-2-2-2-22-2-22222000000000000000000002222-2-2-2-2-2-22222-2-2-2-2-22-2-2222200000000000000000000
χ292-22-22i−2i2i−2i002-20022-2-20000002i−2ii2−i22−22−2i2−i20000000000002-22-22i−2i2i−2i002-20022-2-20000002i−2ii2−i22−22−2i2−i2000000000000
χ302-22-22i−2i2i−2i002-20022-2-20000002i−2i−i2i2−22−22−i2i20000000000002-22-22i−2i2i−2i002-20022-2-20000002i−2i−i2i2−22−22−i2i2000000000000
χ312-22-22i−2i2i−2i002-200-2-222000000−2i2i2−2−i2i2i2−i2−220000000000002-22-22i−2i2i−2i002-200-2-222000000−2i2i2−2−i2i2i2−i2−22000000000000
χ322-22-22i−2i2i−2i002-200-2-222000000−2i2i−22i2−i2−i2i22−20000000000002-22-22i−2i2i−2i002-200-2-222000000−2i2i−22i2−i2−i2i22−2000000000000
χ332-22-2−2i2i−2i2i002-20022-2-2000000−2i2ii2−i2−22−22i2−i20000000000002-22-2−2i2i−2i2i002-20022-2-2000000−2i2ii2−i2−22−22i2−i2000000000000
χ342-22-2−2i2i−2i2i002-20022-2-2000000−2i2i−i2i22−22−2−i2i20000000000002-22-2−2i2i−2i2i002-20022-2-2000000−2i2i−i2i22−22−2−i2i2000000000000
χ352-22-2−2i2i−2i2i002-200-2-2220000002i−2i2−2i2−i2−i2i2−220000000000002-22-2−2i2i−2i2i002-200-2-2220000002i−2i2−2i2−i2−i2i2−22000000000000
χ362-22-2−2i2i−2i2i002-200-2-2220000002i−2i−22−i2i2i2−i22−20000000000002-22-2−2i2i−2i2i002-200-2-2220000002i−2i−22−i2i2i2−i22−2000000000000
χ3744-4-4000000004-422−2222−220022−2200000000000000000000000044-4-4000000004-422−2222−220022−22000000000000000000000000
χ3844-4-4000000004-4−2222−222200−222200000000000000000000000044-4-4000000004-4−2222−222200−2222000000000000000000000000
χ3944-4-400000000-4422−2222−2200−222200000000000000000000000044-4-400000000-4422−2222−2200−2222000000000000000000000000
χ4044-4-400000000-44−2222−22220022−2200000000000000000000000044-4-400000000-44−2222−22220022−22000000000000000000000000
χ414-44-44i−4i−4i4i00-4400000000000000000000000000000000004-44-44i−4i−4i4i00-440000000000000000000000000000000000
χ424-44-4−4i4i4i−4i00-4400000000000000000000000000000000004-44-4−4i4i4i−4i00-440000000000000000000000000000000000
χ434-4-4400004i−4i000022−22−222200002i2−2i200000000000000000000004-4-4400004i−4i000022−22−222200002i2−2i20000000000000000000000
χ444-4-4400004i−4i0000−222222−220000−2i22i200000000000000000000004-4-4400004i−4i0000−222222−220000−2i22i20000000000000000000000
χ454-4-440000−4i4i000022−22−22220000−2i22i200000000000000000000004-4-440000−4i4i000022−22−22220000−2i22i20000000000000000000000
χ464-4-440000−4i4i0000−222222−2200002i2−2i200000000000000000000004-4-440000−4i4i0000−222222−2200002i2−2i20000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ481111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4911111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ5111111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111
χ5211111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ5311111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1
χ5411111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111
χ551111-1-1-1-11111-1-1-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i1-11-1-1-1-1-11111-1-1-1-1111111-11-1-111-1-1−i−iii−i−iii−i−iii−i−iii-11-11
χ561111-1-1-1-11111-1-1-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-11-1-1-1-11111-1-1-1-1111111-11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i1-11-1
χ571111-1-1-1-11111-1-1-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-11-1-1-1-11111-1-1-1-1111111-11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii1-11-1
χ581111-1-1-1-11111-1-1-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii1-11-1-1-1-1-11111-1-1-1-1111111-11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-11-11
χ591111-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-11111-1-1-111-1
χ601111-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-111-1-11111-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-111-1-1-1-1111-1-11
χ611111-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111-1-111-1-1-1-111-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-111-1-11111-1-11-1-11
χ621111-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-11111-1-1-1-111-111-1
χ6322222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222222200000000000000000000
χ6422222222-2-222-2-22222-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-2-2-222-2-222-2-2-2-2222222-2-200000000000000000000
χ65222222-2-222-2-2-2-20000-2200000000000000i2−i2i2−i2i2−i2i2−i20000-2-2-2-2-2-222-2-2222200002-200000000000000−i2i2−i2i2−i2i2−i2i20000
χ66222222-2-222-2-2-2-20000-2200000000000000−i2i2−i2i2−i2i2−i2i20000-2-2-2-2-2-222-2-2222200002-200000000000000i2−i2i2−i2i2−i2i2−i20000
χ67222222-2-2-2-2-2-22200002-2000000000000002−22−2−22−220000-2-2-2-2-2-2222222-2-20000-2200000000000000−22−222−22−20000
χ68222222-2-2-2-2-2-22200002-200000000000000−22−222−22−20000-2-2-2-2-2-2222222-2-20000-22000000000000002−22−2−22−220000
χ692222-2-22222-2-2220000-2-2000000000000002−2−222−2−220000-2-2-2-222-2-2-2-222-2-200002200000000000000−222−2−222−20000
χ702222-2-22222-2-2220000-2-200000000000000−222−2−222−20000-2-2-2-222-2-2-2-222-2-2000022000000000000002−2−222−2−220000
χ712222-2-222-2-2-2-2-2-200002200000000000000i2−i2−i2i2−i2i2i2−i20000-2-2-2-222-2-22222220000-2-200000000000000−i2i2i2−i2i2−i2−i2i20000
χ722222-2-222-2-2-2-2-2-200002200000000000000−i2i2i2−i2i2−i2−i2i20000-2-2-2-222-2-22222220000-2-200000000000000i2−i2−i2i2−i2i2i2−i20000
χ732222-2-2-2-22222-2-222222-2-2-222-2-200000000000000000000-2-2-2-22222-2-2-2-222-2-2-2-2-2222-2-22200000000000000000000
χ742222-2-2-2-2-2-22222-2-2-2-2-22-2-2222200000000000000000000-2-2-2-2222222-2-2-2-222222-222-2-2-2-200000000000000000000
χ752-22-22i−2i2i−2i002-20022-2-20000002i−2ii2−i22−22−2i2−i2000000000000-22-22−2i2i−2i2i00-2200-2-222000000−2i2i−i2i2−22−22−i2i2000000000000
χ762-22-22i−2i2i−2i002-20022-2-20000002i−2i−i2i2−22−22−i2i2000000000000-22-22−2i2i−2i2i00-2200-2-222000000−2i2ii2−i22−22−2i2−i2000000000000
χ772-22-22i−2i2i−2i002-200-2-222000000−2i2i2−2−i2i2i2−i2−22000000000000-22-22−2i2i−2i2i00-220022-2-20000002i−2i−22i2−i2−i2i22−2000000000000
χ782-22-22i−2i2i−2i002-200-2-222000000−2i2i−22i2−i2−i2i22−2000000000000-22-22−2i2i−2i2i00-220022-2-20000002i−2i2−2−i2i2i2−i2−22000000000000
χ792-22-2−2i2i−2i2i002-20022-2-2000000−2i2ii2−i2−22−22i2−i2000000000000-22-222i−2i2i−2i00-2200-2-2220000002i−2i−i2i22−22−2−i2i2000000000000
χ802-22-2−2i2i−2i2i002-20022-2-2000000−2i2i−i2i22−22−2−i2i2000000000000-22-222i−2i2i−2i00-2200-2-2220000002i−2ii2−i2−22−22i2−i2000000000000
χ812-22-2−2i2i−2i2i002-200-2-2220000002i−2i2−2i2−i2−i2i2−22000000000000-22-222i−2i2i−2i00-220022-2-2000000−2i2i−22−i2i2i2−i22−2000000000000
χ822-22-2−2i2i−2i2i002-200-2-2220000002i−2i−22−i2i2i2−i22−2000000000000-22-222i−2i2i−2i00-220022-2-2000000−2i2i2−2i2−i2−i2i2−22000000000000
χ8344-4-4000000004-422−2222−220022−22000000000000000000000000-4-44400000000-44−2222−222200−2222000000000000000000000000
χ8444-4-4000000004-4−2222−222200−2222000000000000000000000000-4-44400000000-4422−2222−220022−22000000000000000000000000
χ8544-4-400000000-4422−2222−2200−2222000000000000000000000000-4-444000000004-4−2222−22220022−22000000000000000000000000
χ8644-4-400000000-44−2222−22220022−22000000000000000000000000-4-444000000004-422−2222−2200−2222000000000000000000000000
χ874-44-44i−4i−4i4i00-440000000000000000000000000000000000-44-44−4i4i4i−4i004-40000000000000000000000000000000000
χ884-44-4−4i4i4i−4i00-440000000000000000000000000000000000-44-444i−4i−4i4i004-40000000000000000000000000000000000
χ894-4-4400004i−4i000022−22−222200002i2−2i20000000000000000000000-444-40000−4i4i0000−222222−220000−2i22i20000000000000000000000
χ904-4-4400004i−4i0000−222222−220000−2i22i20000000000000000000000-444-40000−4i4i000022−22−222200002i2−2i20000000000000000000000
χ914-4-440000−4i4i000022−22−22220000−2i22i20000000000000000000000-444-400004i−4i0000−222222−2200002i2−2i20000000000000000000000
χ924-4-440000−4i4i0000−222222−2200002i2−2i20000000000000000000000-444-400004i−4i000022−22−22220000−2i22i20000000000000000000000

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