Finite Group Databasebeta

← Group #481464

Character table — Group #481464

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222224444444488888888888888881616161611112222222222222244444444888888888888888816161616
order122222222244448888448888884444444416161616161616162444222222222244448888448888884444444416161616161616162444
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
χ5111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11
χ6111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1
χ7111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ8111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11
χ91111-1-111-1-11-1-11-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i11-1-11111-1-111-1-11-1-11-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i11-1-1
χ101111-1-111-1-11-1-11-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-1111111-1-111-1-11-1-11-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-111
χ111111-1-111-1-11-1-11-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-1111111-1-111-1-11-1-11-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-111
χ121111-1-111-1-11-1-11-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii11-1-11111-1-111-1-11-1-11-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii11-1-1
χ131111-1-1-1-1111-1-111111-1111-1-1-1-111-1-1-1-11111-1-1-1-1111-11-11111-1-1-1-1111-1-111111-1111-1-1-1-111-1-1-1-11111-1-1-1-1111-11-1
χ141111-1-1-1-1111-1-111111-1111-1-1-1-111-1-1-1-111-1-11111-1-1-11-111111-1-1-1-1111-1-111111-1111-1-1-1-111-1-1-1-111-1-11111-1-1-11-11
χ151111-1-1-1-1111-1-111111-1111-1-1-1-1-1-11111-1-111-1-1-1-111-11-111111-1-1-1-1111-1-111111-1111-1-1-1-1-1-11111-1-111-1-1-1-111-11-11
χ161111-1-1-1-1111-1-111111-1111-1-1-1-1-1-11111-1-1-1-11111-1-11-11-11111-1-1-1-1111-1-111111-1111-1-1-1-1-1-11111-1-1-1-11111-1-11-11-1
χ1722222222222222-2-2-2-222-2-2-2-2-2-20000000000000000000022222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000
χ182222222222-2-2-2-20000-2-2000000000000002−22−22−22−200002222222222-2-2-2-20000-2-2000000000000002−22−22−22−20000
χ192222222222-2-2-2-20000-2-200000000000000−22−22−22−2200002222222222-2-2-2-20000-2-200000000000000−22−22−22−220000
χ20222222-2-2-2-222222222-2-2-2-2-2-22200000000000000000000222222-2-2-2-222222222-2-2-2-2-2-22200000000000000000000
χ21222222-2-2-2-2-2-2-2-200002200000000000000i2−i2i2−i2−i2i2−i2i20000222222-2-2-2-2-2-2-2-200002200000000000000i2−i2i2−i2−i2i2−i2i20000
χ22222222-2-2-2-2-2-2-2-200002200000000000000−i2i2−i2i2i2−i2i2−i20000222222-2-2-2-2-2-2-2-200002200000000000000−i2i2−i2i2i2−i2i2−i20000
χ232222-2-222-2-22-2-2222222-2-2-222-2-2000000000000000000002222-2-222-2-22-2-2222222-2-2-222-2-200000000000000000000
χ242222-2-222-2-2-222-20000-2200000000000000i2−i2−i2i2i2−i2−i2i200002222-2-222-2-2-222-20000-2200000000000000i2−i2−i2i2i2−i2−i2i20000
χ252222-2-222-2-2-222-20000-2200000000000000−i2i2i2−i2−i2i2i2−i200002222-2-222-2-2-222-20000-2200000000000000−i2i2i2−i2−i2i2i2−i20000
χ262222-2-2-2-2222-2-22-2-2-2-2-22-2-22222000000000000000000002222-2-2-2-2222-2-22-2-2-2-2-22-2-2222200000000000000000000
χ272222-2-2-2-222-222-200002-2000000000000002−2−22−222−200002222-2-2-2-222-222-200002-2000000000000002−2−22−222−20000
χ282222-2-2-2-222-222-200002-200000000000000−222−22−2−2200002222-2-2-2-222-222-200002-200000000000000−222−22−2−220000
χ292-2-222-2000022-2-22i2i−2i−2i0000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000002-2-222-2000022-2-22i2i−2i−2i0000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ302-2-222-2000022-2-22i2i−2i−2i0000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000002-2-222-2000022-2-22i2i−2i−2i0000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ312-2-222-2000022-2-2−2i−2i2i2i000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000002-2-222-2000022-2-2−2i−2i2i2i000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ322-2-222-2000022-2-2−2i−2i2i2i000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000002-2-222-2000022-2-2−2i−2i2i2i000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ332-2-22-2200002-22-22i2i−2i−2i000000−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000002-2-22-2200002-22-22i2i−2i−2i000000−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ342-2-22-2200002-22-22i2i−2i−2i000000−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000002-2-22-2200002-22-22i2i−2i−2i000000−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ352-2-22-2200002-22-2−2i−2i2i2i0000002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000002-2-22-2200002-22-2−2i−2i2i2i0000002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ362-2-22-2200002-22-2−2i−2i2i2i0000002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000002-2-22-2200002-22-2−2i−2i2i2i0000002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ3744-4-400004-4000022−2222−220022−2200000000000000000000000044-4-400004-4000022−2222−220022−22000000000000000000000000
χ3844-4-400004-40000−2222−222200−222200000000000000000000000044-4-400004-40000−2222−222200−2222000000000000000000000000
χ3944-4-40000-44000022−2222−2200−222200000000000000000000000044-4-40000-44000022−2222−2200−2222000000000000000000000000
χ4044-4-40000-440000−2222−22220022−2200000000000000000000000044-4-40000-440000−2222−22220022−22000000000000000000000000
χ414-44-4004-40000002i2−2i2−2i22i200002i2−2i200000000000000000000004-44-4004-40000002i2−2i2−2i22i200002i2−2i20000000000000000000000
χ424-44-4004-4000000−2i22i22i2−2i20000−2i22i200000000000000000000004-44-4004-4000000−2i22i22i2−2i20000−2i22i20000000000000000000000
χ434-44-400-440000002i2−2i2−2i22i20000−2i22i200000000000000000000004-44-400-440000002i2−2i2−2i22i20000−2i22i20000000000000000000000
χ444-44-400-44000000−2i22i22i2−2i200002i2−2i200000000000000000000004-44-400-44000000−2i22i22i2−2i200002i2−2i20000000000000000000000
χ454-4-444-40000-4-444000000000000000000000000000000004-4-444-40000-4-44400000000000000000000000000000000
χ464-4-44-440000-44-44000000000000000000000000000000004-4-44-440000-44-4400000000000000000000000000000000
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
χ51111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-111-1
χ52111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ53111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11
χ54111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-111-1
χ551111-1-111-1-11-1-11-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i11-1-1-1-1-1-111-1-111-111-11111-11-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-111
χ561111-1-111-1-11-1-11-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-1-1-111-1-111-111-11111-11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i11-1-1
χ571111-1-111-1-11-1-11-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-1-1-111-1-111-111-11111-11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii11-1-1
χ581111-1-111-1-11-1-11-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii11-1-1-1-1-1-111-1-111-111-11111-11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-111
χ591111-1-1-1-1111-1-111111-1111-1-1-1-111-1-1-1-11111-1-1-1-1111-11-1-1-1-1-11111-1-1-111-1-1-1-1-11-1-1-11111-1-11111-1-1-1-11111-1-1-11-11
χ601111-1-1-1-1111-1-111111-1111-1-1-1-111-1-1-1-111-1-11111-1-1-11-11-1-1-1-11111-1-1-111-1-1-1-1-11-1-1-11111-1-11111-1-111-1-1-1-1111-11-1
χ611111-1-1-1-1111-1-111111-1111-1-1-1-1-1-11111-1-111-1-1-1-111-11-11-1-1-1-11111-1-1-111-1-1-1-1-11-1-1-1111111-1-1-1-111-1-11111-1-11-11-1
χ621111-1-1-1-1111-1-111111-1111-1-1-1-1-1-11111-1-1-1-11111-1-11-11-1-1-1-1-11111-1-1-111-1-1-1-1-11-1-1-1111111-1-1-1-11111-1-1-1-111-11-11
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
χ642222222222-2-2-2-20000-2-2000000000000002−22−22−22−20000-2-2-2-2-2-2-2-2-2-2222200002200000000000000−22−22−22−220000
χ652222222222-2-2-2-20000-2-200000000000000−22−22−22−220000-2-2-2-2-2-2-2-2-2-22222000022000000000000002−22−22−22−20000
χ66222222-2-2-2-222222222-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-200000000000000000000
χ67222222-2-2-2-2-2-2-2-200002200000000000000i2−i2i2−i2−i2i2−i2i20000-2-2-2-2-2-2222222220000-2-200000000000000−i2i2−i2i2i2−i2i2−i20000
χ68222222-2-2-2-2-2-2-2-200002200000000000000−i2i2−i2i2i2−i2i2−i20000-2-2-2-2-2-2222222220000-2-200000000000000i2−i2i2−i2−i2i2−i2i20000
χ692222-2-222-2-22-2-2222222-2-2-222-2-200000000000000000000-2-2-2-222-2-222-222-2-2-2-2-2-2222-2-22200000000000000000000
χ702222-2-222-2-2-222-20000-2200000000000000i2−i2−i2i2i2−i2−i2i20000-2-2-2-222-2-2222-2-2200002-200000000000000−i2i2i2−i2−i2i2i2−i20000
χ712222-2-222-2-2-222-20000-2200000000000000−i2i2i2−i2−i2i2i2−i20000-2-2-2-222-2-2222-2-2200002-200000000000000i2−i2−i2i2i2−i2−i2i20000
χ722222-2-2-2-2222-2-22-2-2-2-2-22-2-2222200000000000000000000-2-2-2-22222-2-2-222-222222-222-2-2-2-200000000000000000000
χ732222-2-2-2-222-222-200002-2000000000000002−2−22−222−20000-2-2-2-22222-2-22-2-220000-2200000000000000−222−22−2−220000
χ742222-2-2-2-222-222-200002-200000000000000−222−22−2−220000-2-2-2-22222-2-22-2-220000-22000000000000002−2−22−222−20000
χ752-2-222-2000022-2-22i2i−2i−2i0000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000-222-2-220000-2-222−2i−2i2i2i000000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ762-2-222-2000022-2-22i2i−2i−2i0000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000-222-2-220000-2-222−2i−2i2i2i000000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ772-2-222-2000022-2-2−2i−2i2i2i000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000-222-2-220000-2-2222i2i−2i−2i0000002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ782-2-222-2000022-2-2−2i−2i2i2i000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000-222-2-220000-2-2222i2i−2i−2i0000002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ792-2-22-2200002-22-22i2i−2i−2i000000−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000-222-22-20000-22-22−2i−2i2i2i0000002i−2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ802-2-22-2200002-22-22i2i−2i−2i000000−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000-222-22-20000-22-22−2i−2i2i2i0000002i−2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ812-2-22-2200002-22-2−2i−2i2i2i0000002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000-222-22-20000-22-222i2i−2i−2i000000−2i2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ822-2-22-2200002-22-2−2i−2i2i2i0000002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000-222-22-20000-22-222i2i−2i−2i000000−2i2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ8344-4-400004-4000022−2222−220022−22000000000000000000000000-4-4440000-440000−2222−222200−2222000000000000000000000000
χ8444-4-400004-40000−2222−222200−2222000000000000000000000000-4-4440000-44000022−2222−220022−22000000000000000000000000
χ8544-4-40000-44000022−2222−2200−2222000000000000000000000000-4-44400004-40000−2222−22220022−22000000000000000000000000
χ8644-4-40000-440000−2222−22220022−22000000000000000000000000-4-44400004-4000022−2222−2200−2222000000000000000000000000
χ874-44-4004-40000002i2−2i2−2i22i200002i2−2i20000000000000000000000-44-4400-44000000−2i22i22i2−2i20000−2i22i20000000000000000000000
χ884-44-4004-4000000−2i22i22i2−2i20000−2i22i20000000000000000000000-44-4400-440000002i2−2i2−2i22i200002i2−2i20000000000000000000000
χ894-44-400-440000002i2−2i2−2i22i20000−2i22i20000000000000000000000-44-44004-4000000−2i22i22i2−2i200002i2−2i20000000000000000000000
χ904-44-400-44000000−2i22i22i2−2i200002i2−2i20000000000000000000000-44-44004-40000002i2−2i2−2i22i20000−2i22i20000000000000000000000
χ914-4-444-40000-4-44400000000000000000000000000000000-444-4-44000044-4-400000000000000000000000000000000
χ924-4-44-440000-44-4400000000000000000000000000000000-444-44-400004-44-400000000000000000000000000000000

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