Finite Group Databasebeta

← Group #483039

Character table — Group #483039

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222224444444488888888888888881616161611112222222222222244444444888888888888888816161616
order122222444444448888448888888888888816161616161616162244222222444444448888448888888888888816161616161616162244
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
χ5111111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ7111111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ8111111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91111-1-111-1-111-1-1-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i1-11-11111-1-111-1-111-1-1-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111-1-111-1-111-1-1-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-111111-1-111-1-111-1-1-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111-1-111-1-111-1-1-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-111111-1-111-1-111-1-1-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111-1-111-1-111-1-1-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii1-11-11111-1-111-1-111-1-1-1-1-1-11-111-1-111−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
χ1822222222-2-2-2-2-2-20000-2200000000000000i2−i2i2−i2i2−i2i2−i2000022222222-2-2-2-2-2-20000-2200000000000000i2−i2i2−i2i2−i2i2−i20000
χ1922222222-2-2-2-2-2-20000-2200000000000000−i2i2−i2i2−i2i2−i2i2000022222222-2-2-2-2-2-20000-2200000000000000−i2i2−i2i2−i2i2−i2i20000
χ20222222-2-22222-2-22222-2-2-2-2-2-22200000000000000000000222222-2-22222-2-22222-2-2-2-2-2-22200000000000000000000
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
χ252222-2-222-2-222-2-222222-2-2-222-2-2000000000000000000002222-2-222-2-222-2-222222-2-2-222-2-200000000000000000000
χ262222-2-2-2-222-2-2-2-200002200000000000000i2−i2−i2i2−i2i2i2−i200002222-2-2-2-222-2-2-2-200002200000000000000i2−i2−i2i2−i2i2i2−i20000
χ272222-2-2-2-222-2-2-2-200002200000000000000−i2i2i2−i2i2−i2−i2i200002222-2-2-2-222-2-2-2-200002200000000000000−i2i2i2−i2i2−i2−i2i20000
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
χ292-2-222-2002-22-20022-2-20000002-2i2−i2i2−i2i2−i2i2−i20000000000002-2-222-2002-22-20022-2-20000002-2i2−i2i2−i2i2−i2i2−i2000000000000
χ302-2-222-2002-22-20022-2-20000002-2−i2i2−i2i2−i2i2−i2i20000000000002-2-222-2002-22-20022-2-20000002-2−i2i2−i2i2−i2i2−i2i2000000000000
χ312-2-222-2002-22-200-2-222000000-222−22−2−22−220000000000002-2-222-2002-22-200-2-222000000-222−22−2−22−22000000000000
χ322-2-222-2002-22-200-2-222000000-22−22−222−22−20000000000002-2-222-2002-22-200-2-222000000-22−22−222−22−2000000000000
χ332-2-22-2200-222-20022-2-2000000-22i2−i2−i2i2−i2i2i2−i20000000000002-2-22-2200-222-20022-2-2000000-22i2−i2−i2i2−i2i2i2−i2000000000000
χ342-2-22-2200-222-20022-2-2000000-22−i2i2i2−i2i2−i2−i2i20000000000002-2-22-2200-222-20022-2-2000000-22−i2i2i2−i2i2−i2−i2i2000000000000
χ352-2-22-2200-222-200-2-2220000002-22−2−222−2−220000000000002-2-22-2200-222-200-2-2220000002-22−2−222−2−22000000000000
χ362-2-22-2200-222-200-2-2220000002-2−222−2−222−20000000000002-2-22-2200-222-200-2-2220000002-2−222−2−222−2000000000000
χ3744-4-4000000004i−4i2i2−2i22i2−2i20022−2200000000000000000000000044-4-4000000004i−4i2i2−2i22i2−2i20022−22000000000000000000000000
χ3844-4-4000000004i−4i−2i22i2−2i22i200−222200000000000000000000000044-4-4000000004i−4i−2i22i2−2i22i200−2222000000000000000000000000
χ3944-4-400000000−4i4i2i2−2i22i2−2i200−222200000000000000000000000044-4-400000000−4i4i2i2−2i22i2−2i200−2222000000000000000000000000
χ4044-4-400000000−4i4i−2i22i2−2i22i20022−2200000000000000000000000044-4-400000000−4i4i−2i22i2−2i22i20022−22000000000000000000000000
χ414-44-4004i−4i0000002i2−2i2−2i22i2000022−2200000000000000000000004-44-4004i−4i0000002i2−2i2−2i22i2000022−220000000000000000000000
χ424-44-4004i−4i000000−2i22i22i2−2i20000−222200000000000000000000004-44-4004i−4i000000−2i22i22i2−2i20000−22220000000000000000000000
χ434-44-400−4i4i0000002i2−2i2−2i22i20000−222200000000000000000000004-44-400−4i4i0000002i2−2i2−2i22i20000−22220000000000000000000000
χ444-44-400−4i4i000000−2i22i22i2−2i2000022−2200000000000000000000004-44-400−4i4i000000−2i22i22i2−2i2000022−220000000000000000000000
χ454-4-444-400-44-4400000000000000000000000000000000004-4-444-400-44-440000000000000000000000000000000000
χ464-4-44-44004-4-4400000000000000000000000000000000004-4-44-44004-4-440000000000000000000000000000000000
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
χ51111111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111
χ52111111-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ53111111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1
χ54111111-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111
χ551111-1-111-1-111-1-1-1-1-1-11-111-1-111ii−i−iii−i−iii−i−iii−i−i1-11-1-1-1-1-111-1-111-1-1111111-11-1-111-1-1−i−iii−i−iii−i−iii−i−iii-11-11
χ561111-1-111-1-111-1-1-1-1-1-11-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-11-1-1-1-111-1-111-1-1111111-11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i1-11-1
χ571111-1-111-1-111-1-1-1-1-1-11-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-11-1-1-1-111-1-111-1-1111111-11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii1-11-1
χ581111-1-111-1-111-1-1-1-1-1-11-111-1-111−i−iii−i−iii−i−iii−i−iii1-11-1-1-1-1-111-1-111-1-1111111-11-1-111-1-1ii−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
χ6422222222-2-2-2-2-2-20000-2200000000000000i2−i2i2−i2i2−i2i2−i20000-2-2-2-2-2-2-2-222222200002-200000000000000−i2i2−i2i2−i2i2−i2i20000
χ6522222222-2-2-2-2-2-20000-2200000000000000−i2i2−i2i2−i2i2−i2i20000-2-2-2-2-2-2-2-222222200002-200000000000000i2−i2i2−i2i2−i2i2−i20000
χ66222222-2-22222-2-22222-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-222-2-2-2-222-2-2-2-2222222-2-200000000000000000000
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
χ712222-2-222-2-222-2-222222-2-2-222-2-200000000000000000000-2-2-2-222-2-222-2-222-2-2-2-2-2222-2-22200000000000000000000
χ722222-2-2-2-222-2-2-2-200002200000000000000i2−i2−i2i2−i2i2i2−i20000-2-2-2-22222-2-222220000-2-200000000000000−i2i2i2−i2i2−i2−i2i20000
χ732222-2-2-2-222-2-2-2-200002200000000000000−i2i2i2−i2i2−i2−i2i20000-2-2-2-22222-2-222220000-2-200000000000000i2−i2−i2i2−i2i2i2−i20000
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
χ752-2-222-2002-22-20022-2-20000002-2i2−i2i2−i2i2−i2i2−i2000000000000-222-2-2200-22-2200-2-222000000-22−i2i2−i2i2−i2i2−i2i2000000000000
χ762-2-222-2002-22-20022-2-20000002-2−i2i2−i2i2−i2i2−i2i2000000000000-222-2-2200-22-2200-2-222000000-22i2−i2i2−i2i2−i2i2−i2000000000000
χ772-2-222-2002-22-200-2-222000000-222−22−2−22−22000000000000-222-2-2200-22-220022-2-20000002-2−22−222−22−2000000000000
χ782-2-222-2002-22-200-2-222000000-22−22−222−22−2000000000000-222-2-2200-22-220022-2-20000002-22−22−2−22−22000000000000
χ792-2-22-2200-222-20022-2-2000000-22i2−i2−i2i2−i2i2i2−i2000000000000-222-22-2002-2-2200-2-2220000002-2−i2i2i2−i2i2−i2−i2i2000000000000
χ802-2-22-2200-222-20022-2-2000000-22−i2i2i2−i2i2−i2−i2i2000000000000-222-22-2002-2-2200-2-2220000002-2i2−i2−i2i2−i2i2i2−i2000000000000
χ812-2-22-2200-222-200-2-2220000002-22−2−222−2−22000000000000-222-22-2002-2-220022-2-2000000-22−222−2−222−2000000000000
χ822-2-22-2200-222-200-2-2220000002-2−222−2−222−2000000000000-222-22-2002-2-220022-2-2000000-222−2−222−2−22000000000000
χ8344-4-4000000004i−4i2i2−2i22i2−2i20022−22000000000000000000000000-4-44400000000−4i4i−2i22i2−2i22i200−2222000000000000000000000000
χ8444-4-4000000004i−4i−2i22i2−2i22i200−2222000000000000000000000000-4-44400000000−4i4i2i2−2i22i2−2i20022−22000000000000000000000000
χ8544-4-400000000−4i4i2i2−2i22i2−2i200−2222000000000000000000000000-4-444000000004i−4i−2i22i2−2i22i20022−22000000000000000000000000
χ8644-4-400000000−4i4i−2i22i2−2i22i20022−22000000000000000000000000-4-444000000004i−4i2i2−2i22i2−2i200−2222000000000000000000000000
χ874-44-4004i−4i0000002i2−2i2−2i22i2000022−220000000000000000000000-44-4400−4i4i000000−2i22i22i2−2i20000−22220000000000000000000000
χ884-44-4004i−4i000000−2i22i22i2−2i20000−22220000000000000000000000-44-4400−4i4i0000002i2−2i2−2i22i2000022−220000000000000000000000
χ894-44-400−4i4i0000002i2−2i2−2i22i20000−22220000000000000000000000-44-44004i−4i000000−2i22i22i2−2i2000022−220000000000000000000000
χ904-44-400−4i4i000000−2i22i22i2−2i2000022−220000000000000000000000-44-44004i−4i0000002i2−2i2−2i22i20000−22220000000000000000000000
χ914-4-444-400-44-440000000000000000000000000000000000-444-4-44004-44-40000000000000000000000000000000000
χ924-4-44-44004-4-440000000000000000000000000000000000-444-44-400-444-40000000000000000000000000000000000

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