Finite Group Databasebeta

← Group #239596

Character table — Group #239596

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888224444448888888844442222222244444444448888888822444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-111111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1
χ7111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ922222222222-2-2-22-2-2-2000000000022-2-20000000000000022222222222-2-2-22-2-2-2000000000022-2-200000000000000
χ1022222222222-2-2-22-2-2-20000000000-2-2220000000000000022222222222-2-2-22-2-2-20000000000-2-22200000000000000
χ1122222222-2-2-2222-22-2-200000000220000-2-200000000000022222222-2-2-2222-22-2-200000000220000-2-2000000000000
χ1222222222-2-2-2222-22-2-200000000-2-200002200000000000022222222-2-2-2222-22-2-200000000-2-2000022000000000000
χ1322222222-2-2-2-2-2-2-2-222000000000000000000000000002-222222222-2-2-2-2-2-2-2-222000000000000000000000000002-2
χ1422222222-2-2-2-2-2-2-2-22200000000000000000000000000-2222222222-2-2-2-2-2-2-2-22200000000000000000000000000-22
χ1522-22-22-2-22-2-200020002222−2−2−2−200002i−2i000000i2i2−i2−i2000022-22-22-2-22-2-200020002222−2−2−2−200002i−2i000000i2i2−i2−i20000
χ1622-22-22-2-22-2-200020002222−2−2−2−20000−2i2i000000−i2−i2i2i2000022-22-22-2-22-2-200020002222−2−2−2−20000−2i2i000000−i2−i2i2i20000
χ1722-22-22-2-22-2-20002000−2−2−2−2222200002i−2i000000−i2−i2i2i2000022-22-22-2-22-2-20002000−2−2−2−2222200002i−2i000000−i2−i2i2i20000
χ1822-22-22-2-22-2-20002000−2−2−2−222220000−2i2i000000i2i2−i2−i2000022-22-22-2-22-2-20002000−2−2−2−222220000−2i2i000000i2i2−i2−i20000
χ1922-2-2-2-22200022-20-20022−2−222−2−20000002i−2ii2i2−i2−i20000000022-2-2-2-22200022-20-20022−2−222−2−20000002i−2ii2i2−i2−i200000000
χ2022-2-2-2-22200022-20-20022−2−222−2−2000000−2i2i−i2−i2i2i20000000022-2-2-2-22200022-20-20022−2−222−2−2000000−2i2i−i2−i2i2i200000000
χ2122-2-2-2-22200022-20-200−2−222−2−2220000002i−2i−i2−i2i2i20000000022-2-2-2-22200022-20-200−2−222−2−2220000002i−2i−i2−i2i2i200000000
χ2222-2-2-2-22200022-20-200−2−222−2−222000000−2i2ii2i2−i2−i20000000022-2-2-2-22200022-20-200−2−222−2−222000000−2i2ii2i2−i2−i200000000
χ232-22-2-22-2222-22-22-2-2-22000000000000000000002i−2i2i−2i00002-22-2-22-2222-22-22-2-2-22000000000000000000002i−2i2i−2i0000
χ242-22-2-22-2222-22-22-2-2-2200000000000000000000−2i2i−2i2i00002-22-2-22-2222-22-22-2-2-2200000000000000000000−2i2i−2i2i0000
χ252-22-2-22-2222-2-22-2-222-22i−2i2i−2i2i−2i2i−2i000000000000000000002-22-2-22-2222-2-22-2-222-22i−2i2i−2i2i−2i2i−2i00000000000000000000
χ262-22-2-22-2222-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i000000000000000000002-22-2-22-2222-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ272-22-2-22-22-2-222-222-22-20000000000000000000000002i−2i002-22-2-22-22-2-222-222-22-20000000000000000000000002i−2i00
χ282-22-2-22-22-2-222-222-22-2000000000000000000000000−2i2i002-22-2-22-22-2-222-222-22-2000000000000000000000000−2i2i00
χ292-22-2-22-22-2-22-22-222-2200000000000000002-22-2000000002-22-2-22-22-2-22-22-222-2200000000000000002-22-200000000
χ302-22-2-22-22-2-22-22-222-220000000000000000-22-22000000002-22-2-22-22-2-22-22-222-220000000000000000-22-2200000000
χ312-2-222-2-22000-2220-200i2−i2−i2i2i2−i2−i2i22-2000000i2−i2−i2i2000000002-2-222-2-22000-2220-200i2−i2−i2i2i2−i2−i2i22-2000000i2−i2−i2i200000000
χ322-2-222-2-22000-2220-200i2−i2−i2i2i2−i2−i2i2-22000000−i2i2i2−i2000000002-2-222-2-22000-2220-200i2−i2−i2i2i2−i2−i2i2-22000000−i2i2i2−i200000000
χ332-2-222-2-22000-2220-200−i2i2i2−i2−i2i2i2−i22-2000000−i2i2i2−i2000000002-2-222-2-22000-2220-200−i2i2i2−i2−i2i2i2−i22-2000000−i2i2i2−i200000000
χ342-2-222-2-22000-2220-200−i2i2i2−i2−i2i2i2−i2-22000000i2−i2−i2i2000000002-2-222-2-22000-2220-200−i2i2i2−i2−i2i2i2−i2-22000000i2−i2−i2i200000000
χ352-2-2-2222-22-22000-2000i2−i2i2−i2−i2i2−i2i2002i−2i000000002−2−2200002-2-2-2222-22-22000-2000i2−i2i2−i2−i2i2−i2i2002i−2i000000002−2−220000
χ362-2-2-2222-22-22000-2000i2−i2i2−i2−i2i2−i2i200−2i2i00000000−222−200002-2-2-2222-22-22000-2000i2−i2i2−i2−i2i2−i2i200−2i2i00000000−222−20000
χ372-2-2-2222-22-22000-2000−i2i2−i2i2i2−i2i2−i2002i−2i00000000−222−200002-2-2-2222-22-22000-2000−i2i2−i2i2i2−i2i2−i2002i−2i00000000−222−20000
χ382-2-2-2222-22-22000-2000−i2i2−i2i2i2−i2i2−i200−2i2i000000002−2−2200002-2-2-2222-22-22000-2000−i2i2−i2i2i2−i2i2−i200−2i2i000000002−2−220000
χ39444-44-4-4-4000000000022-2-2-2-22200000000000000000000444-44-4-4-4000000000022-2-2-2-22200000000000000000000
χ40444-44-4-4-40000000000-2-22222-2-200000000000000000000444-44-4-4-40000000000-2-22222-2-200000000000000000000
χ4144-44-44-4-4-444000-4000000000000000000000000000000044-44-44-4-4-444000-40000000000000000000000000000000
χ4244-4-4-4-444000-4-440400000000000000000000000000000044-4-4-4-444000-4-4404000000000000000000000000000000
χ434-444-4-44-400000000002i−2i−2i2i−2i2i2i−2i000000000000000000004-444-4-44-400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ444-444-4-44-40000000000−2i2i2i−2i2i−2i−2i2i000000000000000000004-444-4-44-40000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ454-4-444-4-440004-4-4040000000000000000000000000000004-4-444-4-440004-4-404000000000000000000000000000000
χ464-4-4-4444-4-44-4000400000000000000000000000000000004-4-4-4444-4-44-400040000000000000000000000000000000
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
χ481111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ4911111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111
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
χ51111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ52111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-111
χ53111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-111
χ54111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1
χ5522222222222-2-2-22-2-2-2000000000022-2-200000000000000-2-2-2-2-2-2-2-2-2-2-2222-22220000000000-2-22200000000000000
χ5622222222222-2-2-22-2-2-20000000000-2-22200000000000000-2-2-2-2-2-2-2-2-2-2-2222-2222000000000022-2-200000000000000
χ5722222222-2-2-2222-22-2-200000000220000-2-2000000000000-2-2-2-2-2-2-2-2222-2-2-22-22200000000-2-2000022000000000000
χ5822222222-2-2-2222-22-2-200000000-2-2000022000000000000-2-2-2-2-2-2-2-2222-2-2-22-22200000000220000-2-2000000000000
χ5922222222-2-2-2-2-2-2-2-222000000000000000000000000002-2-2-2-2-2-2-2-2-222222222-2-200000000000000000000000000-22
χ6022222222-2-2-2-2-2-2-2-22200000000000000000000000000-22-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000002-2
χ6122-22-22-2-22-2-200020002222−2−2−2−200002i−2i000000i2i2−i2−i20000-2-22-22-222-222000-2000−2−2−2−222220000−2i2i000000−i2−i2i2i20000
χ6222-22-22-2-22-2-200020002222−2−2−2−20000−2i2i000000−i2−i2i2i20000-2-22-22-222-222000-2000−2−2−2−2222200002i−2i000000i2i2−i2−i20000
χ6322-22-22-2-22-2-20002000−2−2−2−2222200002i−2i000000−i2−i2i2i20000-2-22-22-222-222000-20002222−2−2−2−20000−2i2i000000i2i2−i2−i20000
χ6422-22-22-2-22-2-20002000−2−2−2−222220000−2i2i000000i2i2−i2−i20000-2-22-22-222-222000-20002222−2−2−2−200002i−2i000000−i2−i2i2i20000
χ6522-2-2-2-22200022-20-20022−2−222−2−20000002i−2ii2i2−i2−i200000000-2-22222-2-2000-2-220200−2−222−2−222000000−2i2i−i2−i2i2i200000000
χ6622-2-2-2-22200022-20-20022−2−222−2−2000000−2i2i−i2−i2i2i200000000-2-22222-2-2000-2-220200−2−222−2−2220000002i−2ii2i2−i2−i200000000
χ6722-2-2-2-22200022-20-200−2−222−2−2220000002i−2i−i2−i2i2i200000000-2-22222-2-2000-2-22020022−2−222−2−2000000−2i2ii2i2−i2−i200000000
χ6822-2-2-2-22200022-20-200−2−222−2−222000000−2i2ii2i2−i2−i200000000-2-22222-2-2000-2-22020022−2−222−2−20000002i−2i−i2−i2i2i200000000
χ692-22-2-22-2222-22-22-2-2-22000000000000000000002i−2i2i−2i0000-22-222-22-2-2-22-22-2222-200000000000000000000−2i2i−2i2i0000
χ702-22-2-22-2222-22-22-2-2-2200000000000000000000−2i2i−2i2i0000-22-222-22-2-2-22-22-2222-2000000000000000000002i−2i2i−2i0000
χ712-22-2-22-2222-2-22-2-222-22i−2i2i−2i2i−2i2i−2i00000000000000000000-22-222-22-2-2-222-222-2-22−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ722-22-2-22-2222-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i00000000000000000000-22-222-22-2-2-222-222-2-222i−2i2i−2i2i−2i2i−2i00000000000000000000
χ732-22-2-22-22-2-222-222-22-20000000000000000000000002i−2i00-22-222-22-222-2-22-2-22-22000000000000000000000000−2i2i00
χ742-22-2-22-22-2-222-222-22-2000000000000000000000000−2i2i00-22-222-22-222-2-22-2-22-220000000000000000000000002i−2i00
χ752-22-2-22-22-2-22-22-222-2200000000000000002-22-200000000-22-222-22-222-22-22-2-22-20000000000000000-22-2200000000
χ762-22-2-22-22-2-22-22-222-220000000000000000-22-2200000000-22-222-22-222-22-22-2-22-200000000000000002-22-200000000
χ772-2-222-2-22000-2220-200i2−i2−i2i2i2−i2−i2i22-2000000i2−i2−i2i200000000-222-2-222-20002-2-20200−i2i2i2−i2−i2i2i2−i2-22000000−i2i2i2−i200000000
χ782-2-222-2-22000-2220-200i2−i2−i2i2i2−i2−i2i2-22000000−i2i2i2−i200000000-222-2-222-20002-2-20200−i2i2i2−i2−i2i2i2−i22-2000000i2−i2−i2i200000000
χ792-2-222-2-22000-2220-200−i2i2i2−i2−i2i2i2−i22-2000000−i2i2i2−i200000000-222-2-222-20002-2-20200i2−i2−i2i2i2−i2−i2i2-22000000i2−i2−i2i200000000
χ802-2-222-2-22000-2220-200−i2i2i2−i2−i2i2i2−i2-22000000i2−i2−i2i200000000-222-2-222-20002-2-20200i2−i2−i2i2i2−i2−i2i22-2000000−i2i2i2−i200000000
χ812-2-2-2222-22-22000-2000i2−i2i2−i2−i2i2−i2i2002i−2i000000002−2−220000-2222-2-2-22-22-20002000−i2i2−i2i2i2−i2i2−i200−2i2i00000000−222−20000
χ822-2-2-2222-22-22000-2000i2−i2i2−i2−i2i2−i2i200−2i2i00000000−222−20000-2222-2-2-22-22-20002000−i2i2−i2i2i2−i2i2−i2002i−2i000000002−2−220000
χ832-2-2-2222-22-22000-2000−i2i2−i2i2i2−i2i2−i2002i−2i00000000−222−20000-2222-2-2-22-22-20002000i2−i2i2−i2−i2i2−i2i200−2i2i000000002−2−220000
χ842-2-2-2222-22-22000-2000−i2i2−i2i2i2−i2i2−i200−2i2i000000002−2−220000-2222-2-2-22-22-20002000i2−i2i2−i2−i2i2−i2i2002i−2i00000000−222−20000
χ85444-44-4-4-4000000000022-2-2-2-22200000000000000000000-4-4-44-44440000000000-2-22222-2-200000000000000000000
χ86444-44-4-4-40000000000-2-22222-2-200000000000000000000-4-4-44-4444000000000022-2-2-2-22200000000000000000000
χ8744-44-44-4-4-444000-40000000000000000000000000000000-4-44-44-4444-4-400040000000000000000000000000000000
χ8844-4-4-4-444000-4-4404000000000000000000000000000000-4-44444-4-400044-40-4000000000000000000000000000000
χ894-444-4-44-400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000-44-4-444-440000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ904-444-4-44-40000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000-44-4-444-4400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ914-4-444-4-440004-4-404000000000000000000000000000000-444-4-444-4000-4440-4000000000000000000000000000000
χ924-4-4-4444-4-44-400040000000000000000000000000000000-4444-4-4-444-44000-40000000000000000000000000000000

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