Finite Group Databasebeta

← Group #239595

Character table — Group #239595

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888444444448888888844442222222244444444448888888844444444888888884444
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
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
χ1322222222-2-2-2-2-2-2-2-2220000000000000000000000002-20022222222-2-2-2-2-2-2-2-2220000000000000000000000002-200
χ1422222222-2-2-2-2-2-2-2-222000000000000000000000000-220022222222-2-2-2-2-2-2-2-222000000000000000000000000-2200
χ15222-22-2-2-222-2000-20002222−2−2−2−200002-200000022−2−20000222-22-2-2-222-2000-20002222−2−2−2−200002-200000022−2−20000
χ16222-22-2-2-222-2000-20002222−2−2−2−20000-22000000−2−2220000222-22-2-2-222-2000-20002222−2−2−2−20000-22000000−2−2220000
χ17222-22-2-2-222-2000-2000−2−2−2−2222200002-2000000−2−2220000222-22-2-2-222-2000-2000−2−2−2−2222200002-2000000−2−2220000
χ18222-22-2-2-222-2000-2000−2−2−2−222220000-2200000022−2−20000222-22-2-2-222-2000-2000−2−2−2−222220000-2200000022−2−20000
χ1922-22-2-22-20002-2-20200i2i2−i2−i2i2i2−i2−i20000002i−2i22−2−20000000022-22-2-22-20002-2-20200i2i2−i2−i2i2i2−i2−i20000002i−2i22−2−200000000
χ2022-22-2-22-20002-2-20200i2i2−i2−i2i2i2−i2−i2000000−2i2i−2−2220000000022-22-2-22-20002-2-20200i2i2−i2−i2i2i2−i2−i2000000−2i2i−2−22200000000
χ2122-22-2-22-20002-2-20200−i2−i2i2i2−i2−i2i2i20000002i−2i−2−2220000000022-22-2-22-20002-2-20200−i2−i2i2i2−i2−i2i2i20000002i−2i−2−22200000000
χ2222-22-2-22-20002-2-20200−i2−i2i2i2−i2−i2i2i2000000−2i2i22−2−20000000022-22-2-22-20002-2-20200−i2−i2i2i2−i2−i2i2i2000000−2i2i22−2−200000000
χ232-22-2-2-22200022-20-2002−22−22−22−22i−2i000000i2−i2i2−i2000000002-22-2-2-22200022-20-2002−22−22−22−22i−2i000000i2−i2i2−i200000000
χ242-22-2-2-22200022-20-2002−22−22−22−2−2i2i000000−i2i2−i2i2000000002-22-2-2-22200022-20-2002−22−22−22−2−2i2i000000−i2i2−i2i200000000
χ252-22-2-2-22200022-20-200−22−22−22−222i−2i000000−i2i2−i2i2000000002-22-2-2-22200022-20-200−22−22−22−222i−2i000000−i2i2−i2i200000000
χ262-22-2-2-22200022-20-200−22−22−22−22−2i2i000000i2−i2i2−i2000000002-22-2-2-22200022-20-200−22−22−22−22−2i2i000000i2−i2i2−i200000000
χ272-2-222-2-222-22000-2000i2−i2−i2i2−i2i2i2−i2002i−2i000000002−22−200002-2-222-2-222-22000-2000i2−i2−i2i2−i2i2i2−i2002i−2i000000002−22−20000
χ282-2-222-2-222-22000-2000i2−i2−i2i2−i2i2i2−i200−2i2i00000000−22−2200002-2-222-2-222-22000-2000i2−i2−i2i2−i2i2i2−i200−2i2i00000000−22−220000
χ292-2-222-2-222-22000-2000−i2i2i2−i2i2−i2−i2i2002i−2i00000000−22−2200002-2-222-2-222-22000-2000−i2i2i2−i2i2−i2−i2i2002i−2i00000000−22−220000
χ302-2-222-2-222-22000-2000−i2i2i2−i2i2−i2−i2i200−2i2i000000002−22−200002-2-222-2-222-22000-2000−i2i2i2−i2i2−i2−i2i200−2i2i000000002−22−20000
χ312-2-2-2222-22-2-22-222-22-22i−2i−2i2i2i−2i−2i2i000000000000000000002-2-2-2222-22-2-22-222-22-22i−2i−2i2i2i−2i−2i2i00000000000000000000
χ322-2-2-2222-22-2-22-222-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000002-2-2-2222-22-2-22-222-22-2−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ332-2-2-2222-22-2-2-22-222-22000000000000000000002-2-2200002-2-2-2222-22-2-2-22-222-22000000000000000000002-2-220000
χ342-2-2-2222-22-2-2-22-222-2200000000000000000000-222-200002-2-2-2222-22-2-2-22-222-2200000000000000000000-222-20000
χ352-2-2-2222-2-2222-22-2-2-2200000000000000002i−2i−2i2i000000002-2-2-2222-2-2222-22-2-2-2200000000000000002i−2i−2i2i00000000
χ362-2-2-2222-2-2222-22-2-2-220000000000000000−2i2i2i−2i000000002-2-2-2222-2-2222-22-2-2-220000000000000000−2i2i2i−2i00000000
χ372-2-2-2222-2-222-22-2-222-2000000000000000000000000002i−2i2-2-2-2222-2-222-22-2-222-2000000000000000000000000002i−2i
χ382-2-2-2222-2-222-22-2-222-200000000000000000000000000−2i2i2-2-2-2222-2-222-22-2-222-200000000000000000000000000−2i2i
χ39444-44-4-4-4-4-4400040000000000000000000000000000000444-44-4-4-4-4-4400040000000000000000000000000000000
χ4044-44-4-44-4000-4440-400000000000000000000000000000044-44-4-44-4000-4440-4000000000000000000000000000000
χ4144-4-4-44-4400000000002i2i−2i−2i−2i−2i2i2i0000000000000000000044-4-4-44-4400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4244-4-4-44-440000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000044-4-4-44-440000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ434-444-44-4-400000000002-22-2-22-22000000000000000000004-444-44-4-400000000002-22-2-22-2200000000000000000000
χ444-444-44-4-40000000000-22-222-22-2000000000000000000004-444-44-4-40000000000-22-222-22-200000000000000000000
χ454-44-4-4-444000-4-44040000000000000000000000000000004-44-4-4-444000-4-4404000000000000000000000000000000
χ464-4-444-4-44-44-4000400000000000000000000000000000004-4-444-4-44-44-400040000000000000000000000000000000
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
χ51111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111
χ52111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-111-1-1
χ53111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1
χ54111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
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
χ5922222222-2-2-2-2-2-2-2-2220000000000000000000000002-200-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000-2200
χ6022222222-2-2-2-2-2-2-2-222000000000000000000000000-2200-2-2-2-2-2-2-2-222222222-2-20000000000000000000000002-200
χ61222-22-2-2-222-2000-20002222−2−2−2−200002-200000022−2−20000-2-2-22-2222-2-220002000−2−2−2−222220000-22000000−2−2220000
χ62222-22-2-2-222-2000-20002222−2−2−2−20000-22000000−2−2220000-2-2-22-2222-2-220002000−2−2−2−2222200002-200000022−2−20000
χ63222-22-2-2-222-2000-2000−2−2−2−2222200002-2000000−2−2220000-2-2-22-2222-2-2200020002222−2−2−2−20000-2200000022−2−20000
χ64222-22-2-2-222-2000-2000−2−2−2−222220000-2200000022−2−20000-2-2-22-2222-2-2200020002222−2−2−2−200002-2000000−2−2220000
χ6522-22-2-22-20002-2-20200i2i2−i2−i2i2i2−i2−i20000002i−2i22−2−200000000-2-22-222-22000-2220-200−i2−i2i2i2−i2−i2i2i2000000−2i2i−2−22200000000
χ6622-22-2-22-20002-2-20200i2i2−i2−i2i2i2−i2−i2000000−2i2i−2−22200000000-2-22-222-22000-2220-200−i2−i2i2i2−i2−i2i2i20000002i−2i22−2−200000000
χ6722-22-2-22-20002-2-20200−i2−i2i2i2−i2−i2i2i20000002i−2i−2−22200000000-2-22-222-22000-2220-200i2i2−i2−i2i2i2−i2−i2000000−2i2i22−2−200000000
χ6822-22-2-22-20002-2-20200−i2−i2i2i2−i2−i2i2i2000000−2i2i22−2−200000000-2-22-222-22000-2220-200i2i2−i2−i2i2i2−i2−i20000002i−2i−2−22200000000
χ692-22-2-2-22200022-20-2002−22−22−22−22i−2i000000i2−i2i2−i200000000-22-2222-2-2000-2-220200−22−22−22−22−2i2i000000−i2i2−i2i200000000
χ702-22-2-2-22200022-20-2002−22−22−22−2−2i2i000000−i2i2−i2i200000000-22-2222-2-2000-2-220200−22−22−22−222i−2i000000i2−i2i2−i200000000
χ712-22-2-2-22200022-20-200−22−22−22−222i−2i000000−i2i2−i2i200000000-22-2222-2-2000-2-2202002−22−22−22−2−2i2i000000i2−i2i2−i200000000
χ722-22-2-2-22200022-20-200−22−22−22−22−2i2i000000i2−i2i2−i200000000-22-2222-2-2000-2-2202002−22−22−22−22i−2i000000−i2i2−i2i200000000
χ732-2-222-2-222-22000-2000i2−i2−i2i2−i2i2i2−i2002i−2i000000002−22−20000-222-2-222-2-22-20002000−i2i2i2−i2i2−i2−i2i200−2i2i00000000−22−220000
χ742-2-222-2-222-22000-2000i2−i2−i2i2−i2i2i2−i200−2i2i00000000−22−220000-222-2-222-2-22-20002000−i2i2i2−i2i2−i2−i2i2002i−2i000000002−22−20000
χ752-2-222-2-222-22000-2000−i2i2i2−i2i2−i2−i2i2002i−2i00000000−22−220000-222-2-222-2-22-20002000i2−i2−i2i2−i2i2i2−i200−2i2i000000002−22−20000
χ762-2-222-2-222-22000-2000−i2i2i2−i2i2−i2−i2i200−2i2i000000002−22−20000-222-2-222-2-22-20002000i2−i2−i2i2−i2i2i2−i2002i−2i00000000−22−220000
χ772-2-2-2222-22-2-22-222-22-22i−2i−2i2i2i−2i−2i2i00000000000000000000-2222-2-2-22-222-22-2-22-22−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ782-2-2-2222-22-2-22-222-22-2−2i2i2i−2i−2i2i2i−2i00000000000000000000-2222-2-2-22-222-22-2-22-222i−2i−2i2i2i−2i−2i2i00000000000000000000
χ792-2-2-2222-22-2-2-22-222-22000000000000000000002-2-220000-2222-2-2-22-2222-22-2-22-200000000000000000000-222-20000
χ802-2-2-2222-22-2-2-22-222-2200000000000000000000-222-20000-2222-2-2-22-2222-22-2-22-2000000000000000000002-2-220000
χ812-2-2-2222-2-2222-22-2-2-2200000000000000002i−2i−2i2i00000000-2222-2-2-222-2-2-22-2222-20000000000000000−2i2i2i−2i00000000
χ822-2-2-2222-2-2222-22-2-2-220000000000000000−2i2i2i−2i00000000-2222-2-2-222-2-2-22-2222-200000000000000002i−2i−2i2i00000000
χ832-2-2-2222-2-222-22-2-222-2000000000000000000000000002i−2i-2222-2-2-222-2-22-222-2-2200000000000000000000000000−2i2i
χ842-2-2-2222-2-222-22-2-222-200000000000000000000000000−2i2i-2222-2-2-222-2-22-222-2-22000000000000000000000000002i−2i
χ85444-44-4-4-4-4-4400040000000000000000000000000000000-4-4-44-444444-4000-40000000000000000000000000000000
χ8644-44-4-44-4000-4440-4000000000000000000000000000000-4-44-444-440004-4-404000000000000000000000000000000
χ8744-4-4-44-4400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000-4-4444-44-40000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ8844-4-4-44-440000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000-4-4444-44-400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ894-444-44-4-400000000002-22-2-22-2200000000000000000000-44-4-44-4440000000000-22-222-22-200000000000000000000
χ904-444-44-4-40000000000-22-222-22-200000000000000000000-44-4-44-44400000000002-22-2-22-2200000000000000000000
χ914-44-4-4-444000-4-4404000000000000000000000000000000-44-4444-4-400044-40-4000000000000000000000000000000
χ924-4-444-4-44-44-400040000000000000000000000000000000-444-4-444-44-44000-40000000000000000000000000000000

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