Finite Group Databasebeta

← Group #243155

Character table — Group #243155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888444488888888888844442222222244444444448888888844448888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
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
χ92222222222-2-22-2-22-2-22222-2-2-2-2000000000000000000002222222222-2-22-2-22-2-22222-2-2-2-200000000000000000000
χ102222222222-2-22-2-22-2-2-2-2-2-22222000000000000000000002222222222-2-22-2-22-2-2-2-2-2-2222200000000000000000000
χ1122222222-2-222-222-2-2-20000000022-2-2000000000000000022222222-2-222-222-2-2-20000000022-2-20000000000000000
χ1222222222-2-222-222-2-2-200000000-2-222000000000000000022222222-2-222-222-2-2-200000000-2-2220000000000000000
χ1322222222-2-2-2-2-2-2-2-222000000000000000000002i2i−2i−2i000022222222-2-2-2-2-2-2-2-222000000000000000000002i2i−2i−2i0000
χ1422222222-2-2-2-2-2-2-2-22200000000000000000000−2i−2i2i2i000022222222-2-2-2-2-2-2-2-22200000000000000000000−2i−2i2i2i0000
χ15222-2-2-22-22-200-2002002i2i−2i−2i00000000i2i2−i2−i222−2−200000000222-2-2-22-22-200-2002002i2i−2i−2i00000000i2i2−i2−i222−2−200000000
χ16222-2-2-22-22-200-2002002i2i−2i−2i00000000−i2−i2i2i2−2−22200000000222-2-2-22-22-200-2002002i2i−2i−2i00000000−i2−i2i2i2−2−22200000000
χ17222-2-2-22-22-200-200200−2i−2i2i2i00000000i2i2−i2−i2−2−22200000000222-2-2-22-22-200-200200−2i−2i2i2i00000000i2i2−i2−i2−2−22200000000
χ18222-2-2-22-22-200-200200−2i−2i2i2i00000000−i2−i2i2i222−2−200000000222-2-2-22-22-200-200200−2i−2i2i2i00000000−i2−i2i2i222−2−200000000
χ192-2222-2-2-2222-2-22-2-22-200000000000000002-22-2000000002-2222-2-2-2222-2-22-2-22-200000000000000002-22-200000000
χ202-2222-2-2-2222-2-22-2-22-20000000000000000-22-22000000002-2222-2-2-2222-2-22-2-22-20000000000000000-22-2200000000
χ212-2222-2-2-222-22-2-22-2-220000000000002-22-20000000000002-2222-2-2-222-22-2-22-2-220000000000002-22-2000000000000
χ222-2222-2-2-222-22-2-22-2-22000000000000-22-220000000000002-2222-2-2-222-22-2-22-2-22000000000000-22-22000000000000
χ232-2222-2-2-2-2-22-222-22-22000000000000000000000000002i−2i2-2222-2-2-2-2-22-222-22-22000000000000000000000000002i−2i
χ242-2222-2-2-2-2-22-222-22-2200000000000000000000000000−2i2i2-2222-2-2-2-2-22-222-22-2200000000000000000000000000−2i2i
χ252-2222-2-2-2-2-2-222-2222-20000000000000000000000002i−2i002-2222-2-2-2-2-2-222-2222-20000000000000000000000002i−2i00
χ262-2222-2-2-2-2-2-222-2222-2000000000000000000000000−2i2i002-2222-2-2-2-2-2-222-2222-2000000000000000000000000−2i2i00
χ272-22-2-22-222-200200-20000002i2i−2i−2i0000i2−i2−i2i22−2−22000000002-22-2-22-222-200200-20000002i2i−2i−2i0000i2−i2−i2i22−2−2200000000
χ282-22-2-22-222-200200-20000002i2i−2i−2i0000−i2i2i2−i2−222−2000000002-22-2-22-222-200200-20000002i2i−2i−2i0000−i2i2i2−i2−222−200000000
χ292-22-2-22-222-200200-2000000−2i−2i2i2i0000i2−i2−i2i2−222−2000000002-22-2-22-222-200200-2000000−2i−2i2i2i0000i2−i2−i2i2−222−200000000
χ302-22-2-22-222-200200-2000000−2i−2i2i2i0000−i2i2i2−i22−2−22000000002-22-2-22-222-200200-2000000−2i−2i2i2i0000−i2i2i2−i22−2−2200000000
χ312-2-22-222-2002-20-22000i2−i2i2−i2i2−i2i2−i22-20000000000i2−i2i2−i200002-2-22-222-2002-20-22000i2−i2i2−i2i2−i2i2−i22-20000000000i2−i2i2−i20000
χ322-2-22-222-2002-20-22000i2−i2i2−i2i2−i2i2−i2-220000000000−i2i2−i2i200002-2-22-222-2002-20-22000i2−i2i2−i2i2−i2i2−i2-220000000000−i2i2−i2i20000
χ332-2-22-222-2002-20-22000−i2i2−i2i2−i2i2−i2i22-20000000000−i2i2−i2i200002-2-22-222-2002-20-22000−i2i2−i2i2−i2i2−i2i22-20000000000−i2i2−i2i20000
χ342-2-22-222-2002-20-22000−i2i2−i2i2−i2i2−i2i2-220000000000i2−i2i2−i200002-2-22-222-2002-20-22000−i2i2−i2i2−i2i2−i2i2-220000000000i2−i2i2−i20000
χ352-2-22-222-200-2202-2000i2−i2i2−i2−i2i2−i2i2002i−2i000000002−2−2200002-2-22-222-200-2202-2000i2−i2i2−i2−i2i2−i2i2002i−2i000000002−2−220000
χ362-2-22-222-200-2202-2000i2−i2i2−i2−i2i2−i2i200−2i2i00000000−222−200002-2-22-222-200-2202-2000i2−i2i2−i2−i2i2−i2i200−2i2i00000000−222−20000
χ372-2-22-222-200-2202-2000−i2i2−i2i2i2−i2i2−i2002i−2i00000000−222−200002-2-22-222-200-2202-2000−i2i2−i2i2i2−i2i2−i2002i−2i00000000−222−20000
χ382-2-22-222-200-2202-2000−i2i2−i2i2i2−i2i2−i200−2i2i000000002−2−2200002-2-22-222-200-2202-2000−i2i2−i2i2i2−i2i2−i200−2i2i000000002−2−220000
χ39444-4-4-44-4-4400400-4000000000000000000000000000000444-4-4-44-4-4400400-4000000000000000000000000000000
χ4044-44-4-4-4400440-4-4000000000000000000000000000000044-44-4-4-4400440-4-40000000000000000000000000000000
χ4144-44-4-4-4400-4-4044000000000000000000000000000000044-44-4-4-4400-4-40440000000000000000000000000000000
χ4244-4-444-4-40000000000000022−22−22220000000000000000000044-4-444-4-40000000000000022−22−222200000000000000000000
χ4344-4-444-4-400000000000000−222222−220000000000000000000044-4-444-4-400000000000000−222222−2200000000000000000000
χ444-44-4-44-44-4400-40040000000000000000000000000000004-44-4-44-44-4400-4004000000000000000000000000000000
χ454-4-4-44-444000000000022−22−22220000000000000000000000004-4-4-44-444000000000022−22−2222000000000000000000000000
χ464-4-4-44-4440000000000−222222−220000000000000000000000004-4-4-44-4440000000000−222222−22000000000000000000000000
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
χ48111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ4911111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
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
χ52111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1
χ53111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1
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
χ552222222222-2-22-2-22-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-222-222-222-2-2-2-2222200000000000000000000
χ562222222222-2-22-2-22-2-2-2-2-2-2222200000000000000000000-2-2-2-2-2-2-2-2-2-222-222-2222222-2-2-2-200000000000000000000
χ5722222222-2-222-222-2-2-20000000022-2-20000000000000000-2-2-2-2-2-2-2-222-2-22-2-222200000000-2-2220000000000000000
χ5822222222-2-222-222-2-2-200000000-2-2220000000000000000-2-2-2-2-2-2-2-222-2-22-2-22220000000022-2-20000000000000000
χ5922222222-2-2-2-2-2-2-2-222000000000000000000002i2i−2i−2i0000-2-2-2-2-2-2-2-222222222-2-200000000000000000000−2i−2i2i2i0000
χ6022222222-2-2-2-2-2-2-2-22200000000000000000000−2i−2i2i2i0000-2-2-2-2-2-2-2-222222222-2-2000000000000000000002i2i−2i−2i0000
χ61222-2-2-22-22-200-2002002i2i−2i−2i00000000i2i2−i2−i222−2−200000000-2-2-2222-22-2200200-200−2i−2i2i2i00000000−i2−i2i2i2−2−22200000000
χ62222-2-2-22-22-200-2002002i2i−2i−2i00000000−i2−i2i2i2−2−22200000000-2-2-2222-22-2200200-200−2i−2i2i2i00000000i2i2−i2−i222−2−200000000
χ63222-2-2-22-22-200-200200−2i−2i2i2i00000000i2i2−i2−i2−2−22200000000-2-2-2222-22-2200200-2002i2i−2i−2i00000000−i2−i2i2i222−2−200000000
χ64222-2-2-22-22-200-200200−2i−2i2i2i00000000−i2−i2i2i222−2−200000000-2-2-2222-22-2200200-2002i2i−2i−2i00000000i2i2−i2−i2−2−22200000000
χ652-2222-2-2-2222-2-22-2-22-200000000000000002-22-200000000-22-2-2-2222-2-2-222-222-220000000000000000-22-2200000000
χ662-2222-2-2-2222-2-22-2-22-20000000000000000-22-2200000000-22-2-2-2222-2-2-222-222-2200000000000000002-22-200000000
χ672-2222-2-2-222-22-2-22-2-220000000000002-22-2000000000000-22-2-2-2222-2-22-222-222-2000000000000-22-22000000000000
χ682-2222-2-2-222-22-2-22-2-22000000000000-22-22000000000000-22-2-2-2222-2-22-222-222-20000000000002-22-2000000000000
χ692-2222-2-2-2-2-22-222-22-22000000000000000000000000002i−2i-22-2-2-222222-22-2-22-22-200000000000000000000000000−2i2i
χ702-2222-2-2-2-2-22-222-22-2200000000000000000000000000−2i2i-22-2-2-222222-22-2-22-22-2000000000000000000000000002i−2i
χ712-2222-2-2-2-2-2-222-2222-20000000000000000000000002i−2i00-22-2-2-2222222-2-22-2-2-22000000000000000000000000−2i2i00
χ722-2222-2-2-2-2-2-222-2222-2000000000000000000000000−2i2i00-22-2-2-2222222-2-22-2-2-220000000000000000000000002i−2i00
χ732-22-2-22-222-200200-20000002i2i−2i−2i0000i2−i2−i2i22−2−2200000000-22-222-22-2-2200-2002000000−2i−2i2i2i0000−i2i2i2−i2−222−200000000
χ742-22-2-22-222-200200-20000002i2i−2i−2i0000−i2i2i2−i2−222−200000000-22-222-22-2-2200-2002000000−2i−2i2i2i0000i2−i2−i2i22−2−2200000000
χ752-22-2-22-222-200200-2000000−2i−2i2i2i0000i2−i2−i2i2−222−200000000-22-222-22-2-2200-20020000002i2i−2i−2i0000−i2i2i2−i22−2−2200000000
χ762-22-2-22-222-200200-2000000−2i−2i2i2i0000−i2i2i2−i22−2−2200000000-22-222-22-2-2200-20020000002i2i−2i−2i0000i2−i2−i2i2−222−200000000
χ772-2-22-222-2002-20-22000i2−i2i2−i2i2−i2i2−i22-20000000000i2−i2i2−i20000-222-22-2-2200-2202-2000−i2i2−i2i2−i2i2−i2i2-220000000000−i2i2−i2i20000
χ782-2-22-222-2002-20-22000i2−i2i2−i2i2−i2i2−i2-220000000000−i2i2−i2i20000-222-22-2-2200-2202-2000−i2i2−i2i2−i2i2−i2i22-20000000000i2−i2i2−i20000
χ792-2-22-222-2002-20-22000−i2i2−i2i2−i2i2−i2i22-20000000000−i2i2−i2i20000-222-22-2-2200-2202-2000i2−i2i2−i2i2−i2i2−i2-220000000000i2−i2i2−i20000
χ802-2-22-222-2002-20-22000−i2i2−i2i2−i2i2−i2i2-220000000000i2−i2i2−i20000-222-22-2-2200-2202-2000i2−i2i2−i2i2−i2i2−i22-20000000000−i2i2−i2i20000
χ812-2-22-222-200-2202-2000i2−i2i2−i2−i2i2−i2i2002i−2i000000002−2−220000-222-22-2-22002-20-22000−i2i2−i2i2i2−i2i2−i200−2i2i00000000−222−20000
χ822-2-22-222-200-2202-2000i2−i2i2−i2−i2i2−i2i200−2i2i00000000−222−20000-222-22-2-22002-20-22000−i2i2−i2i2i2−i2i2−i2002i−2i000000002−2−220000
χ832-2-22-222-200-2202-2000−i2i2−i2i2i2−i2i2−i2002i−2i00000000−222−20000-222-22-2-22002-20-22000i2−i2i2−i2−i2i2−i2i200−2i2i000000002−2−220000
χ842-2-22-222-200-2202-2000−i2i2−i2i2i2−i2i2−i200−2i2i000000002−2−220000-222-22-2-22002-20-22000i2−i2i2−i2−i2i2−i2i2002i−2i00000000−222−20000
χ85444-4-4-44-4-4400400-4000000000000000000000000000000-4-4-4444-444-400-4004000000000000000000000000000000
χ8644-44-4-4-4400440-4-40000000000000000000000000000000-4-44-4444-400-4-40440000000000000000000000000000000
χ8744-44-4-4-4400-4-40440000000000000000000000000000000-4-44-4444-400440-4-40000000000000000000000000000000
χ8844-4-444-4-40000000000000022−22−222200000000000000000000-4-444-4-44400000000000000−222222−2200000000000000000000
χ8944-4-444-4-400000000000000−222222−2200000000000000000000-4-444-4-4440000000000000022−22−222200000000000000000000
χ904-44-4-44-44-4400-4004000000000000000000000000000000-44-444-44-44-400400-4000000000000000000000000000000
χ914-4-4-44-444000000000022−22−2222000000000000000000000000-4444-44-4-40000000000−222222−22000000000000000000000000
χ924-4-4-44-4440000000000−222222−22000000000000000000000000-4444-44-4-4000000000022−22−2222000000000000000000000000

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