Finite Group Databasebeta

← Group #239592

Character table — Group #239592

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888224444448888888844442222222244444444448888888822444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1
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
χ6111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111
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
χ922222222222-2-2-22-2-2-200000000002200-2-200000000000022222222222-2-2-22-2-2-200000000002200-2-2000000000000
χ1022222222222-2-2-22-2-2-20000000000-2-2002200000000000022222222222-2-2-22-2-2-20000000000-2-20022000000000000
χ1122222222-2-2-2222-22-2-2000000002200-2-20000000000000022222222-2-2-2222-22-2-2000000002200-2-200000000000000
χ1222222222-2-2-2222-22-2-200000000-2-200220000000000000022222222-2-2-2222-22-2-200000000-2-2002200000000000000
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
χ15222-2-2-22-20002-2-20200i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−200000000222-2-2-22-20002-2-20200i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−200000000
χ16222-2-2-22-20002-2-20200i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−22200000000222-2-2-22-20002-2-20200i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−22200000000
χ17222-2-2-22-20002-2-20200−i2−i2−i2−i2i2i2i2i200002i−2i00−2−22200000000222-2-2-22-20002-2-20200−i2−i2−i2−i2i2i2i2i200002i−2i00−2−22200000000
χ18222-2-2-22-20002-2-20200−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−200000000222-2-2-22-20002-2-20200−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−200000000
χ1922-2-222-2-22-2-2000200022−2−222−2−20000002i−2i0000i2i2−i2−i2000022-2-222-2-22-2-2000200022−2−222−2−20000002i−2i0000i2i2−i2−i20000
χ2022-2-222-2-22-2-2000200022−2−222−2−2000000−2i2i0000−i2−i2i2i2000022-2-222-2-22-2-2000200022−2−222−2−2000000−2i2i0000−i2−i2i2i20000
χ2122-2-222-2-22-2-20002000−2−222−2−2220000002i−2i0000−i2−i2i2i2000022-2-222-2-22-2-20002000−2−222−2−2220000002i−2i0000−i2−i2i2i20000
χ2222-2-222-2-22-2-20002000−2−222−2−222000000−2i2i0000i2i2−i2−i2000022-2-222-2-22-2-20002000−2−222−2−222000000−2i2i0000i2i2−i2−i20000
χ232-22-2-22-2222-2000-2000i2−i2i2−i2i2−i2i2−i2002i−2i000000002−22−200002-22-2-22-2222-2000-2000i2−i2i2−i2i2−i2i2−i2002i−2i000000002−22−20000
χ242-22-2-22-2222-2000-2000i2−i2i2−i2i2−i2i2−i200−2i2i00000000−22−2200002-22-2-22-2222-2000-2000i2−i2i2−i2i2−i2i2−i200−2i2i00000000−22−220000
χ252-22-2-22-2222-2000-2000−i2i2−i2i2−i2i2−i2i2002i−2i00000000−22−2200002-22-2-22-2222-2000-2000−i2i2−i2i2−i2i2−i2i2002i−2i00000000−22−220000
χ262-22-2-22-2222-2000-2000−i2i2−i2i2−i2i2−i2i200−2i2i000000002−22−200002-22-2-22-2222-2000-2000−i2i2−i2i2−i2i2−i2i200−2i2i000000002−22−20000
χ272-2-22-222-22-2222-2-2-2-22000000000000000000002i−2i−2i2i00002-2-22-222-22-2222-2-2-2-22000000000000000000002i−2i−2i2i0000
χ282-2-22-222-22-2222-2-2-2-2200000000000000000000−2i2i2i−2i00002-2-22-222-22-2222-2-2-2-2200000000000000000000−2i2i2i−2i0000
χ292-2-22-222-22-22-2-22-222-22i−2i−2i2i2i−2i−2i2i000000000000000000002-2-22-222-22-22-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000
χ302-2-22-222-22-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000002-2-22-222-22-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ312-2-22-222-2-22-222-22-22-2000000000000000000000000002i−2i2-2-22-222-2-22-222-22-22-2000000000000000000000000002i−2i
χ322-2-22-222-2-22-222-22-22-200000000000000000000000000−2i2i2-2-22-222-2-22-222-22-22-200000000000000000000000000−2i2i
χ332-2-22-222-2-22-2-2-2222-2200000000000000002-22-2000000002-2-22-222-2-22-2-2-2222-2200000000000000002-22-200000000
χ342-2-22-222-2-22-2-2-2222-220000000000000000-22-22000000002-2-22-222-2-22-2-2-2222-220000000000000000-22-2200000000
χ352-2-2-22-222000-22-202002−2−22−222−22-20000002−2−22000000002-2-2-22-222000-22-202002−2−22−222−22-20000002−2−2200000000
χ362-2-2-22-222000-22-202002−2−22−222−2-22000000−222−2000000002-2-2-22-222000-22-202002−2−22−222−2-22000000−222−200000000
χ372-2-2-22-222000-22-20200−222−22−2−222-2000000−222−2000000002-2-2-22-222000-22-20200−222−22−2−222-2000000−222−200000000
χ382-2-2-22-222000-22-20200−222−22−2−22-220000002−2−22000000002-2-2-22-222000-22-20200−222−22−2−22-220000002−2−2200000000
χ39444-4-4-44-4000-4440-4000000000000000000000000000000444-4-4-44-4000-4440-4000000000000000000000000000000
χ4044-44-4-4-4400000000002i2i−2i−2i−2i−2i2i2i0000000000000000000044-44-4-4-4400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4144-44-4-4-440000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000044-44-4-4-440000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4244-4-444-4-4-444000-4000000000000000000000000000000044-4-444-4-4-444000-40000000000000000000000000000000
χ434-4444-4-4-400000000002-22-2-22-22000000000000000000004-4444-4-4-400000000002-22-2-22-2200000000000000000000
χ444-4444-4-4-40000000000-22-222-22-2000000000000000000004-4444-4-4-40000000000-22-222-22-200000000000000000000
χ454-44-4-44-44-4-44000400000000000000000000000000000004-44-4-44-44-4-4400040000000000000000000000000000000
χ464-4-4-44-4440004-440-40000000000000000000000000000004-4-4-44-4440004-440-4000000000000000000000000000000
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
χ481111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111
χ4911111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
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
χ52111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1
χ53111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1
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
χ5522222222222-2-2-22-2-2-200000000002200-2-2000000000000-2-2-2-2-2-2-2-2-2-2-2222-22220000000000-2-20022000000000000
χ5622222222222-2-2-22-2-2-20000000000-2-20022000000000000-2-2-2-2-2-2-2-2-2-2-2222-222200000000002200-2-2000000000000
χ5722222222-2-2-2222-22-2-2000000002200-2-200000000000000-2-2-2-2-2-2-2-2222-2-2-22-22200000000-2-2002200000000000000
χ5822222222-2-2-2222-22-2-200000000-2-2002200000000000000-2-2-2-2-2-2-2-2222-2-2-22-222000000002200-2-200000000000000
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
χ61222-2-2-22-20002-2-20200i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−200000000-2-2-2222-22000-2220-200−i2−i2−i2−i2i2i2i2i20000−2i2i00−2−22200000000
χ62222-2-2-22-20002-2-20200i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−22200000000-2-2-2222-22000-2220-200−i2−i2−i2−i2i2i2i2i200002i−2i0022−2−200000000
χ63222-2-2-22-20002-2-20200−i2−i2−i2−i2i2i2i2i200002i−2i00−2−22200000000-2-2-2222-22000-2220-200i2i2i2i2−i2−i2−i2−i20000−2i2i0022−2−200000000
χ64222-2-2-22-20002-2-20200−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−200000000-2-2-2222-22000-2220-200i2i2i2i2−i2−i2−i2−i200002i−2i00−2−22200000000
χ6522-2-222-2-22-2-2000200022−2−222−2−20000002i−2i0000i2i2−i2−i20000-2-222-2-222-222000-2000−2−222−2−222000000−2i2i0000−i2−i2i2i20000
χ6622-2-222-2-22-2-2000200022−2−222−2−2000000−2i2i0000−i2−i2i2i20000-2-222-2-222-222000-2000−2−222−2−2220000002i−2i0000i2i2−i2−i20000
χ6722-2-222-2-22-2-20002000−2−222−2−2220000002i−2i0000−i2−i2i2i20000-2-222-2-222-222000-200022−2−222−2−2000000−2i2i0000i2i2−i2−i20000
χ6822-2-222-2-22-2-20002000−2−222−2−222000000−2i2i0000i2i2−i2−i20000-2-222-2-222-222000-200022−2−222−2−20000002i−2i0000−i2−i2i2i20000
χ692-22-2-22-2222-2000-2000i2−i2i2−i2i2−i2i2−i2002i−2i000000002−22−20000-22-222-22-2-2-220002000−i2i2−i2i2−i2i2−i2i200−2i2i00000000−22−220000
χ702-22-2-22-2222-2000-2000i2−i2i2−i2i2−i2i2−i200−2i2i00000000−22−220000-22-222-22-2-2-220002000−i2i2−i2i2−i2i2−i2i2002i−2i000000002−22−20000
χ712-22-2-22-2222-2000-2000−i2i2−i2i2−i2i2−i2i2002i−2i00000000−22−220000-22-222-22-2-2-220002000i2−i2i2−i2i2−i2i2−i200−2i2i000000002−22−20000
χ722-22-2-22-2222-2000-2000−i2i2−i2i2−i2i2−i2i200−2i2i000000002−22−20000-22-222-22-2-2-220002000i2−i2i2−i2i2−i2i2−i2002i−2i00000000−22−220000
χ732-2-22-222-22-2222-2-2-2-22000000000000000000002i−2i−2i2i0000-222-22-2-22-22-2-2-22222-200000000000000000000−2i2i2i−2i0000
χ742-2-22-222-22-2222-2-2-2-2200000000000000000000−2i2i2i−2i0000-222-22-2-22-22-2-2-22222-2000000000000000000002i−2i−2i2i0000
χ752-2-22-222-22-22-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000-222-22-2-22-22-222-22-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ762-2-22-222-22-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000-222-22-2-22-22-222-22-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000
χ772-2-22-222-2-22-222-22-22-2000000000000000000000000002i−2i-222-22-2-222-22-2-22-22-2200000000000000000000000000−2i2i
χ782-2-22-222-2-22-222-22-22-200000000000000000000000000−2i2i-222-22-2-222-22-2-22-22-22000000000000000000000000002i−2i
χ792-2-22-222-2-22-2-2-2222-2200000000000000002-22-200000000-222-22-2-222-2222-2-2-22-20000000000000000-22-2200000000
χ802-2-22-222-2-22-2-2-2222-220000000000000000-22-2200000000-222-22-2-222-2222-2-2-22-200000000000000002-22-200000000
χ812-2-2-22-222000-22-202002−2−22−222−22-20000002−2−2200000000-2222-22-2-20002-220-200−222−22−2−22-22000000−222−200000000
χ822-2-2-22-222000-22-202002−2−22−222−2-22000000−222−200000000-2222-22-2-20002-220-200−222−22−2−222-20000002−2−2200000000
χ832-2-2-22-222000-22-20200−222−22−2−222-2000000−222−200000000-2222-22-2-20002-220-2002−2−22−222−2-220000002−2−2200000000
χ842-2-2-22-222000-22-20200−222−22−2−22-220000002−2−2200000000-2222-22-2-20002-220-2002−2−22−222−22-2000000−222−200000000
χ85444-4-4-44-4000-4440-4000000000000000000000000000000-4-4-4444-440004-4-404000000000000000000000000000000
χ8644-44-4-4-4400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000-4-44-4444-40000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ8744-44-4-4-440000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000-4-44-4444-400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ8844-4-444-4-4-444000-40000000000000000000000000000000-4-444-4-4444-4-400040000000000000000000000000000000
χ894-4444-4-4-400000000002-22-2-22-2200000000000000000000-44-4-4-44440000000000-22-222-22-200000000000000000000
χ904-4444-4-4-40000000000-22-222-22-200000000000000000000-44-4-4-444400000000002-22-2-22-2200000000000000000000
χ914-44-4-44-44-4-4400040000000000000000000000000000000-44-444-44-444-4000-40000000000000000000000000000000
χ924-4-4-44-4440004-440-4000000000000000000000000000000-4444-44-4-4000-44-404000000000000000000000000000000

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