Finite Group Databasebeta

← Group #235652

Character table — Group #235652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888444444448888888822442222222244444444448888888844444444888888882244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
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
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
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
χ922222222222-2-2-22-2-2-20000000022-2-2000000000000000022222222222-2-2-22-2-2-20000000022-2-20000000000000000
χ1022222222222-2-2-22-2-2-200000000-2-222000000000000000022222222222-2-2-22-2-2-200000000-2-2220000000000000000
χ1122222222-2-2-2222-22-2-200000000000022-2-200000000000022222222-2-2-2222-22-2-200000000000022-2-2000000000000
χ1222222222-2-2-2222-22-2-2000000000000-2-22200000000000022222222-2-2-2222-22-2-2000000000000-2-222000000000000
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
χ15222-2-2-2-2200022-20-2002222−2−2−2−200002i−2i000000i2i2−i2−i20000222-2-2-2-2200022-20-2002222−2−2−2−200002i−2i000000i2i2−i2−i20000
χ16222-2-2-2-2200022-20-2002222−2−2−2−20000−2i2i000000−i2−i2i2i20000222-2-2-2-2200022-20-2002222−2−2−2−20000−2i2i000000−i2−i2i2i20000
χ17222-2-2-2-2200022-20-200−2−2−2−2222200002i−2i000000−i2−i2i2i20000222-2-2-2-2200022-20-200−2−2−2−2222200002i−2i000000−i2−i2i2i20000
χ18222-2-2-2-2200022-20-200−2−2−2−222220000−2i2i000000i2i2−i2−i20000222-2-2-2-2200022-20-200−2−2−2−222220000−2i2i000000i2i2−i2−i20000
χ1922-222-2-2-22-2-20002000i2i2−i2−i2i2i2−i2−i2002i−2i000022−2−20000000022-222-2-2-22-2-20002000i2i2−i2−i2i2i2−i2−i2002i−2i000022−2−200000000
χ2022-222-2-2-22-2-20002000i2i2−i2−i2i2i2−i2−i200−2i2i0000−2−2220000000022-222-2-2-22-2-20002000i2i2−i2−i2i2i2−i2−i200−2i2i0000−2−22200000000
χ2122-222-2-2-22-2-20002000−i2−i2i2i2−i2−i2i2i2002i−2i0000−2−2220000000022-222-2-2-22-2-20002000−i2−i2i2i2−i2−i2i2i2002i−2i0000−2−22200000000
χ2222-222-2-2-22-2-20002000−i2−i2i2i2−i2−i2i2i200−2i2i000022−2−20000000022-222-2-2-22-2-20002000−i2−i2i2i2−i2−i2i2i200−2i2i000022−2−200000000
χ232-222-22-2-2-22-20002000i2−i2i2−i2i2−i2i2−i22i−2i0000002−22−2000000002-222-22-2-2-22-20002000i2−i2i2−i2i2−i2i2−i22i−2i0000002−22−200000000
χ242-222-22-2-2-22-20002000i2−i2i2−i2i2−i2i2−i2−2i2i000000−22−22000000002-222-22-2-2-22-20002000i2−i2i2−i2i2−i2i2−i2−2i2i000000−22−2200000000
χ252-222-22-2-2-22-20002000−i2i2−i2i2−i2i2−i2i22i−2i000000−22−22000000002-222-22-2-2-22-20002000−i2i2−i2i2−i2i2−i2i22i−2i000000−22−2200000000
χ262-222-22-2-2-22-20002000−i2i2−i2i2−i2i2−i2i2−2i2i0000002−22−2000000002-222-22-2-2-22-20002000−i2i2−i2i2−i2i2−i2i2−2i2i0000002−22−200000000
χ272-2-22-2-22222-22-22-2-22-2000000000000000000002i−2i2i−2i00002-2-22-2-22222-22-22-2-22-2000000000000000000002i−2i2i−2i0000
χ282-2-22-2-22222-22-22-2-22-200000000000000000000−2i2i−2i2i00002-2-22-2-22222-22-22-2-22-200000000000000000000−2i2i−2i2i0000
χ292-2-22-2-22222-2-22-2-22-22000000000000000000000000002-22-2-22-2-22222-2-22-2-22-22000000000000000000000000002-2
χ302-2-22-2-22222-2-22-2-22-2200000000000000000000000000-222-2-22-2-22222-2-22-2-22-2200000000000000000000000000-22
χ312-2-22-2-222-2-222-222-2-222-2-222-2-22000000000000000000002-2-22-2-222-2-222-222-2-222-2-222-2-2200000000000000000000
χ322-2-22-2-222-2-222-222-2-22-222-2-222-2000000000000000000002-2-22-2-222-2-222-222-2-22-222-2-222-200000000000000000000
χ332-2-22-2-222-2-22-22-2222-200000000000000002-2-22000000002-2-22-2-222-2-22-22-2222-200000000000000002-2-2200000000
χ342-2-22-2-222-2-22-22-2222-20000000000000000-222-2000000002-2-22-2-222-2-22-22-2222-20000000000000000-222-200000000
χ352-2-2-222-220002-2-202002−2−22−222−20000002-200002−2−2200002-2-2-222-220002-2-202002−2−22−222−20000002-200002−2−220000
χ362-2-2-222-220002-2-202002−2−22−222−2000000-220000−222−200002-2-2-222-220002-2-202002−2−22−222−2000000-220000−222−20000
χ372-2-2-222-220002-2-20200−222−22−2−220000002-20000−222−200002-2-2-222-220002-2-20200−222−22−2−220000002-20000−222−20000
χ382-2-2-222-220002-2-20200−222−22−2−22000000-2200002−2−2200002-2-2-222-220002-2-20200−222−22−2−22000000-2200002−2−220000
χ39444-4-4-4-44000-4-4404000000000000000000000000000000444-4-4-4-44000-4-4404000000000000000000000000000000
χ4044-444-4-4-4-444000-4000000000000000000000000000000044-444-4-4-4-444000-40000000000000000000000000000000
χ4144-4-4-444-400000000002i2i−2i−2i−2i−2i2i2i0000000000000000000044-4-4-444-400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4244-4-4-444-40000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000044-4-4-444-40000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ434-444-44-4-44-44000-400000000000000000000000000000004-444-44-4-44-44000-40000000000000000000000000000000
χ444-44-44-44-400000000002i−2i2i−2i−2i2i−2i2i000000000000000000004-44-44-44-400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ454-44-44-44-40000000000−2i2i−2i2i2i−2i2i−2i000000000000000000004-44-44-44-40000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ464-4-4-444-44000-4440-40000000000000000000000000000004-4-4-444-44000-4440-4000000000000000000000000000000
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
χ48111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ4911111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
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
χ52111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ53111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
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
χ5522222222222-2-2-22-2-2-20000000022-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2222-222200000000-2-2220000000000000000
χ5622222222222-2-2-22-2-2-200000000-2-2220000000000000000-2-2-2-2-2-2-2-2-2-2-2222-22220000000022-2-20000000000000000
χ5722222222-2-2-2222-22-2-200000000000022-2-2000000000000-2-2-2-2-2-2-2-2222-2-2-22-222000000000000-2-222000000000000
χ5822222222-2-2-2222-22-2-2000000000000-2-222000000000000-2-2-2-2-2-2-2-2222-2-2-22-22200000000000022-2-2000000000000
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
χ61222-2-2-2-2200022-20-2002222−2−2−2−200002i−2i000000i2i2−i2−i20000-2-2-22222-2000-2-220200−2−2−2−222220000−2i2i000000−i2−i2i2i20000
χ62222-2-2-2-2200022-20-2002222−2−2−2−20000−2i2i000000−i2−i2i2i20000-2-2-22222-2000-2-220200−2−2−2−2222200002i−2i000000i2i2−i2−i20000
χ63222-2-2-2-2200022-20-200−2−2−2−2222200002i−2i000000−i2−i2i2i20000-2-2-22222-2000-2-2202002222−2−2−2−20000−2i2i000000i2i2−i2−i20000
χ64222-2-2-2-2200022-20-200−2−2−2−222220000−2i2i000000i2i2−i2−i20000-2-2-22222-2000-2-2202002222−2−2−2−200002i−2i000000−i2−i2i2i20000
χ6522-222-2-2-22-2-20002000i2i2−i2−i2i2i2−i2−i2002i−2i000022−2−200000000-2-22-2-2222-222000-2000−i2−i2i2i2−i2−i2i2i200−2i2i0000−2−22200000000
χ6622-222-2-2-22-2-20002000i2i2−i2−i2i2i2−i2−i200−2i2i0000−2−22200000000-2-22-2-2222-222000-2000−i2−i2i2i2−i2−i2i2i2002i−2i000022−2−200000000
χ6722-222-2-2-22-2-20002000−i2−i2i2i2−i2−i2i2i2002i−2i0000−2−22200000000-2-22-2-2222-222000-2000i2i2−i2−i2i2i2−i2−i200−2i2i000022−2−200000000
χ6822-222-2-2-22-2-20002000−i2−i2i2i2−i2−i2i2i200−2i2i000022−2−200000000-2-22-2-2222-222000-2000i2i2−i2−i2i2i2−i2−i2002i−2i0000−2−22200000000
χ692-222-22-2-2-22-20002000i2−i2i2−i2i2−i2i2−i22i−2i0000002−22−200000000-22-2-22-2222-22000-2000−i2i2−i2i2−i2i2−i2i2−2i2i000000−22−2200000000
χ702-222-22-2-2-22-20002000i2−i2i2−i2i2−i2i2−i2−2i2i000000−22−2200000000-22-2-22-2222-22000-2000−i2i2−i2i2−i2i2−i2i22i−2i0000002−22−200000000
χ712-222-22-2-2-22-20002000−i2i2−i2i2−i2i2−i2i22i−2i000000−22−2200000000-22-2-22-2222-22000-2000i2−i2i2−i2i2−i2i2−i2−2i2i0000002−22−200000000
χ722-222-22-2-2-22-20002000−i2i2−i2i2−i2i2−i2i2−2i2i0000002−22−200000000-22-2-22-2222-22000-2000i2−i2i2−i2i2−i2i2−i22i−2i000000−22−2200000000
χ732-2-22-2-22222-22-22-2-22-2000000000000000000002i−2i2i−2i0000-222-222-2-2-2-22-22-222-2200000000000000000000−2i2i−2i2i0000
χ742-2-22-2-22222-22-22-2-22-200000000000000000000−2i2i−2i2i0000-222-222-2-2-2-22-22-222-22000000000000000000002i−2i2i−2i0000
χ752-2-22-2-22222-2-22-2-22-22000000000000000000000000002-2-222-222-2-2-2-222-222-22-200000000000000000000000000-22
χ762-2-22-2-22222-2-22-2-22-2200000000000000000000000000-22-222-222-2-2-2-222-222-22-2000000000000000000000000002-2
χ772-2-22-2-222-2-222-222-2-222-2-222-2-2200000000000000000000-222-222-2-222-2-22-2-222-2-222-2-222-200000000000000000000
χ782-2-22-2-222-2-222-222-2-22-222-2-222-200000000000000000000-222-222-2-222-2-22-2-222-22-2-222-2-2200000000000000000000
χ792-2-22-2-222-2-22-22-2222-200000000000000002-2-2200000000-222-222-2-222-22-22-2-2-220000000000000000-222-200000000
χ802-2-22-2-222-2-22-22-2222-20000000000000000-222-200000000-222-222-2-222-22-22-2-2-2200000000000000002-2-2200000000
χ812-2-2-222-220002-2-202002−2−22−222−20000002-200002−2−220000-2222-2-22-2000-2220-200−222−22−2−22000000-220000−222−20000
χ822-2-2-222-220002-2-202002−2−22−222−2000000-220000−222−20000-2222-2-22-2000-2220-200−222−22−2−220000002-200002−2−220000
χ832-2-2-222-220002-2-20200−222−22−2−220000002-20000−222−20000-2222-2-22-2000-2220-2002−2−22−222−2000000-2200002−2−220000
χ842-2-2-222-220002-2-20200−222−22−2−22000000-2200002−2−220000-2222-2-22-2000-2220-2002−2−22−222−20000002-20000−222−20000
χ85444-4-4-4-44000-4-4404000000000000000000000000000000-4-4-44444-400044-40-4000000000000000000000000000000
χ8644-444-4-4-4-444000-40000000000000000000000000000000-4-44-4-44444-4-400040000000000000000000000000000000
χ8744-4-4-444-400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000-4-4444-4-440000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ8844-4-4-444-40000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000-4-4444-4-4400000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ894-444-44-4-44-44000-40000000000000000000000000000000-44-4-44-444-44-400040000000000000000000000000000000
χ904-44-44-44-400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000-44-44-44-440000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ914-44-44-44-40000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000-44-44-44-4400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ924-4-4-444-44000-4440-4000000000000000000000000000000-4444-4-44-40004-4-404000000000000000000000000000000

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