Finite Group Databasebeta

← Group #239593

Character table — Group #239593

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
χ922222222222-2-2-22-2-2-200000000220000-2-200000000000022222222222-2-2-22-2-2-200000000220000-2-2000000000000
χ1022222222222-2-2-22-2-2-200000000-2-200002200000000000022222222222-2-2-22-2-2-200000000-2-2000022000000000000
χ1122222222-2-2-2222-22-2-2000000000022-2-20000000000000022222222-2-2-2222-22-2-2000000000022-2-200000000000000
χ1222222222-2-2-2222-22-2-20000000000-2-2220000000000000022222222-2-2-2222-22-2-20000000000-2-22200000000000000
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
χ15222-2-2-22-22-2-20002000i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i200000000222-2-2-22-22-2-20002000i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i200000000
χ16222-2-2-22-22-2-20002000i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i200000000222-2-2-22-22-2-20002000i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i200000000
χ17222-2-2-22-22-2-20002000−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i200000000222-2-2-22-22-2-20002000−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i200000000
χ18222-2-2-22-22-2-20002000−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i200000000222-2-2-22-22-2-20002000−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i200000000
χ1922-2-22-2-2200022-20-200i2i2−i2−i2i2i2−i2−i200002-2000000i2i2−i2−i2000022-2-22-2-2200022-20-200i2i2−i2−i2i2i2−i2−i200002-2000000i2i2−i2−i20000
χ2022-2-22-2-2200022-20-200i2i2−i2−i2i2i2−i2−i20000-22000000−i2−i2i2i2000022-2-22-2-2200022-20-200i2i2−i2−i2i2i2−i2−i20000-22000000−i2−i2i2i20000
χ2122-2-22-2-2200022-20-200−i2−i2i2i2−i2−i2i2i200002-2000000−i2−i2i2i2000022-2-22-2-2200022-20-200−i2−i2i2i2−i2−i2i2i200002-2000000−i2−i2i2i20000
χ2222-2-22-2-2200022-20-200−i2−i2i2i2−i2−i2i2i20000-22000000i2i2−i2−i2000022-2-22-2-2200022-20-200−i2−i2i2i2−i2−i2i2i20000-22000000i2i2−i2−i20000
χ232-222-2-2-2222-22-22-2-2-22000000000000000000002i−2i2i−2i00002-222-2-2-2222-22-22-2-2-22000000000000000000002i−2i2i−2i0000
χ242-222-2-2-2222-22-22-2-2-2200000000000000000000−2i2i−2i2i00002-222-2-2-2222-22-22-2-2-2200000000000000000000−2i2i−2i2i0000
χ252-222-2-2-2222-2-22-2-222-20000000000000000000000002i−2i002-222-2-2-2222-2-22-2-222-20000000000000000000000002i−2i00
χ262-222-2-2-2222-2-22-2-222-2000000000000000000000000−2i2i002-222-2-2-2222-2-22-2-222-2000000000000000000000000−2i2i00
χ272-222-2-2-22-2-222-222-22-22i−2i2i−2i2i−2i2i−2i000000000000000000002-222-2-2-22-2-222-222-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000
χ282-222-2-2-22-2-222-222-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000002-222-2-2-22-2-222-222-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ292-222-2-2-22-2-22-22-222-2200000000000000002-22-2000000002-222-2-2-22-2-22-22-222-2200000000000000002-22-200000000
χ302-222-2-2-22-2-22-22-222-220000000000000000-22-22000000002-222-2-2-22-2-22-22-222-220000000000000000-22-2200000000
χ312-22-222-2-2-22-200020002−22−2−22−220000002i−2ii2−i2−i2i2000000002-22-222-2-2-22-200020002−22−2−22−220000002i−2ii2−i2−i2i200000000
χ322-22-222-2-2-22-200020002−22−2−22−22000000−2i2i−i2i2i2−i2000000002-22-222-2-2-22-200020002−22−2−22−22000000−2i2i−i2i2i2−i200000000
χ332-22-222-2-2-22-20002000−22−222−22−20000002i−2i−i2i2i2−i2000000002-22-222-2-2-22-20002000−22−222−22−20000002i−2i−i2i2i2−i200000000
χ342-22-222-2-2-22-20002000−22−222−22−2000000−2i2ii2−i2−i2i2000000002-22-222-2-2-22-20002000−22−222−22−2000000−2i2ii2−i2−i2i200000000
χ352-2-2-2-22220002-2-202002−2−222−2−22002-2000000002−2−2200002-2-2-2-22220002-2-202002−2−222−2−22002-2000000002−2−220000
χ362-2-2-2-22220002-2-202002−2−222−2−2200-2200000000−222−200002-2-2-2-22220002-2-202002−2−222−2−2200-2200000000−222−20000
χ372-2-2-2-22220002-2-20200−222−2−222−2002-200000000−222−200002-2-2-2-22220002-2-20200−222−2−222−2002-200000000−222−20000
χ382-2-2-2-22220002-2-20200−222−2−222−200-22000000002−2−2200002-2-2-2-22220002-2-20200−222−2−222−200-22000000002−2−220000
χ39444-4-4-44-4-444000-40000000000000000000000000000000444-4-4-44-4-444000-40000000000000000000000000000000
χ4044-44-44-4-4000000000022-2-2-2-2220000000000000000000044-44-44-4-4000000000022-2-2-2-22200000000000000000000
χ4144-44-44-4-40000000000-2-22222-2-20000000000000000000044-44-44-4-40000000000-2-22222-2-200000000000000000000
χ4244-4-44-4-44000-4-440400000000000000000000000000000044-4-44-4-44000-4-4404000000000000000000000000000000
χ434-44-444-4-44-44000-400000000000000000000000000000004-44-444-4-44-44000-40000000000000000000000000000000
χ444-4-444-44-400000000002i−2i−2i2i−2i2i2i−2i000000000000000000004-4-444-44-400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ454-4-444-44-40000000000−2i2i2i−2i2i−2i−2i2i000000000000000000004-4-444-44-40000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ464-4-4-4-4444000-4440-40000000000000000000000000000004-4-4-4-4444000-4440-4000000000000000000000000000000
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
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
χ5522222222222-2-2-22-2-2-200000000220000-2-2000000000000-2-2-2-2-2-2-2-2-2-2-2222-222200000000-2-2000022000000000000
χ5622222222222-2-2-22-2-2-200000000-2-2000022000000000000-2-2-2-2-2-2-2-2-2-2-2222-222200000000220000-2-2000000000000
χ5722222222-2-2-2222-22-2-2000000000022-2-200000000000000-2-2-2-2-2-2-2-2222-2-2-22-2220000000000-2-22200000000000000
χ5822222222-2-2-2222-22-2-20000000000-2-22200000000000000-2-2-2-2-2-2-2-2222-2-2-22-222000000000022-2-200000000000000
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
χ61222-2-2-22-22-2-20002000i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i200000000-2-2-2222-22-222000-2000−i2−i2−i2−i2i2i2i2i2-22000000−i2−i2i2i200000000
χ62222-2-2-22-22-2-20002000i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i200000000-2-2-2222-22-222000-2000−i2−i2−i2−i2i2i2i2i22-2000000i2i2−i2−i200000000
χ63222-2-2-22-22-2-20002000−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i200000000-2-2-2222-22-222000-2000i2i2i2i2−i2−i2−i2−i2-22000000i2i2−i2−i200000000
χ64222-2-2-22-22-2-20002000−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i200000000-2-2-2222-22-222000-2000i2i2i2i2−i2−i2−i2−i22-2000000−i2−i2i2i200000000
χ6522-2-22-2-2200022-20-200i2i2−i2−i2i2i2−i2−i200002-2000000i2i2−i2−i20000-2-222-222-2000-2-220200−i2−i2i2i2−i2−i2i2i20000-22000000−i2−i2i2i20000
χ6622-2-22-2-2200022-20-200i2i2−i2−i2i2i2−i2−i20000-22000000−i2−i2i2i20000-2-222-222-2000-2-220200−i2−i2i2i2−i2−i2i2i200002-2000000i2i2−i2−i20000
χ6722-2-22-2-2200022-20-200−i2−i2i2i2−i2−i2i2i200002-2000000−i2−i2i2i20000-2-222-222-2000-2-220200i2i2−i2−i2i2i2−i2−i20000-22000000i2i2−i2−i20000
χ6822-2-22-2-2200022-20-200−i2−i2i2i2−i2−i2i2i20000-22000000i2i2−i2−i20000-2-222-222-2000-2-220200i2i2−i2−i2i2i2−i2−i200002-2000000−i2−i2i2i20000
χ692-222-2-2-2222-22-22-2-2-22000000000000000000002i−2i2i−2i0000-22-2-2222-2-2-22-22-2222-200000000000000000000−2i2i−2i2i0000
χ702-222-2-2-2222-22-22-2-2-2200000000000000000000−2i2i−2i2i0000-22-2-2222-2-2-22-22-2222-2000000000000000000002i−2i2i−2i0000
χ712-222-2-2-2222-2-22-2-222-20000000000000000000000002i−2i00-22-2-2222-2-2-222-222-2-22000000000000000000000000−2i2i00
χ722-222-2-2-2222-2-22-2-222-2000000000000000000000000−2i2i00-22-2-2222-2-2-222-222-2-220000000000000000000000002i−2i00
χ732-222-2-2-22-2-222-222-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000-22-2-2222-222-2-22-2-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ742-222-2-2-22-2-222-222-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000-22-2-2222-222-2-22-2-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000
χ752-222-2-2-22-2-22-22-222-2200000000000000002-22-200000000-22-2-2222-222-22-22-2-22-20000000000000000-22-2200000000
χ762-222-2-2-22-2-22-22-222-220000000000000000-22-2200000000-22-2-2222-222-22-22-2-22-200000000000000002-22-200000000
χ772-22-222-2-2-22-200020002−22−2−22−220000002i−2ii2−i2−i2i200000000-22-22-2-2222-22000-2000−22−222−22−2000000−2i2i−i2i2i2−i200000000
χ782-22-222-2-2-22-200020002−22−2−22−22000000−2i2i−i2i2i2−i200000000-22-22-2-2222-22000-2000−22−222−22−20000002i−2ii2−i2−i2i200000000
χ792-22-222-2-2-22-20002000−22−222−22−20000002i−2i−i2i2i2−i200000000-22-22-2-2222-22000-20002−22−2−22−22000000−2i2ii2−i2−i2i200000000
χ802-22-222-2-2-22-20002000−22−222−22−2000000−2i2ii2−i2−i2i200000000-22-22-2-2222-22000-20002−22−2−22−220000002i−2i−i2i2i2−i200000000
χ812-2-2-2-22220002-2-202002−2−222−2−22002-2000000002−2−220000-22222-2-2-2000-2220-200−222−2−222−200-2200000000−222−20000
χ822-2-2-2-22220002-2-202002−2−222−2−2200-2200000000−222−20000-22222-2-2-2000-2220-200−222−2−222−2002-2000000002−2−220000
χ832-2-2-2-22220002-2-20200−222−2−222−2002-200000000−222−20000-22222-2-2-2000-2220-2002−2−222−2−2200-22000000002−2−220000
χ842-2-2-2-22220002-2-20200−222−2−222−200-22000000002−2−220000-22222-2-2-2000-2220-2002−2−222−2−22002-200000000−222−20000
χ85444-4-4-44-4-444000-40000000000000000000000000000000-4-4-4444-444-4-400040000000000000000000000000000000
χ8644-44-44-4-4000000000022-2-2-2-22200000000000000000000-4-44-44-4440000000000-2-22222-2-200000000000000000000
χ8744-44-44-4-40000000000-2-22222-2-200000000000000000000-4-44-44-444000000000022-2-2-2-22200000000000000000000
χ8844-4-44-4-44000-4-4404000000000000000000000000000000-4-444-444-400044-40-4000000000000000000000000000000
χ894-44-444-4-44-44000-40000000000000000000000000000000-44-44-4-444-44-400040000000000000000000000000000000
χ904-4-444-44-400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000-444-4-44-440000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ914-4-444-44-40000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000-444-4-44-4400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ924-4-4-4-4444000-4440-4000000000000000000000000000000-44444-4-4-40004-4-404000000000000000000000000000000

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