Finite Group Databasebeta

← Group #239583

Character table — Group #239583

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888224444448888888822442222222244444444448888888822444444888888882244
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
χ922222222222-2-2-22-2-2-2000000002200-2-20000000000000022222222222-2-2-22-2-2-2000000002200-2-200000000000000
χ1022222222222-2-2-22-2-2-200000000-2-200220000000000000022222222222-2-2-22-2-2-200000000-2-2002200000000000000
χ1122222222-2-2-2222-22-2-200000000002200-2-200000000000022222222-2-2-2222-22-2-200000000002200-2-2000000000000
χ1222222222-2-2-2222-22-2-20000000000-2-2002200000000000022222222-2-2-2222-22-2-20000000000-2-20022000000000000
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
χ152222-2-2-2-22-2-20002000i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−2000000002222-2-2-2-22-2-20002000i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−200000000
χ162222-2-2-2-22-2-20002000i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−222000000002222-2-2-2-22-2-20002000i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−22200000000
χ172222-2-2-2-22-2-20002000−i2−i2−i2−i2i2i2i2i200002i−2i00−2−222000000002222-2-2-2-22-2-20002000−i2−i2−i2−i2i2i2i2i200002i−2i00−2−22200000000
χ182222-2-2-2-22-2-20002000−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−2000000002222-2-2-2-22-2-20002000−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−200000000
χ1922-2-2-222-200022-20-200i2i2−i2−i2i2i2−i2−i2002-200000000i2i2−i2−i2000022-2-2-222-200022-20-200i2i2−i2−i2i2i2−i2−i2002-200000000i2i2−i2−i20000
χ2022-2-2-222-200022-20-200i2i2−i2−i2i2i2−i2−i200-2200000000−i2−i2i2i2000022-2-2-222-200022-20-200i2i2−i2−i2i2i2−i2−i200-2200000000−i2−i2i2i20000
χ2122-2-2-222-200022-20-200−i2−i2i2i2−i2−i2i2i2002-200000000−i2−i2i2i2000022-2-2-222-200022-20-200−i2−i2i2i2−i2−i2i2i2002-200000000−i2−i2i2i20000
χ2222-2-2-222-200022-20-200−i2−i2i2i2−i2−i2i2i200-2200000000i2i2−i2−i2000022-2-2-222-200022-20-200−i2−i2i2i2−i2−i2i2i200-2200000000i2i2−i2−i20000
χ232-22-2-2-2220002-2-202002−22−22−22−20000002-200002−22−200002-22-2-2-2220002-2-202002−22−22−22−20000002-200002−22−20000
χ242-22-2-2-2220002-2-202002−22−22−22−2000000-220000−22−2200002-22-2-2-2220002-2-202002−22−22−22−2000000-220000−22−220000
χ252-22-2-2-2220002-2-20200−22−22−22−220000002-20000−22−2200002-22-2-2-2220002-2-20200−22−22−22−220000002-20000−22−220000
χ262-22-2-2-2220002-2-20200−22−22−22−22000000-2200002−22−200002-22-2-2-2220002-2-20200−22−22−22−22000000-2200002−22−20000
χ272-2-222-22-222-22-22-2-2-22000000000000000000002i−2i−2i2i00002-2-222-22-222-22-22-2-2-22000000000000000000002i−2i−2i2i0000
χ282-2-222-22-222-22-22-2-2-2200000000000000000000−2i2i2i−2i00002-2-222-22-222-22-22-2-2-2200000000000000000000−2i2i2i−2i0000
χ292-2-222-22-222-2-22-2-222-2000000000000000000000000002i−2i2-2-222-22-222-2-22-2-222-2000000000000000000000000002i−2i
χ302-2-222-22-222-2-22-2-222-200000000000000000000000000−2i2i2-2-222-22-222-2-22-2-222-200000000000000000000000000−2i2i
χ312-2-222-22-2-2-222-222-22-22i−2i−2i2i2i−2i−2i2i000000000000000000002-2-222-22-2-2-222-222-22-22i−2i−2i2i2i−2i−2i2i00000000000000000000
χ322-2-222-22-2-2-222-222-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000002-2-222-22-2-2-222-222-22-2−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ332-2-222-22-2-2-22-22-222-2200000000000000002-22-2000000002-2-222-22-2-2-22-22-222-2200000000000000002-22-200000000
χ342-2-222-22-2-2-22-22-222-220000000000000000-22-22000000002-2-222-22-2-2-22-22-222-220000000000000000-22-2200000000
χ352-2-22-22-22-22-200020002−2−22−222−22-20000002−2−22000000002-2-22-22-22-22-200020002−2−22−222−22-20000002−2−2200000000
χ362-2-22-22-22-22-200020002−2−22−222−2-22000000−222−2000000002-2-22-22-22-22-200020002−2−22−222−2-22000000−222−200000000
χ372-2-22-22-22-22-20002000−222−22−2−222-2000000−222−2000000002-2-22-22-22-22-20002000−222−22−2−222-2000000−222−200000000
χ382-2-22-22-22-22-20002000−222−22−2−22-220000002−2−22000000002-2-22-22-22-22-20002000−222−22−2−22-220000002−2−2200000000
χ394444-4-4-4-4-444000-400000000000000000000000000000004444-4-4-4-4-444000-40000000000000000000000000000000
χ4044-4-44-4-44000000000022-2-2-2-2220000000000000000000044-4-44-4-44000000000022-2-2-2-22200000000000000000000
χ4144-4-44-4-440000000000-2-22222-2-20000000000000000000044-4-44-4-440000000000-2-22222-2-200000000000000000000
χ4244-4-4-444-4000-4-440400000000000000000000000000000044-4-4-444-4000-4-4404000000000000000000000000000000
χ434-44-444-4-400000000002i−2i2i−2i−2i2i−2i2i000000000000000000004-44-444-4-400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ444-44-444-4-40000000000−2i2i−2i2i2i−2i2i−2i000000000000000000004-44-444-4-40000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ454-44-4-4-444000-4440-40000000000000000000000000000004-44-4-4-444000-4440-4000000000000000000000000000000
χ464-4-44-44-444-44000-400000000000000000000000000000004-4-44-44-444-44000-40000000000000000000000000000000
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
χ5522222222222-2-2-22-2-2-2000000002200-2-200000000000000-2-2-2-2-2-2-2-2-2-2-2222-222200000000-2-2002200000000000000
χ5622222222222-2-2-22-2-2-200000000-2-2002200000000000000-2-2-2-2-2-2-2-2-2-2-2222-2222000000002200-2-200000000000000
χ5722222222-2-2-2222-22-2-200000000002200-2-2000000000000-2-2-2-2-2-2-2-2222-2-2-22-2220000000000-2-20022000000000000
χ5822222222-2-2-2222-22-2-20000000000-2-20022000000000000-2-2-2-2-2-2-2-2222-2-2-22-22200000000002200-2-2000000000000
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
χ612222-2-2-2-22-2-20002000i2i2i2i2−i2−i2−i2−i200002i−2i0022−2−200000000-2-2-2-22222-222000-2000−i2−i2−i2−i2i2i2i2i20000−2i2i00−2−22200000000
χ622222-2-2-2-22-2-20002000i2i2i2i2−i2−i2−i2−i20000−2i2i00−2−22200000000-2-2-2-22222-222000-2000−i2−i2−i2−i2i2i2i2i200002i−2i0022−2−200000000
χ632222-2-2-2-22-2-20002000−i2−i2−i2−i2i2i2i2i200002i−2i00−2−22200000000-2-2-2-22222-222000-2000i2i2i2i2−i2−i2−i2−i20000−2i2i0022−2−200000000
χ642222-2-2-2-22-2-20002000−i2−i2−i2−i2i2i2i2i20000−2i2i0022−2−200000000-2-2-2-22222-222000-2000i2i2i2i2−i2−i2−i2−i200002i−2i00−2−22200000000
χ6522-2-2-222-200022-20-200i2i2−i2−i2i2i2−i2−i2002-200000000i2i2−i2−i20000-2-2222-2-22000-2-220200−i2−i2i2i2−i2−i2i2i200-2200000000−i2−i2i2i20000
χ6622-2-2-222-200022-20-200i2i2−i2−i2i2i2−i2−i200-2200000000−i2−i2i2i20000-2-2222-2-22000-2-220200−i2−i2i2i2−i2−i2i2i2002-200000000i2i2−i2−i20000
χ6722-2-2-222-200022-20-200−i2−i2i2i2−i2−i2i2i2002-200000000−i2−i2i2i20000-2-2222-2-22000-2-220200i2i2−i2−i2i2i2−i2−i200-2200000000i2i2−i2−i20000
χ6822-2-2-222-200022-20-200−i2−i2i2i2−i2−i2i2i200-2200000000i2i2−i2−i20000-2-2222-2-22000-2-220200i2i2−i2−i2i2i2−i2−i2002-200000000−i2−i2i2i20000
χ692-22-2-2-2220002-2-202002−22−22−22−20000002-200002−22−20000-22-2222-2-2000-2220-200−22−22−22−22000000-220000−22−220000
χ702-22-2-2-2220002-2-202002−22−22−22−2000000-220000−22−220000-22-2222-2-2000-2220-200−22−22−22−220000002-200002−22−20000
χ712-22-2-2-2220002-2-20200−22−22−22−220000002-20000−22−220000-22-2222-2-2000-2220-2002−22−22−22−2000000-2200002−22−20000
χ722-22-2-2-2220002-2-20200−22−22−22−22000000-2200002−22−20000-22-2222-2-2000-2220-2002−22−22−22−20000002-20000−22−220000
χ732-2-222-22-222-22-22-2-2-22000000000000000000002i−2i−2i2i0000-222-2-22-22-2-22-22-2222-200000000000000000000−2i2i2i−2i0000
χ742-2-222-22-222-22-22-2-2-2200000000000000000000−2i2i2i−2i0000-222-2-22-22-2-22-22-2222-2000000000000000000002i−2i−2i2i0000
χ752-2-222-22-222-2-22-2-222-2000000000000000000000000002i−2i-222-2-22-22-2-222-222-2-2200000000000000000000000000−2i2i
χ762-2-222-22-222-2-22-2-222-200000000000000000000000000−2i2i-222-2-22-22-2-222-222-2-22000000000000000000000000002i−2i
χ772-2-222-22-2-2-222-222-22-22i−2i−2i2i2i−2i−2i2i00000000000000000000-222-2-22-2222-2-22-2-22-22−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ782-2-222-22-2-2-222-222-22-2−2i2i2i−2i−2i2i2i−2i00000000000000000000-222-2-22-2222-2-22-2-22-222i−2i−2i2i2i−2i−2i2i00000000000000000000
χ792-2-222-22-2-2-22-22-222-2200000000000000002-22-200000000-222-2-22-2222-22-22-2-22-20000000000000000-22-2200000000
χ802-2-222-22-2-2-22-22-222-220000000000000000-22-2200000000-222-2-22-2222-22-22-2-22-200000000000000002-22-200000000
χ812-2-22-22-22-22-200020002−2−22−222−22-20000002−2−2200000000-222-22-22-22-22000-2000−222−22−2−22-22000000−222−200000000
χ822-2-22-22-22-22-200020002−2−22−222−2-22000000−222−200000000-222-22-22-22-22000-2000−222−22−2−222-20000002−2−2200000000
χ832-2-22-22-22-22-20002000−222−22−2−222-2000000−222−200000000-222-22-22-22-22000-20002−2−22−222−2-220000002−2−2200000000
χ842-2-22-22-22-22-20002000−222−22−2−22-220000002−2−2200000000-222-22-22-22-22000-20002−2−22−222−22-2000000−222−200000000
χ854444-4-4-4-4-444000-40000000000000000000000000000000-4-4-4-444444-4-400040000000000000000000000000000000
χ8644-4-44-4-44000000000022-2-2-2-22200000000000000000000-4-444-444-40000000000-2-22222-2-200000000000000000000
χ8744-4-44-4-440000000000-2-22222-2-200000000000000000000-4-444-444-4000000000022-2-2-2-22200000000000000000000
χ8844-4-4-444-4000-4-4404000000000000000000000000000000-4-4444-4-4400044-40-4000000000000000000000000000000
χ894-44-444-4-400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000-44-44-4-4440000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ904-44-444-4-40000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000-44-44-4-44400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ914-44-4-4-444000-4440-4000000000000000000000000000000-44-4444-4-40004-4-404000000000000000000000000000000
χ924-4-44-44-444-44000-40000000000000000000000000000000-444-44-44-4-44-400040000000000000000000000000000000

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