Finite Group Databasebeta

← Group #490421

Character table — Group #490421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222222244444444488888888888888883232111122222222222244444444488888888888888883232
order122244448888888848888888822448888161616161616161624222244448888888848888888822448888161616161616161624
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1
χ611111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11
χ711111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ811111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1
χ9222222222222-2-2-2-22-2-222-2-2-2-2000000000000000000222222222222-2-2-2-22-2-222-2-2-2-2000000000000000000
χ1022222222-2-2-2-2-2-2-2-22-2-2-2-2222200000000000000000022222222-2-2-2-2-2-2-2-22-2-2-2-22222000000000000000000
χ11222222-2-200002222-2-2-200000022-2-200000000000000222222-2-200002222-2-2-200000022-2-200000000000000
χ12222222-2-200002222-2-2-2000000-2-22200000000000000222222-2-200002222-2-2-2000000-2-22200000000000000
χ13222222-2-20000-2-2-2-2-22200000000002i2i−2i−2i0000000000222222-2-20000-2-2-2-2-22200000000002i2i−2i−2i0000000000
χ14222222-2-20000-2-2-2-2-2220000000000−2i−2i2i2i0000000000222222-2-20000-2-2-2-2-2220000000000−2i−2i2i2i0000000000
χ152222-2-22222220000-200-2-200000000000022−2−222−2−2002222-2-22222220000-200-2-200000000000022−2−222−2−200
χ162222-2-22222220000-200-2-2000000000000−2−222−2−222002222-2-22222220000-200-2-2000000000000−2−222−2−22200
χ172222-2-222-2-2-2-20000-2002200000000000022−2−2−2−222002222-2-222-2-2-2-20000-2002200000000000022−2−2−2−22200
χ182222-2-222-2-2-2-20000-20022000000000000−2−22222−2−2002222-2-222-2-2-2-20000-20022000000000000−2−22222−2−200
χ1922-2-22-200i2i2−i2−i222-2-2000i2−i2i2i2−i2−i2002i−2i2−22−2000000000022-2-22-200i2i2−i2−i222-2-2000i2−i2i2i2−i2−i2002i−2i2−22−20000000000
χ2022-2-22-200i2i2−i2−i222-2-2000i2−i2i2i2−i2−i200−2i2i−22−22000000000022-2-22-200i2i2−i2−i222-2-2000i2−i2i2i2−i2−i200−2i2i−22−220000000000
χ2122-2-22-200i2i2−i2−i2-2-222000i2−i2−i2−i2i2i22-200i2−i2−i2i2000000000022-2-22-200i2i2−i2−i2-2-222000i2−i2−i2−i2i2i22-200i2−i2−i2i20000000000
χ2222-2-22-200i2i2−i2−i2-2-222000i2−i2−i2−i2i2i2-2200−i2i2i2−i2000000000022-2-22-200i2i2−i2−i2-2-222000i2−i2−i2−i2i2i2-2200−i2i2i2−i20000000000
χ2322-2-22-200−i2−i2i2i222-2-2000−i2i2−i2−i2i2i2002i−2i−22−22000000000022-2-22-200−i2−i2i2i222-2-2000−i2i2−i2−i2i2i2002i−2i−22−220000000000
χ2422-2-22-200−i2−i2i2i222-2-2000−i2i2−i2−i2i2i200−2i2i2−22−2000000000022-2-22-200−i2−i2i2i222-2-2000−i2i2−i2−i2i2i200−2i2i2−22−20000000000
χ2522-2-22-200−i2−i2i2i2-2-222000−i2i2i2i2−i2−i22-200−i2i2i2−i2000000000022-2-22-200−i2−i2i2i2-2-222000−i2i2i2i2−i2−i22-200−i2i2i2−i20000000000
χ2622-2-22-200−i2−i2i2i2-2-222000−i2i2i2i2−i2−i2-2200i2−i2−i2i2000000000022-2-22-200−i2−i2i2i2-2-222000−i2i2i2i2−i2−i2-2200i2−i2−i2i20000000000
χ272-22-2002-22i−2i2i−2i2−22−202−200i2−i2i2−i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7002-22-2002-22i−2i2i−2i2−22−202−200i2−i2i2−i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700
χ282-22-2002-22i−2i2i−2i2−22−202−200i2−i2i2−i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7002-22-2002-22i−2i2i−2i2−22−202−200i2−i2i2−i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700
χ292-22-2002-22i−2i2i−2i−22−220−2200−i2i2−i2i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5002-22-2002-22i−2i2i−2i−22−220−2200−i2i2−i2i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500
χ302-22-2002-22i−2i2i−2i−22−220−2200−i2i2−i2i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5002-22-2002-22i−2i2i−2i−22−220−2200−i2i2−i2i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500
χ312-22-2002-2−2i2i−2i2i2−22−202−200−i2i2−i2i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7002-22-2002-2−2i2i−2i2i2−22−202−200−i2i2−i2i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700
χ322-22-2002-2−2i2i−2i2i2−22−202−200−i2i2−i2i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7002-22-2002-2−2i2i−2i2i2−22−202−200−i2i2−i2i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700
χ332-22-2002-2−2i2i−2i2i−22−220−2200i2−i2i2−i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5002-22-2002-2−2i2i−2i2i−22−220−2200i2−i2i2−i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500
χ342-22-2002-2−2i2i−2i2i−22−220−2200i2−i2i2−i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5002-22-2002-2−2i2i−2i2i−22−220−2200i2−i2i2−i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500
χ354444-4-4-4-4000000004000000000000000000000000004444-4-4-4-400000000400000000000000000000000000
χ3644-4-4-44002i22i2−2i2−2i20000000−2i22i2000000000000000000000044-4-4-44002i22i2−2i2−2i20000000−2i22i20000000000000000000000
χ3744-4-4-4400−2i2−2i22i22i200000002i2−2i2000000000000000000000044-4-4-4400−2i2−2i22i22i200000002i2−2i20000000000000000000000
χ384-44-400-44000022−2222−220−22220000000000000000000000004-44-400-44000022−2222−220−2222000000000000000000000000
χ394-44-400-440000−2222−2222022−220000000000000000000000004-44-400-440000−2222−2222022−22000000000000000000000000
χ404-4-44000022−22−222222−22−2222000002-2-220000000000000000004-4-44000022−22−222222−22−2222000002-2-22000000000000000000
χ414-4-44000022−22−2222−222222−2200000-222-20000000000000000004-4-44000022−22−2222−222222−2200000-222-2000000000000000000
χ424-4-440000−222222−2222−22−222200000-222-20000000000000000004-4-440000−222222−2222−22−222200000-222-2000000000000000000
χ434-4-440000−222222−22−222222−22000002-2-220000000000000000004-4-440000−222222−22−222222−22000002-2-22000000000000000000
χ441111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ45111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ461111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ471111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ4811111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11
χ4911111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1
χ5011111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1
χ5111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11
χ52222222222222-2-2-2-22-2-222-2-2-2-2000000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222-222-2-22222000000000000000000
χ5322222222-2-2-2-2-2-2-2-22-2-2-2-22222000000000000000000-2-2-2-2-2-2-2-222222222-22222-2-2-2-2000000000000000000
χ54222222-2-200002222-2-2-200000022-2-200000000000000-2-2-2-2-2-2220000-2-2-2-2222000000-2-22200000000000000
χ55222222-2-200002222-2-2-2000000-2-22200000000000000-2-2-2-2-2-2220000-2-2-2-222200000022-2-200000000000000
χ56222222-2-20000-2-2-2-2-22200000000002i2i−2i−2i0000000000-2-2-2-2-2-222000022222-2-20000000000−2i−2i2i2i0000000000
χ57222222-2-20000-2-2-2-2-2220000000000−2i−2i2i2i0000000000-2-2-2-2-2-222000022222-2-200000000002i2i−2i−2i0000000000
χ582222-2-22222220000-200-2-200000000000022−2−222−2−200-2-2-2-222-2-2-2-2-2-2000020022000000000000−2−222−2−22200
χ592222-2-22222220000-200-2-2000000000000−2−222−2−22200-2-2-2-222-2-2-2-2-2-200002002200000000000022−2−222−2−200
χ602222-2-222-2-2-2-20000-2002200000000000022−2−2−2−22200-2-2-2-222-2-222220000200-2-2000000000000−2−22222−2−200
χ612222-2-222-2-2-2-20000-20022000000000000−2−22222−2−200-2-2-2-222-2-222220000200-2-200000000000022−2−2−2−22200
χ6222-2-22-200i2i2−i2−i222-2-2000i2−i2i2i2−i2−i2002i−2i2−22−20000000000-2-222-2200−i2−i2i2i2-2-222000−i2i2−i2−i2i2i200−2i2i−22−220000000000
χ6322-2-22-200i2i2−i2−i222-2-2000i2−i2i2i2−i2−i200−2i2i−22−220000000000-2-222-2200−i2−i2i2i2-2-222000−i2i2−i2−i2i2i2002i−2i2−22−20000000000
χ6422-2-22-200i2i2−i2−i2-2-222000i2−i2−i2−i2i2i22-200i2−i2−i2i20000000000-2-222-2200−i2−i2i2i222-2-2000−i2i2i2i2−i2−i2-2200−i2i2i2−i20000000000
χ6522-2-22-200i2i2−i2−i2-2-222000i2−i2−i2−i2i2i2-2200−i2i2i2−i20000000000-2-222-2200−i2−i2i2i222-2-2000−i2i2i2i2−i2−i22-200i2−i2−i2i20000000000
χ6622-2-22-200−i2−i2i2i222-2-2000−i2i2−i2−i2i2i2002i−2i−22−220000000000-2-222-2200i2i2−i2−i2-2-222000i2−i2i2i2−i2−i200−2i2i2−22−20000000000
χ6722-2-22-200−i2−i2i2i222-2-2000−i2i2−i2−i2i2i200−2i2i2−22−20000000000-2-222-2200i2i2−i2−i2-2-222000i2−i2i2i2−i2−i2002i−2i−22−220000000000
χ6822-2-22-200−i2−i2i2i2-2-222000−i2i2i2i2−i2−i22-200−i2i2i2−i20000000000-2-222-2200i2i2−i2−i222-2-2000i2−i2−i2−i2i2i2-2200i2−i2−i2i20000000000
χ6922-2-22-200−i2−i2i2i2-2-222000−i2i2i2i2−i2−i2-2200i2−i2−i2i20000000000-2-222-2200i2i2−i2−i222-2-2000i2−i2−i2−i2i2i22-200−i2i2i2−i20000000000
χ702-22-2002-22i−2i2i−2i2−22−202−200i2−i2i2−i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700-22-2200-22−2i2i−2i2i−22−220−2200−i2i2−i2i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700
χ712-22-2002-22i−2i2i−2i2−22−202−200i2−i2i2−i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700-22-2200-22−2i2i−2i2i−22−220−2200−i2i2−i2i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700
χ722-22-2002-22i−2i2i−2i−22−220−2200−i2i2−i2i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500-22-2200-22−2i2i−2i2i2−22−202−200i2−i2i2−i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500
χ732-22-2002-22i−2i2i−2i−22−220−2200−i2i2−i2i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500-22-2200-22−2i2i−2i2i2−22−202−200i2−i2i2−i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500
χ742-22-2002-2−2i2i−2i2i2−22−202−200−i2i2−i2i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700-22-2200-222i−2i2i−2i−22−220−2200i2−i2i2−i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700
χ752-22-2002-2−2i2i−2i2i2−22−202−200−i2i2−i2i200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700-22-2200-222i−2i2i−2i−22−220−2200i2−i2i2−i200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700
χ762-22-2002-2−2i2i−2i2i−22−220−2200i2−i2i2−i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500-22-2200-222i−2i2i−2i2−22−202−200−i2i2−i2i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500
χ772-22-2002-2−2i2i−2i2i−22−220−2200i2−i2i2−i200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500-22-2200-222i−2i2i−2i2−22−202−200−i2i2−i2i200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500
χ784444-4-4-4-400000000400000000000000000000000000-4-4-4-4444400000000-400000000000000000000000000
χ7944-4-4-44002i22i2−2i2−2i20000000−2i22i20000000000000000000000-4-4444-400−2i2−2i22i22i200000002i2−2i20000000000000000000000
χ8044-4-4-4400−2i2−2i22i22i200000002i2−2i20000000000000000000000-4-4444-4002i22i2−2i2−2i20000000−2i22i20000000000000000000000
χ814-44-400-44000022−2222−220−2222000000000000000000000000-44-44004-40000−2222−2222022−22000000000000000000000000
χ824-44-400-440000−2222−2222022−22000000000000000000000000-44-44004-4000022−2222−220−2222000000000000000000000000
χ834-4-44000022−22−222222−22−2222000002-2-22000000000000000000-444-40000−222222−22−222222−2200000-222-2000000000000000000
χ844-4-44000022−22−2222−222222−2200000-222-2000000000000000000-444-40000−222222−2222−22−2222000002-2-22000000000000000000
χ854-4-440000−222222−2222−22−222200000-222-2000000000000000000-444-4000022−22−2222−222222−22000002-2-22000000000000000000
χ864-4-440000−222222−22−222222−22000002-2-22000000000000000000-444-4000022−22−222222−22−222200000-222-2000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.