Finite Group Databasebeta

← Group #490447

Character table — Group #490447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222222244444444488888888888888883232111122222222222244444444488888888888888883232
order122244448888888848888888822448888161616161616161644222244448888888848888888822448888161616161616161644
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
χ51111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1
χ61111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11
χ71111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ81111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1
χ922222222-2-22222-2-22-2-222-2-2-2-200000000000000000022222222-2-22222-2-22-2-222-2-2-2-2000000000000000000
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
χ1122222-2-2200222200-200-2-200000000000022−2−222−2−20022222-2-2200222200-200-2-200000000000022−2−222−2−200
χ1222222-2-2200222200-200-2-2000000000000−2−222−2−2220022222-2-2200222200-200-2-2000000000000−2−222−2−22200
χ1322222-2-2200-2-2-2-200-2002200000000000022−2−2−2−2220022222-2-2200-2-2-2-200-2002200000000000022−2−2−2−22200
χ1422222-2-2200-2-2-2-200-20022000000000000−2−22222−2−20022222-2-2200-2-2-2-200-20022000000000000−2−22222−2−200
χ152222-222-222000022-2-2-200000022-2-2000000000000002222-222-222000022-2-2-200000022-2-200000000000000
χ162222-222-222000022-2-2-2000000-2-222000000000000002222-222-222000022-2-2-2000000-2-22200000000000000
χ172222-222-2-2-20000-2-2-22200000000002i2i−2i−2i00000000002222-222-2-2-20000-2-2-22200000000002i2i−2i−2i0000000000
χ182222-222-2-2-20000-2-2-2220000000000−2i−2i2i2i00000000002222-222-2-2-20000-2-2-2220000000000−2i−2i2i2i0000000000
χ192-22-2-20022−222-2-22−202−20022−2−200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5002-22-2-20022−222-2-22−202−20022−2−200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500
χ202-22-2-20022−222-2-22−202−20022−2−200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5002-22-2-20022−222-2-22−202−20022−2−200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500
χ212-22-2-20022−2-2-2222−202−200−2−22200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5002-22-2-20022−2-2-2222−202−200−2−22200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500
χ222-22-2-20022−2-2-2222−202−200−2−22200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5002-22-2-20022−2-2-2222−202−200−2−22200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500
χ232-22-2-2002−2222-2-2−220−2200−2−22200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7002-22-2-2002−2222-2-2−220−2200−2−22200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700
χ242-22-2-2002−2222-2-2−220−2200−2−22200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7002-22-2-2002−2222-2-2−220−2200−2−22200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700
χ252-22-2-2002−22-2-222−220−220022−2−200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7002-22-2-2002−22-2-222−220−220022−2−200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700
χ262-22-2-2002−22-2-222−220−220022−2−200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7002-22-2-2002−22-2-222−220−220022−2−200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700
χ272-2-2202-20222−22−2-2-20002−22−22−2002i−2ii2−i2i2−i200000000002-2-2202-20222−22−2-2-20002−22−22−2002i−2ii2−i2i2−i20000000000
χ282-2-2202-20222−22−2-2-20002−22−22−200−2i2i−i2i2−i2i200000000002-2-2202-20222−22−2-2-20002−22−22−200−2i2i−i2i2−i2i20000000000
χ292-2-2202-2022−22−22-2-2000−22−22−22002i−2i−i2i2−i2i200000000002-2-2202-2022−22−22-2-2000−22−22−22002i−2i−i2i2−i2i20000000000
χ302-2-2202-2022−22−22-2-2000−22−22−2200−2i2ii2−i2i2−i200000000002-2-2202-2022−22−22-2-2000−22−22−2200−2i2ii2−i2i2−i20000000000
χ312-2-2202-20-2-22−22−2220002−2−22−222-2002−2−2200000000002-2-2202-20-2-22−22−2220002−2−22−222-2002−2−220000000000
χ322-2-2202-20-2-22−22−2220002−2−22−22-2200−222−200000000002-2-2202-20-2-22−22−2220002−2−22−22-2200−222−20000000000
χ332-2-2202-20-2-2−22−2222000−222−22−22-200−222−200000000002-2-2202-20-2-2−22−2222000−222−22−22-200−222−20000000000
χ342-2-2202-20-2-2−22−2222000−222−22−2-22002−2−2200000000002-2-2202-20-2-2−22−2222000−222−22−2-22002−2−220000000000
χ354444-4-4-4-4000000004000000000000000000000000004444-4-4-4-400000000400000000000000000000000000
χ3644-4-4000022−2222−22−2222−2222000002-2-2200000000000000000044-4-4000022−2222−22−2222−2222000002-2-22000000000000000000
χ3744-4-4000022−22−222222−22−222200000-222-200000000000000000044-4-4000022−22−222222−22−222200000-222-2000000000000000000
χ3844-4-40000−222222−22−222222−2200000-222-200000000000000000044-4-40000−222222−22−222222−2200000-222-2000000000000000000
χ3944-4-40000−2222−222222−2222−22000002-2-2200000000000000000044-4-40000−2222−222222−2222−22000002-2-22000000000000000000
χ404-44-4400-422−22000022−220−22220000000000000000000000004-44-4400-422−22000022−220−2222000000000000000000000000
χ414-44-4400-4−22220000−2222022−220000000000000000000000004-44-4400-4−22220000−2222022−22000000000000000000000000
χ424-4-440-4400022−2222−2200000−222200000000000000000000004-4-440-4400022−2222−2200000−22220000000000000000000000
χ434-4-440-44000−2222−22220000022−2200000000000000000000004-4-440-44000−2222−22220000022−220000000000000000000000
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
χ481111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11
χ491111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1
χ501111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1
χ511111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11
χ5222222222-2-22222-2-22-2-222-2-2-2-2000000000000000000-2-2-2-2-2-2-2-222-2-2-2-222-222-2-22222000000000000000000
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
χ5422222-2-2200222200-200-2-200000000000022−2−222−2−200-2-2-2-2-222-200-2-2-2-20020022000000000000−2−222−2−22200
χ5522222-2-2200222200-200-2-2000000000000−2−222−2−22200-2-2-2-2-222-200-2-2-2-2002002200000000000022−2−222−2−200
χ5622222-2-2200-2-2-2-200-2002200000000000022−2−2−2−22200-2-2-2-2-222-200222200200-2-2000000000000−2−22222−2−200
χ5722222-2-2200-2-2-2-200-20022000000000000−2−22222−2−200-2-2-2-2-222-200222200200-2-200000000000022−2−2−2−22200
χ582222-222-222000022-2-2-200000022-2-200000000000000-2-2-2-22-2-22-2-20000-2-2222000000-2-22200000000000000
χ592222-222-222000022-2-2-2000000-2-22200000000000000-2-2-2-22-2-22-2-20000-2-222200000022-2-200000000000000
χ602222-222-2-2-20000-2-2-22200000000002i2i−2i−2i0000000000-2-2-2-22-2-22220000222-2-20000000000−2i−2i2i2i0000000000
χ612222-222-2-2-20000-2-2-2220000000000−2i−2i2i2i0000000000-2-2-2-22-2-22220000222-2-200000000002i2i−2i−2i0000000000
χ622-22-2-20022−222-2-22−202−20022−2−200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500-22-22200-2−22-2-222−220−2200−2−22200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500
χ632-22-2-20022−222-2-22−202−20022−2−200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500-22-22200-2−22-2-222−220−2200−2−22200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500
χ642-22-2-20022−2-2-2222−202−200−2−22200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500-22-22200-2−2222-2-2−220−220022−2−200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500
χ652-22-2-20022−2-2-2222−202−200−2−22200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500-22-22200-2−2222-2-2−220−220022−2−200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500
χ662-22-2-2002−2222-2-2−220−2200−2−22200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700-22-22200-22−2-2-2222−202−20022−2−200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700
χ672-22-2-2002−2222-2-2−220−2200−2−22200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700-22-22200-22−2-2-2222−202−20022−2−200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700
χ682-22-2-2002−22-2-222−220−220022−2−200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700-22-22200-22−222-2-22−202−200−2−22200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700
χ692-22-2-2002−22-2-222−220−220022−2−200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700-22-22200-22−222-2-22−202−200−2−22200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700
χ702-2-2202-20222−22−2-2-20002−22−22−2002i−2ii2−i2i2−i20000000000-222-20-220-2-2−22−2222000−22−22−2200−2i2i−i2i2−i2i20000000000
χ712-2-2202-20222−22−2-2-20002−22−22−200−2i2i−i2i2−i2i20000000000-222-20-220-2-2−22−2222000−22−22−22002i−2ii2−i2i2−i20000000000
χ722-2-2202-2022−22−22-2-2000−22−22−22002i−2i−i2i2−i2i20000000000-222-20-220-2-22−22−2220002−22−22−200−2i2ii2−i2i2−i20000000000
χ732-2-2202-2022−22−22-2-2000−22−22−2200−2i2ii2−i2i2−i20000000000-222-20-220-2-22−22−2220002−22−22−2002i−2i−i2i2−i2i20000000000
χ742-2-2202-20-2-22−22−2220002−2−22−222-2002−2−220000000000-222-20-22022−22−22-2-2000−222−22−2-2200−222−20000000000
χ752-2-2202-20-2-22−22−2220002−2−22−22-2200−222−20000000000-222-20-22022−22−22-2-2000−222−22−22-2002−2−220000000000
χ762-2-2202-20-2-2−22−2222000−222−22−22-200−222−20000000000-222-20-220222−22−2-2-20002−2−22−22-22002−2−220000000000
χ772-2-2202-20-2-2−22−2222000−222−22−2-22002−2−220000000000-222-20-220222−22−2-2-20002−2−22−222-200−222−20000000000
χ784444-4-4-4-400000000400000000000000000000000000-4-4-4-4444400000000-400000000000000000000000000
χ7944-4-4000022−2222−22−2222−2222000002-2-22000000000000000000-4-4440000−2222−222222−2222−2200000-222-2000000000000000000
χ8044-4-4000022−22−222222−22−222200000-222-2000000000000000000-4-4440000−222222−22−222222−22000002-2-22000000000000000000
χ8144-4-40000−222222−22−222222−2200000-222-2000000000000000000-4-444000022−22−222222−22−2222000002-2-22000000000000000000
χ8244-4-40000−2222−222222−2222−22000002-2-22000000000000000000-4-444000022−2222−22−2222−222200000-222-2000000000000000000
χ834-44-4400-422−22000022−220−2222000000000000000000000000-44-44-4004−22220000−2222022−22000000000000000000000000
χ844-44-4400-4−22220000−2222022−22000000000000000000000000-44-44-400422−22000022−220−2222000000000000000000000000
χ854-4-440-4400022−2222−2200000−22220000000000000000000000-444-404-4000−2222−22220000022−220000000000000000000000
χ864-4-440-44000−2222−22220000022−220000000000000000000000-444-404-400022−2222−2200000−22220000000000000000000000

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