Finite Group Databasebeta

← Group #72226927

Character table — Group #72226927

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134
size112222222222222222222444444444444444444444444444444444444888888888888888888888888888888888888888883232323232323232323232323232323232323232323232323232323232323232128128128128
order1222244448888161616161616161644888888888888881616161616161616161616161616161616161616488881616161632323232323232323232323232323232323232323232323232323232323232324488161616163232323232323232323232323232323232323232323232322288
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111iiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−ii−ii−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11-1i−i
χ1011-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111iiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−ii−ii−iii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-11−ii
χ1111-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111iiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−ii−ii−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-11−ii
χ1211-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111iiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−ii−ii−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-111111-1i−i
χ1311-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiii−ii−iii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-111111-1−ii
χ1411-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiii−ii−iii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-11i−i
χ1511-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−ii−ii−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-11i−i
χ1611-11-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−ii−ii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11-1−ii
χ1722222222222222222-2-2-2-222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-222222222-2-22-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222222-2-2-2-222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-222222222-2-22-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222222222000000000000000000000000000000000000
χ192222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2222-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-222000000000000000000000000000000002222-2-2-2-20000000000000000000000000000
χ202222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2222-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-22200000000000000000000000000000000-2-2-2-222220000000000000000000000000000
χ212222222222222-2-2-2-2-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-20000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ222222222222222-2-2-2-2-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222222-2-200002222-2-222-2000000002-2-2002222-2-2-2-20000000022-2000000-2-222−2−222−2−222−2−22222−2−2−2−222−2−22222−2−2−2−222-2-20000000000002−22−22−22−2000000000000
χ2422222222222-2-200002222-2-222-2000000002-2-2002222-2-2-2-20000000022-2000000-2-222−2−222−2−222−2−22222−2−2−2−222−2−22222−2−2−2−2-2-222000000000000−22−22−22−22000000000000
χ2522222222222-2-200002222-2-222-2000000002-2-2002222-2-2-2-20000000022-2000000-2-2−2−222−2−222−2−222−2−2−2−22222−2−222−2−2−2−2222222-2-2000000000000−22−22−22−22000000000000
χ2622222222222-2-200002222-2-222-2000000002-2-2002222-2-2-2-20000000022-2000000-2-2−2−222−2−222−2−222−2−2−2−22222−2−222−2−2−2−22222-2-2220000000000002−22−22−22−2000000000000
χ2722222222222-2-20000-2-2-2-2-2-222-2000000002-2-200-2-2-2-2222200000000-2-2-20000002222−2−222−2−222−2−2−2−2−2−2222222−2−2−2−2−2−2222200002i−2i2i−2i00000000i2−i2−i2i2i2−i2−i2i2000000000000
χ2822222222222-2-20000-2-2-2-2-2-222-2000000002-2-200-2-2-2-2222200000000-2-2-20000002222−2−222−2−222−2−2−2−2−2−2222222−2−2−2−2−2−222220000−2i2i−2i2i00000000−i2i2i2−i2−i2i2i2−i2000000000000
χ2922222222222-2-20000-2-2-2-2-2-222-2000000002-2-200-2-2-2-2222200000000-2-2-200000022−2−222−2−222−2−2222222−2−2−2−2−2−2222222−2−2−2−200002i−2i2i−2i00000000−i2i2i2−i2−i2i2i2−i2000000000000
χ3022222222222-2-20000-2-2-2-2-2-222-2000000002-2-200-2-2-2-2222200000000-2-2-200000022−2−222−2−222−2−2222222−2−2−2−2−2−2222222−2−2−2−20000−2i2i−2i2i00000000i2−i2−i2i2i2−i2−i2i2000000000000
χ31222222222-2-22222220000-2-2-2-2200000000-222220000000022-2-2-2-22200-20000-2-20022222222-2-2-2-200000000-2-2-2-2000000000000000022−2−222−2−20000000022−2−222−2−20000
χ32222222222-2-22222220000-2-2-2-2200000000-222220000000022-2-2-2-22200-20000-2-20022222222-2-2-2-200000000-2-2-2-20000000000000000−2−222−2−22200000000−2−222−2−2220000
χ33222222222-2-22222220000-2-2-2-2200000000-222220000000022-2-2-2-22200-20000-2-200-2-2-2-2-2-2-2-22222000000002222000000000000000022−2−222−2−200000000−2−222−2−2220000
χ34222222222-2-22222220000-2-2-2-2200000000-222220000000022-2-2-2-22200-20000-2-200-2-2-2-2-2-2-2-222220000000022220000000000000000−2−222−2−2220000000022−2−222−2−20000
χ35222-2-22-2-220022-2-2-2-222−2−2000022222−2−2−2−20-2-2222−22−222−2−2220000-2-22−2022−2−2002−2000000002-22-222−2−222−2−22-22-222−2−222−2−200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ36222-2-22-2-220022-2-2-2-222−2−2000022222−2−2−2−20-2-2222−22−222−2−2220000-2-22−2022−2−2002−2000000002-22-222−2−222−2−22-22-222−2−222−2−200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ37222-2-22-2-220022-2-2-2-222−2−2000022222−2−2−2−20-2-2222−22−222−2−2220000-2-22−2022−2−2002−200000000-22-22−2−222−2−222-22-22−2−222−2−22200000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ38222-2-22-2-220022-2-2-2-222−2−2000022222−2−2−2−20-2-2222−22−222−2−2220000-2-22−2022−2−2002−200000000-22-22−2−222−2−222-22-22−2−222−2−22200000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ39222-2-22-2-220022-2-2-2-2−2−22200002−2−2−2−222220-2-222−22−22−2−222220000-2-2−220−2−22200−22000000002-22-2−2−222−2−2222-22-2−2−222−2−22200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ40222-2-22-2-220022-2-2-2-2−2−22200002−2−2−2−222220-2-222−22−22−2−222220000-2-2−220−2−22200−22000000002-22-2−2−222−2−2222-22-2−2−222−2−22200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ41222-2-22-2-220022-2-2-2-2−2−22200002−2−2−2−222220-2-222−22−22−2−222220000-2-2−220−2−22200−2200000000-22-2222−2−222−2−2-22-2222−2−222−2−200000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ42222-2-22-2-220022-2-2-2-2−2−22200002−2−2−2−222220-2-222−22−22−2−222220000-2-2−220−2−22200−2200000000-22-2222−2−222−2−2-22-2222−2−222−2−200000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ4322-22-222-2-222222222222222-2-2-22222222222-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ4422-22-222-2-222222222222222-2-2-22222222222-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ4522-22-222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-222-2-2-222-2-2-2-2-2-2222222-2-222-22222-2-222000000000000000000000000000000002i−2i2i−2i−2i−2i2i2i0000000000000000000000000000
χ4622-22-222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-222-2-2-222-2-2-2-2-2-2222222-2-222-22222-2-22200000000000000000000000000000000−2i2i−2i2i2i2i−2i−2i0000000000000000000000000000
χ4722-22-222-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-222-222-2-2222222-2-2-2-2-2-222-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i000000000000000000000000000000000000
χ4822-22-222-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-222-222-2-2222222-2-2-2-2-2-222-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000000000000000
χ4922-22-222-2-222-2-200002222-2-2-2-22000000002-2200-2-222-2-2-2-200000000-2-2200000022i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200002-2-2200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ5022-22-222-2-222-2-200002222-2-2-2-22000000002-2200-2-222-2-2-2-200000000-2-2200000022i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i20000-222-200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ5122-22-222-2-222-2-200002222-2-2-2-22000000002-2200-2-222-2-2-2-200000000-2-2200000022−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200002-2-2200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ5222-22-222-2-222-2-200002222-2-2-2-22000000002-2200-2-222-2-2-2-200000000-2-2200000022−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i20000-222-200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ5322-22-222-2-222-2-20000-2-2-2-2-2-2-2-22000000002-220022-2-2222200000000222000000-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i−2i2i0000000000002−22−2−22−22000000000000
χ5422-22-222-2-222-2-20000-2-2-2-2-2-2-2-22000000002-220022-2-2222200000000222000000-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i2i−2i000000000000−22−222−22−2000000000000
χ5522-22-222-2-222-2-20000-2-2-2-2-2-2-2-22000000002-220022-2-2222200000000222000000-2-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i−2i2i000000000000−22−222−22−2000000000000
χ5622-22-222-2-222-2-20000-2-2-2-2-2-2-2-22000000002-220022-2-2222200000000222000000-2-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2i2i2i−2i0000000000002−22−2−22−22000000000000
χ5722-22-222-2-2-2-222-2-2-2-20000-2-222-200000000-22-22200000000-2-22222220020000-2-2002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000002i2i2i2i0000000000000000i2i2−i2−i2−i2−i2i2i20000000022−2−2−2−2220000
χ5822-22-222-2-2-2-222-2-2-2-20000-2-222-200000000-22-22200000000-2-22222220020000-2-2002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000002i2i2i2i0000000000000000−i2−i2i2i2i2i2−i2−i200000000−2−22222−2−20000
χ5922-22-222-2-2-2-222-2-2-2-20000-2-222-200000000-22-22200000000-2-22222220020000-2-200−2i−2i−2i−2i2i2i2i2i2i2i2i2i00000000−2i−2i−2i−2i0000000000000000i2i2−i2−i2−i2−i2i2i200000000−2−22222−2−20000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.