Finite Group Databasebeta

← Group #11797708

Character table — Group #11797708

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1449991449992881818182881818182881818182881818182881818182881818182881818188323272727283232727272
order1332442662444121244482424888824248881648481616161648481616161648481616161648481616164121244441212444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-1
χ3111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i
χ4111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii
χ541-200041-200041-200041-200041-200041-200041-200041-200041-200041-200041-2000
χ64-210004-210004-210004-210004-210004-210004-210004-210004-210004-210004-21000
χ7111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ81111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111
χ9111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i-1-1-11−ii-1-1-11−ii
χ10111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii-1-1-11i−i-1-1-11i−i
χ1141-200041-200041-200041-200041-200041-200041-200041-200041-2000-4-12000-4-12000
χ124-210004-210004-210004-210004-210004-210004-210004-210004-21000-42-1000-42-1000
χ13111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ141111-1-11111-1-11111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111
χ15111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i-1-1-11−ii-1-1-11−ii-1-1-11−ii-1-1-11−ii111-1i−i-1-1-11−ii
χ16111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii-1-1-11i−i-1-1-11i−i-1-1-11i−i-1-1-11i−i111-1−ii-1-1-11i−i
χ1741-200041-200041-200041-200041-2000-4-12000-4-12000-4-12000-4-1200041-2000-4-12000
χ184-210004-210004-210004-210004-21000-42-1000-42-1000-42-1000-42-10004-21000-42-1000
χ19111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ201111-1-11111-1-11111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1
χ21111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i-1-1-11−ii-1-1-11−ii-1-1-11−ii-1-1-11−ii-1-1-11−ii111-1i−i
χ22111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii-1-1-11i−i-1-1-11i−i-1-1-11i−i-1-1-11i−i-1-1-11i−i111-1−ii
χ2341-200041-200041-200041-200041-2000-4-12000-4-12000-4-12000-4-12000-4-1200041-2000
χ244-210004-210004-210004-210004-21000-42-1000-42-1000-42-1000-42-1000-42-10004-21000
χ25222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ262222-2-22222-2-22222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ27222-22i−2i222-22i−2i222-22i−2i-2-2-22−2i2i-2-2-22−2i2i000000000000000000000000000000000000
χ28222-2−2i2i222-2−2i2i222-2−2i2i-2-2-222i−2i-2-2-222i−2i000000000000000000000000000000000000
χ2982-400082-400082-4000-8-24000-8-24000000000000000000000000000000000000000
χ308-420008-420008-42000-84-2000-84-2000000000000000000000000000000000000000
χ31222222222222-2-2-2-2-2-2000000000000222222222222−2−2−2−2−2−2−2−2−2−2−2−2000000000000
χ322222-2-22222-2-2-2-2-2-2220000000000002222−2−22222−2−2−2−2−2−222−2−2−2−222000000000000
χ33222-22i−2i222-22i−2i-2-2-22−2i2i000000000000222−2i2−i2222−2i2−i2−2−2−22−i2i2−2−2−22−i2i2000000000000
χ34222-2−2i2i222-2−2i2i-2-2-222i−2i000000000000222−2−i2i2222−2−i2i2−2−2−22i2−i2−2−2−22i2−i2000000000000
χ3582-400082-4000-8-24000000000000000422−22000422−22000−42−222000−42−222000000000000000
χ368-420008-42000-84-200000000000000042−22200042−222000−4222−2000−4222−2000000000000000
χ37222222222222-2-2-2-2-2-2000000000000−2−2−2−2−2−2−2−2−2−2−2−2222222222222000000000000
χ382222-2-22222-2-2-2-2-2-222000000000000−2−2−2−222−2−2−2−2222222−2−22222−2−2000000000000
χ39222-22i−2i222-22i−2i-2-2-22−2i2i000000000000−2−2−22−i2i2−2−2−22−i2i2222−2i2−i2222−2i2−i2000000000000
χ40222-2−2i2i222-2−2i2i-2-2-222i−2i000000000000−2−2−22i2−i2−2−2−22i2−i2222−2−i2i2222−2−i2i2000000000000
χ4182-400082-4000-8-24000000000000000−42−222000−42−222000422−22000422−22000000000000000
χ428-420008-42000-84-2000000000000000−4222−2000−4222−200042−22200042−222000000000000000
χ43222222-2-2-2-2-2-2000000222222−2−2−2−2−2−2ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5000000000000
χ442222-2-2-2-2-2-2220000002222−2−2−2−2−2−222ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000
χ45222-22i−2i-2-2-22−2i2i000000222−2i2−i2−2−2−22−i2i2ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ46222-2−2i2i-2-2-222i−2i000000222−2−i2i2−2−2−22i2−i2ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4782-4000-8-24000000000422−22000−42−2220004ζ−4ζ7ζ−ζ7−2ζ+2ζ7000−4ζ+4ζ7−ζ+ζ72ζ−2ζ70004ζ3−4ζ5ζ3−ζ5−2ζ3+2ζ5000−4ζ3+4ζ5−ζ3+ζ52ζ3−2ζ5000000000000000
χ488-42000-84-200000000042−222000−4222−20004ζ−4ζ7−2ζ+2ζ7ζ−ζ7000−4ζ+4ζ72ζ−2ζ7−ζ+ζ70004ζ3−4ζ5−2ζ3+2ζ5ζ3−ζ5000−4ζ3+4ζ52ζ3−2ζ5−ζ3+ζ5000000000000000
χ49222222-2-2-2-2-2-2000000222222−2−2−2−2−2−2−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5000000000000
χ502222-2-2-2-2-2-2220000002222−2−2−2−2−2−222−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000
χ51222-22i−2i-2-2-22−2i2i000000222−2i2−i2−2−2−22−i2i2−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ52222-2−2i2i-2-2-222i−2i000000222−2−i2i2−2−2−22i2−i2−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ5382-4000-8-24000000000422−22000−42−222000−4ζ+4ζ7−ζ+ζ72ζ−2ζ70004ζ−4ζ7ζ−ζ7−2ζ+2ζ7000−4ζ3+4ζ5−ζ3+ζ52ζ3−2ζ50004ζ3−4ζ5ζ3−ζ5−2ζ3+2ζ5000000000000000
χ548-42000-84-200000000042−222000−4222−2000−4ζ+4ζ72ζ−2ζ7−ζ+ζ70004ζ−4ζ7−2ζ+2ζ7ζ−ζ7000−4ζ3+4ζ52ζ3−2ζ5−ζ3+ζ50004ζ3−4ζ5−2ζ3+2ζ5ζ3−ζ5000000000000000
χ55222222-2-2-2-2-2-2000000−2−2−2−2−2−2222222ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7000000000000
χ562222-2-2-2-2-2-222000000−2−2−2−2222222−2−2ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000
χ57222-22i−2i-2-2-22−2i2i000000−2−2−22−i2i2222−2i2−i2ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ58222-2−2i2i-2-2-222i−2i000000−2−2−22i2−i2222−2−i2i2ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ5982-4000-8-24000000000−42−222000422−220004ζ3−4ζ5ζ3−ζ5−2ζ3+2ζ5000−4ζ3+4ζ5−ζ3+ζ52ζ3−2ζ5000−4ζ+4ζ7−ζ+ζ72ζ−2ζ70004ζ−4ζ7ζ−ζ7−2ζ+2ζ7000000000000000
χ608-42000-84-2000000000−4222−200042−2220004ζ3−4ζ5−2ζ3+2ζ5ζ3−ζ5000−4ζ3+4ζ52ζ3−2ζ5−ζ3+ζ5000−4ζ+4ζ72ζ−2ζ7−ζ+ζ70004ζ−4ζ7−2ζ+2ζ7ζ−ζ7000000000000000
χ61222222-2-2-2-2-2-2000000−2−2−2−2−2−2222222−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7000000000000
χ622222-2-2-2-2-2-222000000−2−2−2−2222222−2−2−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000
χ63222-22i−2i-2-2-22−2i2i000000−2−2−22−i2i2222−2i2−i2−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ64222-2−2i2i-2-2-222i−2i000000−2−2−22i2−i2222−2−i2i2−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ6582-4000-8-24000000000−42−222000422−22000−4ζ3+4ζ5−ζ3+ζ52ζ3−2ζ50004ζ3−4ζ5ζ3−ζ5−2ζ3+2ζ50004ζ−4ζ7ζ−ζ7−2ζ+2ζ7000−4ζ+4ζ7−ζ+ζ72ζ−2ζ7000000000000000
χ668-42000-84-2000000000−4222−200042−222000−4ζ3+4ζ52ζ3−2ζ5−ζ3+ζ50004ζ3−4ζ5−2ζ3+2ζ5ζ3−ζ50004ζ−4ζ7−2ζ+2ζ7ζ−ζ7000−4ζ+4ζ72ζ−2ζ7−ζ+ζ7000000000000000

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