Finite Group Databasebeta

← Group #10593779

Character table — Group #10593779

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size1122244444488888899999916161616181818181818181818363636363636
order124882233661212242424244488886666244448888448888
χ1111111111111111111111111111111111111111111
χ21111111111111111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1
χ311111111111111111-1-1ii−i−i1111-1ii−i−i-1-1i−i-1-1ii−i−i
χ411111111111111111-1-1−i−iii1111-1−i−iii-1-1−ii-1-1−i−iii
χ511111-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1-1
χ611111-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-11111
χ711111-1-11111111111-1-1ii−i−i-1-1-1-1-1ii−i−i-1-1i−i11−i−iii
χ811111-1-11111111111-1-1−i−iii-1-1-1-1-1−i−iii-1-1−ii11ii−i−i
χ9111-1-11-1111111-1-1-1-111111111-1-11-1-1-1-1-1-1111-11-11-1
χ10111-1-11-1111111-1-1-1-111-1-1-1-111-1-111111-1-1-1-11-1-11-11
χ11111-1-11-1111111-1-1-1-1-1-1ii−i−i11-1-1-1−i−iii11i−i-11i−i−ii
χ12111-1-11-1111111-1-1-1-1-1-1−i−iii11-1-1-1ii−i−i11−ii-11−iii−i
χ13111-1-1-11111111-1-1-1-1111111-1-1111-1-1-1-1-1-111-11-11-11
χ14111-1-1-11111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-1-111-11-1
χ15111-1-1-11111111-1-1-1-1-1-1ii−i−i-1-111-1−i−iii11i−i1-1−iii−i
χ16111-1-1-11111111-1-1-1-1-1-1−i−iii-1-111-1ii−i−i11−ii1-1i−i−ii
χ1722-200002222-2-200002222220000-2000000-2-2000000
χ1822-200002222-2-2000022-2-2-2-20000-200000022000000
χ1922-200002222-2-20000-2-22i2i−2i−2i00002000000−2i2i000000
χ2022-200002222-2-20000-2-2−2i−2i2i2i000020000002i−2i000000
χ212-202−20022-2-20022−2−22i−2i2ζ−2ζ2ζ3−2ζ3000001+i−1−i1−i−1+ii2−i200000000
χ222-202−20022-2-20022−2−22i−2i−2ζ2ζ−2ζ32ζ300000−1−i1+i−1+i1−ii2−i200000000
χ232-202−20022-2-20022−2−2−2i2i2ζ3−2ζ32ζ−2ζ00000−1+i1−i−1−i1+i−i2i200000000
χ242-202−20022-2-20022−2−2−2i2i−2ζ32ζ3−2ζ2ζ000001−i−1+i1+i−1−i−i2i200000000
χ252-20−220022-2-200−2−2222i−2i2ζ−2ζ2ζ3−2ζ300000−1−i1+i−1+i1−i−i2i200000000
χ262-20−220022-2-200−2−2222i−2i−2ζ2ζ−2ζ32ζ3000001+i−1−i1−i−1+i−i2i200000000
χ272-20−220022-2-200−2−222−2i2i2ζ3−2ζ32ζ−2ζ000001−i−1+i1+i−1−ii2−i200000000
χ282-20−220022-2-200−2−222−2i2i−2ζ32ζ3−2ζ2ζ00000−1+i1−i−1−i1+ii2−i200000000
χ2944444441-21-21-21-21-20000001-21-2000000000000000
χ304444444-21-21-21-21-21000000-21-21000000000000000
χ3144444-4-41-21-21-21-21-2000000-12-12000000000000000
χ3244444-4-4-21-21-21-21-210000002-12-1000000000000000
χ33444-4-44-41-21-21-2-12-120000001-2-12000000000000000
χ34444-4-44-4-21-21-212-12-1000000-212-1000000000000000
χ35444-4-4-441-21-21-2-12-12000000-121-2000000000000000
χ36444-4-4-44-21-21-212-12-10000002-1-21000000000000000
χ3788-800002-42-4-2400000000000000000000000000000
χ3888-80000-42-424-200000000000000000000000000000
χ398-8042−42002-4-24002−22−2220000000000000000000000000
χ408-8042−4200-424-200−22222−20000000000000000000000000
χ418-80−4242002-4-2400−2222−220000000000000000000000000
χ428-80−424200-424-20022−2−2220000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.