Finite Group Databasebeta

← Group #11751784

Character table — Group #11751784

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222444444455556688888888881010101010101010122020202020202020202020202024242424303030303030606060
order122236664510101012124444441520203030306060606088881212121244881212242424242424242420202020448888488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1
χ31111111111111111111-1-1111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111-1-11111111111-1-1-1-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ5111111111111111-1-1-1-1111111111111ii−i−i-1-1-1-11-1i−i-1-1iiii−i−i−i−i1111-1-1ii−i−i-1i−i
χ6111111111111111-1-1-1-1111111111111−i−iii-1-1-1-11-1−ii-1-1−i−i−i−iiiii1111-1-1−i−iii-1−ii
χ7111111111111111-1-1-1-1-1-11111111111ii−i−i-1-1-1-1-1-1i−i-1-1iiii−i−i−i−i-1-1-1-111−i−iii1−ii
χ8111111111111111-1-1-1-1-1-11111111111−i−iii-1-1-1-1-1-1−ii-1-1−i−i−i−iiiii-1-1-1-111ii−i−i1i−i
χ911111111-11111-1-11111111-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1
χ1011111111-11111-1-11111111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-111
χ1111111111-11111-1-11111-1-11-1-1111-1-1-1-1111111111-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111
χ1211111111-11111-1-11111-1-11-1-1111-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-111-1-111-1-111111-1-1
χ1311111111-11111-1-1-1-1-1-1111-1-1111-1-1-1-1ii−i−i-1-1-1-1-11−ii11ii−i−i−i−iii11-1-1-1-1ii−i−i1−ii
χ1411111111-11111-1-1-1-1-1-1111-1-1111-1-1-1-1−i−iii-1-1-1-1-11i−i11−i−iiiii−i−i11-1-1-1-1−i−iii1i−i
χ1511111111-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1ii−i−i-1-1-1-111−ii11ii−i−i−i−iii-1-11111−i−iii-1i−i
χ1611111111-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1−i−iii-1-1-1-111i−i11−i−iiiii−i−i-1-11111ii−i−i-1−ii
χ172222-1-1-1-122222-1-1222200-122-1-1-1-1-1-1-12222-1-1-1-10222-1-1-1-1-1-1-1-1-1-10000000000000
χ182222-1-1-1-122222-1-1222200-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-102-2-2-1-1111111110000000000000
χ192222-1-1-1-122222-1-1-2-2-2-200-122-1-1-1-1-1-1-12i2i−2i−2i11110-22i−2i11−i−i−i−iiiii0000000000000
χ202222-1-1-1-122222-1-1-2-2-2-200-122-1-1-1-1-1-1-1−2i−2i2i2i11110-2−2i2i11iiii−i−i−i−i0000000000000
χ212222-1-1-1-1-2222211222200-1-2-2-1-1-111112222-1-1-1-10-2-2-211-1-111-1-1110000000000000
χ222222-1-1-1-1-2222211222200-1-2-2-1-1-11111-2-2-2-2-1-1-1-10-2221111-1-111-1-10000000000000
χ232222-1-1-1-1-2222211-2-2-2-200-1-2-2-1-1-111112i2i−2i−2i111102−2i2i-1-1−i−iiiii−i−i0000000000000
χ242222-1-1-1-1-2222211-2-2-2-200-1-2-2-1-1-11111−2i−2i2i2i1111022i−2i-1-1ii−i−i−i−iii0000000000000
χ2522-2-22-22-2022-2-20022-2-2002002-2-200002-22-222-2-20000002-2002-2000000000000000
χ2622-2-22-22-2022-2-20022-2-2002002-2-20000-22-2222-2-2000000-2200-22000000000000000
χ2722-2-22-22-2022-2-200-2-222002002-2-200002i−2i−2i2i-2-2220000002i−2i00−2i2i000000000000000
χ2822-2-22-22-2022-2-200-2-222002002-2-20000−2i2i2i−2i-2-222000000−2i2i002i−2i000000000000000
χ2922-2-2-11-11022-2-23−322-2-200-100-11133−3−32-22-2-1-11100003−3-113−3-113−30000000000000
χ3022-2-2-11-11022-2-23−322-2-200-100-11133−3−3-22-22-1-11100003−31-1−331-1−330000000000000
χ3122-2-2-11-11022-2-23−3-2-22200-100-11133−3−32i−2i−2i2i11-1-10000−33−iii3−i3i−i−i3i30000000000000
χ3222-2-2-11-11022-2-23−3-2-22200-100-11133−3−3−2i2i2i−2i11-1-10000−33i−i−i3i3−iii3−i30000000000000
χ3322-2-2-11-11022-2-2−3322-2-200-100-111−3−3332-22-2-1-1110000−33-11−33-11−330000000000000
χ3422-2-2-11-11022-2-2−3322-2-200-100-111−3−333-22-22-1-1110000−331-13−31-13−30000000000000
χ3522-2-2-11-11022-2-2−33-2-22200-100-111−3−3332i−2i−2i2i11-1-100003−3−ii−i3i3i−ii3−i30000000000000
χ3622-2-2-11-11022-2-2−33-2-22200-100-111−3−333−2i2i2i−2i11-1-100003−3i−ii3−i3−ii−i3i30000000000000
χ372-22-22-2-2202-2-22002i−2i2i−2i00200-22-2000000002i−2i2i−2i000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109000
χ382-22-22-2-2202-2-22002i−2i2i−2i00200-22-2000000002i−2i2i−2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000
χ392-22-22-2-2202-2-2200−2i2i−2i2i00200-22-200000000−2i2i−2i2i00000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000
χ402-22-22-2-2202-2-2200−2i2i−2i2i00200-22-200000000−2i2i−2i2i000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119000
χ412-2-2222-2-202-22-2002i−2i−2i2i2i−2i200-2-22000000002i−2i−2i2i000000000000002i−2i002-20000000
χ422-2-2222-2-202-22-2002i−2i−2i2i−2i2i200-2-22000000002i−2i−2i2i00000000000000−2i2i00-220000000
χ432-2-2222-2-202-22-200−2i2i2i−2i2i−2i200-2-2200000000−2i2i2i−2i000000000000002i−2i00-220000000
χ442-2-2222-2-202-22-200−2i2i2i−2i−2i2i200-2-2200000000−2i2i2i−2i00000000000000−2i2i002-20000000
χ45444444444-1-1-1-144000044-1-1-1-1-1-1-1-1-1-10000000040000000000000-1-1-1-1000000000
χ46444444444-1-1-1-1440000-4-4-1-1-1-1-1-1-1-1-1-100000000-400000000000001111000000000
χ4744444444-4-1-1-1-1-4-4000044-111-1-1-1111100000000-40000000000000-1-111000000000
χ4844444444-4-1-1-1-1-4-40000-4-4-111-1-1-11111000000004000000000000011-1-1000000000
χ494-44-4-222-204-4-44004i−4i4i−4i00-2002-2200000000−2i2i−2i2i000000000000000000000000000
χ504-44-4-222-204-4-4400−4i4i−4i4i00-2002-22000000002i−2i2i−2i000000000000000000000000000
χ514-4-4444-4-40-11-110000004i−4i-1−5511-1−55−550000000000000000000000−ii−i5i5000000000
χ524-4-4444-4-40-11-110000004i−4i-15−511-15−55−50000000000000000000000−iii5−i5000000000
χ534-4-4444-4-40-11-11000000−4i4i-1−5511-1−55−550000000000000000000000i−ii5−i5000000000
χ544-4-4444-4-40-11-11000000−4i4i-15−511-15−55−50000000000000000000000i−i−i5i5000000000
χ554-4-44-2-22204-44-4004i−4i−4i4i00-20022-200000000−2i2i2i−2i000000000000000000000000000
χ564-4-44-2-22204-44-400−4i4i4i−4i00-20022-2000000002i−2i−2i2i000000000000000000000000000
χ578888-4-4-4-48-2-2-2-2-4-40000001-2-2111111100000000000000000000000000000000000
χ588888-4-4-4-4-8-2-2-2-244000000122111-1-1-1-100000000000000000000000000000000000
χ5988-8-88-88-80-2-22200000000-200-222000000000000000000000000000000000000000
χ6088-8-8-44-440-2-22243−430000001001-1-1−3−33300000000000000000000000000000000000
χ6188-8-8-44-440-2-222−43430000001001-1-133−3−300000000000000000000000000000000000
χ628-88-88-8-880-222-200000000-2002-22000000000000000000000000000000000000000
χ638-88-8-444-40-222-200000000100-11-1−151515−1500000000000000000000000000000000000
χ648-88-8-444-40-222-200000000100-11-115−15−151500000000000000000000000000000000000
χ658-8-88-4-4440-22-22000000001−2525-1-115−55−500000000000000000000000000000000000
χ668-8-88-4-4440-22-2200000000125−25-1-11−55−5500000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.