Finite Group Databasebeta

← Group #72210805

Character table — Group #72210805

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size112226612121212122424242424244848484848489696969696969696128128128128128128128128192192192192
order12488244488848161616161616161616163232323232323232361212242424242488
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ322222222222222222222222200000000-1-1-1-1-1-1-1-10000
χ4222-2-22222-2-2-22-20000000000−i2−i2−i2−i2i2i2i2i2-1-1-1-111110000
χ5222-2-22222-2-2-22-20000000000i2i2i2i2−i2−i2−i2−i2-1-1-1-111110000
χ633333333333333-1-1-1-1-1-1-1-1-1-11111111100000000-1-1-1-1
χ733333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111
χ83333333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1−2i1111ii−i−iii−i−i00000000-1-111
χ93333333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1−2i1111−i−iii−i−iii0000000011-1-1
χ103333333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1+2i1111ii−i−iii−i−i0000000011-1-1
χ113333333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1+2i1111−i−iii−i−iii00000000-1-111
χ1233333-1-1−1+2i−1−2i-1−1+2i−1−2i112ζ7+ζ14+ζ22+2ζ23−2ζ7+ζ14+ζ22−2ζ23−2ζ5−2ζ13−ζ14−ζ222ζ5+2ζ13−ζ14−ζ22i−i1+21−2−1−i2−1+i2−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23000000001-1i−i
χ1333333-1-1−1+2i−1−2i-1−1+2i−1−2i112ζ7+ζ14+ζ22+2ζ23−2ζ7+ζ14+ζ22−2ζ23−2ζ5−2ζ13−ζ14−ζ222ζ5+2ζ13−ζ14−ζ22i−i1+21−2−1−i2−1+i2ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300000000-11−ii
χ1433333-1-1−1+2i−1−2i-1−1+2i−1−2i11−2ζ7+ζ14+ζ22−2ζ232ζ7+ζ14+ζ22+2ζ232ζ5+2ζ13−ζ14−ζ22−2ζ5−2ζ13−ζ14−ζ22i−i1−21+2−1+i2−1−i2−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300000000-11−ii
χ1533333-1-1−1+2i−1−2i-1−1+2i−1−2i11−2ζ7+ζ14+ζ22−2ζ232ζ7+ζ14+ζ22+2ζ232ζ5+2ζ13−ζ14−ζ22−2ζ5−2ζ13−ζ14−ζ22i−i1−21+2−1+i2−1−i2ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23000000001-1i−i
χ1633333-1-1−1−2i−1+2i-1−1−2i−1+2i11−2ζ5−2ζ13−ζ14−ζ222ζ5+2ζ13−ζ14−ζ222ζ7+ζ14+ζ22+2ζ23−2ζ7+ζ14+ζ22−2ζ23−ii1+21−2−1+i2−1−i2ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000001-1−ii
χ1733333-1-1−1−2i−1+2i-1−1−2i−1+2i11−2ζ5−2ζ13−ζ14−ζ222ζ5+2ζ13−ζ14−ζ222ζ7+ζ14+ζ22+2ζ23−2ζ7+ζ14+ζ22−2ζ23−ii1+21−2−1+i2−1−i2−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000-11i−i
χ1833333-1-1−1−2i−1+2i-1−1−2i−1+2i112ζ5+2ζ13−ζ14−ζ22−2ζ5−2ζ13−ζ14−ζ22−2ζ7+ζ14+ζ22−2ζ232ζ7+ζ14+ζ22+2ζ23−ii1−21+2−1−i2−1+i2ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000-11i−i
χ1933333-1-1−1−2i−1+2i-1−1−2i−1+2i112ζ5+2ζ13−ζ14−ζ22−2ζ5−2ζ13−ζ14−ζ22−2ζ7+ζ14+ζ22−2ζ232ζ7+ζ14+ζ22+2ζ23−ii1−21+2−1−i2−1+i2−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13000000001-1−ii
χ20444-4-44444-4-4-44-40000000000000000001111-1-1-1-10000
χ216666666-2-26-2-2-2-2222222-2-2-2-200000000000000000000
χ2266666-2-222-222-2-22+222−222+222−22-2-2−22220000000000000000000000
χ2366666-2-222-222-2-22−222+222−222+22-2-222−220000000000000000000000
χ2466666-2-222-222-2-2−2−2i2−2+2i2−2+2i2−2−2i22200−2i22i200000000000000000000
χ2566666-2-222-222-2-2−2+2i2−2−2i2−2−2i2−2+2i222002i2−2i200000000000000000000
χ2666666-2-2−2+4i−2−4i-2−2+4i−2−4i222i2i−2i−2i−2i2i-2-22200000000000000000000
χ2766666-2-2−2−4i−2+4i-2−2−4i−2+4i22−2i−2i2i2i2i−2i-2-22200000000000000000000
χ28666-6-666-2-2-622-22000000000022−2−2−2−222000000000000
χ29666-6-666-2-2-622-220000000000−2−22222−2−2000000000000
χ30666-6-6-2-2−2+4i−2−4i22−4i2+4i2-200000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i000000000000
χ31666-6-6-2-2−2+4i−2−4i22−4i2+4i2-20000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i000000000000
χ32666-6-6-2-2−2−4i−2+4i22+4i2−4i2-200000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i000000000000
χ33666-6-6-2-2−2−4i−2+4i22+4i2−4i2-20000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000000000
χ3488-8008-8000000000000000000000000022-2-200000000
χ3588-8008-80000000000000000000000000-1-11133−3−30000
χ3688-8008-80000000000000000000000000-1-111−3−3330000
χ37121212-12-12-4-4444-4-4-44000000000000000000000000000000
χ3816-16082−820000000000000000000000000001-13−3ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ230000
χ3916-16082−820000000000000000000000000001-1−33ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ70000
χ4016-16082−82000000000000000000000000000-22002−2−220000
χ4116-160−82820000000000000000000000000001-13−3−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ230000
χ4216-160−82820000000000000000000000000001-1−33−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ70000
χ4316-160−8282000000000000000000000000000-2200−222−20000
χ442424-2400-880000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.