Finite Group Databasebeta

← Group #72213890

Character table — Group #72213890

Order 12000.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29
size124252525120150150150480500500500500500500500500500500600600600600600600750750750
order15244524453688121224242424101020202020444
χ111111111111111111111111111111
χ21111111-1-1111-1-111-1-1-1-11111-1-11-1-1
χ3111-1-11-1i−i111i−i-1-1ii−i−i-11-1-1i−i1i−i
χ4111-1-11-1−ii111−ii-1-1−i−iii-11-1-1−ii1−ii
χ544444-1000-1112211-1-1-1-10-1-1-100000
χ644444-1000-111-2-21111110-1-1-100000
χ7444-4-4-1000-1112i−2i-1-1−i−iii0-11100000
χ8444-4-4-1000-111−2i2i-1-1ii−i−i0-11100000
χ944-44i−4i-1000-11-100i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1301i−i00000
χ1044-44i−4i-1000-11-100i−iζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1301i−i00000
χ1144-44i−4i-1000-1-2200−2i2i000001i−i00000
χ1244-4−4i4i-1000-11-100−iiζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2301−ii00000
χ1344-4−4i4i-1000-11-100−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2301−ii00000
χ1444-4−4i4i-1000-1-22002i−2i000001−ii00000
χ155555501110-1-1-1-1-1-1-1-1-1-1100011111
χ165555501-1-10-1-111-1-111111000-1-11-1-1
χ17555-5-50-1i−i0-1-1−ii11−i−iii-1000i−i1i−i
χ18555-5-50-1−ii0-1-1i−i11ii−i−i-1000−ii1−ii
χ19666661-20010000000000-211100-200
χ20666-6-612001000000000021-1-100-200
χ2166-66i−6i101−i1+i100000000000-1−ii1−i1+i0−1+i−1−i
χ2266-66i−6i10−1+i−1−i100000000000-1−ii−1+i−1−i01−i1+i
χ2366-6−6i6i101+i1−i100000000000-1i−i1+i1−i0−1−i−1+i
χ2466-6−6i6i10−1−i−1+i100000000000-1i−i−1−i−1+i01+i1−i
χ2524-10004444-10000000000-1000-1-1000
χ2624-100044-4-4-10000000000-100011000
χ2724-10004-44i−4i-100000000001000−ii000
χ2824-10004-4−4i4i-100000000001000i−i000
χ2996-4000-400010000000000000000000

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