Finite Group Databasebeta

← Group #91149

Character table — Group #91149

Order 480.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size11112222444455556688881010101010101010101010101010101012121212303030303030
order12443612125102020224488153060604444661212121212121212121240404040888888
χ1111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1111111ii−i−i-1-1-1-1iiii−i−i−i−i1111-1-1ii−i−i
χ6111111111111-1-1-1-1111111−i−iii-1-1-1-1−i−i−i−iiiii1111-1-1−i−iii
χ7111111111111-1-1-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-111−i−iii
χ8111111111111-1-1-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii-1-1-1-111ii−i−i
χ911-1-111-1-111-1-111-1-1i−i11-1-11-11-111-1-111-1-111-1-1ii−i−ii−ii−ii−i
χ1011-1-111-1-111-1-111-1-1i−i11-1-1-11-1111-1-1-1-111-1-111ii−i−ii−i−ii−ii
χ1111-1-111-1-111-1-111-1-1−ii11-1-11-11-111-1-111-1-111-1-1−i−iii−ii−ii−ii
χ1211-1-111-1-111-1-111-1-1−ii11-1-1-11-1111-1-1-1-111-1-111−i−iii−iii−ii−i
χ1311-1-111-1-111-1-1-1-111i−i11-1-1i−i−ii-1-111ii−i−i−i−iiiii−i−i−ii-111-1
χ1411-1-111-1-111-1-1-1-111i−i11-1-1−iii−i-1-111−i−iiiii−i−iii−i−i−ii1-1-11
χ1511-1-111-1-111-1-1-1-111−ii11-1-1i−i−ii-1-111ii−i−i−i−iii−i−iiii−i1-1-11
χ1611-1-111-1-111-1-1-1-111−ii11-1-1−iii−i-1-111−i−iiiii−i−i−i−iiii−i-111-1
χ172222-1-1-1-12222222200-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ182222-1-1-1-12222222200-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000
χ192222-1-1-1-12222-2-2-2-200-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000000000
χ202222-1-1-1-12222-2-2-2-200-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000000000
χ2122-2-2-1-11122-2-222-2-200-1-1112-22-2-1-111-1-111-1-1110000000000
χ2222-2-2-1-11122-2-222-2-200-1-111-22-22-1-11111-1-111-1-10000000000
χ2322-2-2-1-11122-2-2-2-22200-1-1112i−2i−2i2i11-1-1−i−iiiii−i−i0000000000
χ2422-2-2-1-11122-2-2-2-22200-1-111−2i2i2i−2i11-1-1ii−i−i−i−iii0000000000
χ252-22i−2i2-22i−2i2-22i−2i2-22i−2i002-22i−2i00002-22i−2i000000000000000000
χ262-22i−2i2-22i−2i2-22i−2i-22−2i2i002-22i−2i0000-22−2i2i000000000000000000
χ272-22i−2i-11−ii2-22i−2i2-22i−2i00-11−ii0000-11−ii−i3i33−3−i3i33−30000000000
χ282-22i−2i-11−ii2-22i−2i2-22i−2i00-11−ii0000-11−iii3−i3−33i3−i3−330000000000
χ292-22i−2i-11−ii2-22i−2i-22−2i2i00-11−ii00001-1i−i3−3i3−i3−33−i3i30000000000
χ302-22i−2i-11−ii2-22i−2i-22−2i2i00-11−ii00001-1i−i−33−i3i33−3i3−i30000000000
χ312-2−2i2i2-2−2i2i2-2−2i2i2-2−2i2i002-2−2i2i00002-2−2i2i000000000000000000
χ322-2−2i2i2-2−2i2i2-2−2i2i-222i−2i002-2−2i2i0000-222i−2i000000000000000000
χ332-2−2i2i-11i−i2-2−2i2i2-2−2i2i00-11i−i0000-11i−i−i3i3−33−i3i3−330000000000
χ342-2−2i2i-11i−i2-2−2i2i2-2−2i2i00-11i−i0000-11i−ii3−i33−3i3−i33−30000000000
χ352-2−2i2i-11i−i2-2−2i2i-222i−2i00-11i−i00001-1−ii3−3−i3i3−33i3−i30000000000
χ362-2−2i2i-11i−i2-2−2i2i-222i−2i00-11i−i00001-1−ii−33i3−i33−3−i3i30000000000
χ3744444444-1-1-1-1000044-1-1-1-10000000000000000-1-1-1-1000000
χ3844444444-1-1-1-10000-4-4-1-1-1-100000000000000001111000000
χ3944-4-444-4-4-1-11100004i−4i-1-1110000000000000000−i−iii000000
χ4044-4-444-4-4-1-1110000−4i4i-1-1110000000000000000ii−i−i000000
χ414-44i−4i4-44i−4i-11−ii000000-11−ii0000000000000000ζ7+ζ23−ζ31+ζ47−ζ71−ζ79+ζ103−ζ119−ζ7−ζ23+ζ31−ζ47+ζ71+ζ79−ζ103+ζ119−ζ13+ζ29−ζ37−ζ53+ζ61−ζ77+ζ101+ζ109ζ13−ζ29+ζ37+ζ53−ζ61+ζ77−ζ101−ζ109000000
χ424-44i−4i4-44i−4i-11−ii000000-11−ii0000000000000000−ζ7−ζ23+ζ31−ζ47+ζ71+ζ79−ζ103+ζ119ζ7+ζ23−ζ31+ζ47−ζ71−ζ79+ζ103−ζ119ζ13−ζ29+ζ37+ζ53−ζ61+ζ77−ζ101−ζ109−ζ13+ζ29−ζ37−ζ53+ζ61−ζ77+ζ101+ζ109000000
χ434-4−4i4i4-4−4i4i-11i−i000000-11i−i0000000000000000−ζ13+ζ29−ζ37−ζ53+ζ61−ζ77+ζ101+ζ109ζ13−ζ29+ζ37+ζ53−ζ61+ζ77−ζ101−ζ109ζ7+ζ23−ζ31+ζ47−ζ71−ζ79+ζ103−ζ119−ζ7−ζ23+ζ31−ζ47+ζ71+ζ79−ζ103+ζ119000000
χ444-4−4i4i4-4−4i4i-11i−i000000-11i−i0000000000000000ζ13−ζ29+ζ37+ζ53−ζ61+ζ77−ζ101−ζ109−ζ13+ζ29−ζ37−ζ53+ζ61−ζ77+ζ101+ζ109−ζ7−ζ23+ζ31−ζ47+ζ71+ζ79−ζ103+ζ119ζ7+ζ23−ζ31+ζ47−ζ71−ζ79+ζ103−ζ119000000
χ458888-4-4-4-4-2-2-2-2000000111100000000000000000000000000
χ4688-8-8-4-444-2-22200000011-1-100000000000000000000000000
χ478-88i−8i-44−4i4i-22−2i2i0000001-1i−i00000000000000000000000000
χ488-8−8i8i-444i−4i-222i−2i0000001-1−ii00000000000000000000000000

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