Finite Group Databasebeta

← Group #11758039

Character table — Group #11758039

Order 972.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11133333333999999999121212121212121212121212121212121212272727272727272727272727272727272727272727272727
order1333399999924466121212123333339999999999996612121212181818181818363636363636363636363636
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-111-1-1-1-111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111-1i−i-1-1ii−i−i111111111111111111-1-1ii−i−i-1-1-1-1-1-1iiiiii−i−i−i−i−i−i
χ411111111111-1−ii-1-1−i−iii111111111111111111-1-1−i−iii-1-1-1-1-1-1−i−i−i−i−i−iiiiiii
χ511111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ611111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-111-1-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32
χ711111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1i−i-1-1ii−i−i111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1ii−i−i1+i321+i321+i321−i321−i321−i32ζ11ζ11ζ11ζ7ζ7ζ7−ζ11−ζ11−ζ11−ζ7−ζ7−ζ7
χ811111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1−ii-1-1−i−iii111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1−i−iii1+i321+i321+i321−i321−i321−i32−ζ11−ζ11−ζ11−ζ7−ζ7−ζ7ζ11ζ11ζ11ζ7ζ7ζ7
χ911111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ1011111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-111-1-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32
χ1111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1i−i-1-1ii−i−i111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1ii−i−i1−i321−i321−i321+i321+i321+i32ζ7ζ7ζ7ζ11ζ11ζ11−ζ7−ζ7−ζ7−ζ11−ζ11−ζ11
χ1211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1−ii-1-1−i−iii111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1−i−iii1−i321−i321−i321+i321+i321+i32−ζ7−ζ7−ζ7−ζ11−ζ11−ζ11ζ7ζ7ζ7ζ11ζ11ζ11
χ13111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211111111111−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ14111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321-1-111-1-1-1-111−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32
χ15111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1i−i-1-1ii−i−i11−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ7-11+i321−i32-11+i321−i32iζ11ζ7iζ11ζ7−i−ζ11−ζ7−i−ζ11−ζ7
χ16111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1−ii-1-1−i−iii11−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32−ζ11−ζ7ζ11ζ7-11+i321−i32-11+i321−i32−i−ζ11−ζ7−i−ζ11−ζ7iζ11ζ7iζ11ζ7
χ17111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i3211111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32
χ18111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i321-1-111-1-1-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321−1+i321−1−i321+i321−i32-11−i32-11+i321+i321−i32-11−i32-11+i32
χ19111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1i−i-1-1ii−i−i11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i321+i321−i32ζ11ζ7−ζ11−ζ71+i321−i32-11−i32-11+i32ζ11ζ7iζ7iζ11−ζ11−ζ7−i−ζ7−i−ζ11
χ20111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1−ii-1-1−i−iii11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i321+i321−i32−ζ11−ζ7ζ11ζ71+i321−i32-11−i32-11+i32−ζ11−ζ7−i−ζ7−i−ζ11ζ11ζ7iζ7iζ11
χ21111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i32111111111111−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321
χ22111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i3211-1-111-1-1-1-111−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i321+i321−i321+i321−i32−1+i321−1−i32−1−i32−1+i3211−i32-11+i321+i321−i32-11−i32-11+i321+i321−i32-1
χ23111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1i−i-1-1ii−i−i11−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32111+i321−i32ζ11ζ7−ζ11−ζ71−i32-11+i321+i321−i32-1ζ7iζ11ζ11ζ7i−ζ7−i−ζ11−ζ11−ζ7−i
χ24111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1−ii-1-1−i−iii11−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32111+i321−i32−ζ11−ζ7ζ11ζ71−i32-11+i321+i321−i32-1−ζ7−i−ζ11−ζ11−ζ7−iζ7iζ11ζ11ζ7i
χ25111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211111111111−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ26111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321-1-111-1-1-1-111−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32
χ27111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1i−i-1-1ii−i−i11−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11-11−i321+i32-11−i321+i32iζ7ζ11iζ7ζ11−i−ζ7−ζ11−i−ζ7−ζ11
χ28111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1−ii-1-1−i−iii11−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11-11−i321+i32-11−i321+i32−i−ζ7−ζ11−i−ζ7−ζ11iζ7ζ11iζ7ζ11
χ29111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i32111111111111−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321
χ30111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i3211-1-111-1-1-1-111−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i321−i321+i321−i321+i32−1−i321−1+i32−1+i32−1−i3211+i32-11−i321−i321+i32-11+i32-11−i321−i321+i32-1
χ31111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1i−i-1-1ii−i−i11−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32111−i321+i32ζ7ζ11−ζ7−ζ111+i32-11−i321−i321+i32-1ζ11iζ7ζ7ζ11i−ζ11−i−ζ7−ζ7−ζ11−i
χ32111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1−ii-1-1−i−iii11−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32111−i321+i32−ζ7−ζ11ζ7ζ111+i32-11−i321−i321+i32-1−ζ11−i−ζ7−ζ7−ζ11−iζ11iζ7ζ7ζ11i
χ33111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i3211111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32
χ34111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i321-1-111-1-1-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−1−i321−1+i321−i321+i32-11+i32-11−i321−i321+i32-11+i32-11−i32
χ35111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1i−i-1-1ii−i−i11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i321−i321+i32ζ7ζ11−ζ7−ζ111−i321+i32-11+i32-11−i32ζ7ζ11iζ11iζ7−ζ7−ζ11−i−ζ11−i−ζ7
χ36111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1−ii-1-1−i−iii11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i321−i321+i32−ζ7−ζ11ζ7ζ111−i321+i32-11+i32-11−i32−ζ7−ζ11−i−ζ11−i−ζ7ζ7ζ11iζ11iζ7
χ37444444444440000000001-21-21-21-21-21-21-21-21-2000000000000000000000000
χ3844444444444000000000-21-21-21-21-21-21-21-21-21000000000000000000000000
χ3944444−2−2i3−2−2i3−2−2i3−2+2i3−2+2i3−2+2i30000000001-21-21-2−1−i321+i3−1−i321+i3−1−i321+i3−1+i321−i3−1+i321−i3−1+i321−i3000000000000000000000000
χ4044444−2−2i3−2−2i3−2−2i3−2+2i3−2+2i3−2+2i3000000000-21-21-211+i3−1−i321+i3−1−i321+i3−1−i321−i3−1+i321−i3−1+i321−i3−1+i32000000000000000000000000
χ4144444−2+2i3−2+2i3−2+2i3−2−2i3−2−2i3−2−2i30000000001-21-21-2−1+i321−i3−1+i321−i3−1+i321−i3−1−i321+i3−1−i321+i3−1−i321+i3000000000000000000000000
χ4244444−2+2i3−2+2i3−2+2i3−2−2i3−2−2i3−2−2i3000000000-21-21-211−i3−1+i321−i3−1+i321−i3−1+i321+i3−1−i321+i3−1−i321+i3−1−i32000000000000000000000000
χ43444−2−2i3−2+2i34−2−2i3−2+2i34−2−2i3−2+2i30000000001-2−1−i321+i3−1+i321−i31-2−1−i321+i3−1+i321−i31-2−1−i321+i3−1+i321−i3000000000000000000000000
χ44444−2−2i3−2+2i34−2−2i3−2+2i34−2−2i3−2+2i3000000000-211+i3−1−i321−i3−1+i32-211+i3−1−i321−i3−1+i32-211+i3−1−i321−i3−1+i32000000000000000000000000
χ45444−2−2i3−2+2i3−2−2i3−2+2i34−2+2i34−2−2i30000000001-2−1−i321+i3−1+i321−i3−1−i321+i3−1+i321−i31-2−1+i321−i31-2−1−i321+i3000000000000000000000000
χ46444−2−2i3−2+2i3−2−2i3−2+2i34−2+2i34−2−2i3000000000-211+i3−1−i321−i3−1+i321+i3−1−i321−i3−1+i32-211−i3−1+i32-211+i3−1−i32000000000000000000000000
χ47444−2−2i3−2+2i3−2+2i34−2−2i3−2−2i3−2+2i340000000001-2−1−i321+i3−1+i321−i3−1+i321−i31-2−1−i321+i3−1−i321+i3−1+i321−i31-2000000000000000000000000
χ48444−2−2i3−2+2i3−2+2i34−2−2i3−2−2i3−2+2i34000000000-211+i3−1−i321−i3−1+i321−i3−1+i32-211+i3−1−i321+i3−1−i321−i3−1+i32-21000000000000000000000000
χ49444−2+2i3−2−2i34−2+2i3−2−2i34−2+2i3−2−2i30000000001-2−1+i321−i3−1−i321+i31-2−1+i321−i3−1−i321+i31-2−1+i321−i3−1−i321+i3000000000000000000000000
χ50444−2+2i3−2−2i34−2+2i3−2−2i34−2+2i3−2−2i3000000000-211−i3−1+i321+i3−1−i32-211−i3−1+i321+i3−1−i32-211−i3−1+i321+i3−1−i32000000000000000000000000
χ51444−2+2i3−2−2i3−2−2i34−2+2i3−2+2i3−2−2i340000000001-2−1+i321−i3−1−i321+i3−1−i321+i31-2−1+i321−i3−1+i321−i3−1−i321+i31-2000000000000000000000000
χ52444−2+2i3−2−2i3−2−2i34−2+2i3−2+2i3−2−2i34000000000-211−i3−1+i321+i3−1−i321+i3−1−i32-211−i3−1+i321−i3−1+i321+i3−1−i32-21000000000000000000000000
χ53444−2+2i3−2−2i3−2+2i3−2−2i34−2−2i34−2+2i30000000001-2−1+i321−i3−1−i321+i3−1+i321−i3−1−i321+i31-2−1−i321+i31-2−1+i321−i3000000000000000000000000
χ54444−2+2i3−2−2i3−2+2i3−2−2i34−2−2i34−2+2i3000000000-211−i3−1+i321+i3−1−i321−i3−1+i321+i3−1−i32-211+i3−1−i32-211−i3−1+i32000000000000000000000000
χ559−9−9i32−9+9i320000000033i−3i−3−3i32−3+3i323ζ73ζ11−3ζ7−3ζ11000000000000000000000000000000000000000000
χ569−9−9i32−9+9i32000000003−3i3i−3−3i32−3+3i32−3ζ7−3ζ113ζ73ζ11000000000000000000000000000000000000000000
χ579−9−9i32−9+9i3200000000-3333+3i323−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000000000
χ589−9−9i32−9+9i3200000000-3-3-33+3i323−3i323−3i323+3i323−3i323+3i32000000000000000000000000000000000000000000
χ599−9+9i32−9−9i320000000033i−3i−3+3i32−3−3i323ζ113ζ7−3ζ11−3ζ7000000000000000000000000000000000000000000
χ609−9+9i32−9−9i32000000003−3i3i−3+3i32−3−3i32−3ζ11−3ζ73ζ113ζ7000000000000000000000000000000000000000000
χ619−9+9i32−9−9i3200000000-3333−3i323+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000000000
χ629−9+9i32−9−9i3200000000-3-3-33−3i323+3i323+3i323−3i323+3i323−3i32000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.