Finite Group Databasebeta

← Group #72276617

Character table — Group #72276617

Order 4032.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11333333666677771818181818181818181821212121212121212121212132324242424284848484848484848484848484848484848484848484848496969696224224224224
order12222222227143366141414141414141414146666666666663666664444444412121212121212121212121212121212212142423366
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ3111111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211111111−1−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+i321111−1−i32−1+i32−1−i32−1+i32
χ4111111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321111−1−i32−1+i32−1−i32−1+i32
χ5111111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211111111−1+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−i321111−1+i32−1−i32−1+i32−1−i32
χ6111111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321+i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321111−1+i32−1−i32−1+i32−1−i32
χ71-1111-1-1-11-11-111-1-111111-1-1-1-1-1111111-1-1-1-1-1-11-11-11-1i−iiii−i−i−ii−ii−iiii−i−i−iiii−i−i−i11-1-111-1-1
χ81-1111-1-1-11-11-111-1-111111-1-1-1-1-1111111-1-1-1-1-1-11-11-11-1−ii−i−i−iiii−ii−ii−i−i−iiii−i−i−iiii11-1-111-1-1
χ91-1111-1-1-11-11-1−1−i32−1+i321+i321−i3211111-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321-1−1−i321+i32−1+i321−i32i−iiii−i−i−iζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ7911-1-1−1−i32−1+i321+i321−i32
χ101-1111-1-1-11-11-1−1−i32−1+i321+i321−i3211111-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321-1−1−i321+i32−1+i321−i32−ii−i−i−iiii−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ7911-1-1−1−i32−1+i321+i321−i32
χ111-1111-1-1-11-11-1−1+i32−1−i321−i321+i3211111-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321-1−1+i321−i32−1−i321+i32i−iiii−i−i−iζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ8311-1-1−1+i32−1−i321−i321+i32
χ121-1111-1-1-11-11-1−1+i32−1−i321−i321+i3211111-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321-1−1+i321−i32−1−i321+i32−ii−i−i−iiii−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ8311-1-1−1+i32−1−i321−i321+i32
χ1322222222222222222222222222222222222222-1-12222000000000000000000000000-1-1-1-1-1-1-1-1
χ14222222222222−1−i3−1+i3−1−i3−1+i32222222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1−1−i3−1−i3−1+i3−1+i3000000000000000000000000-1-1-1-11+i321−i321+i321−i32
χ15222222222222−1+i3−1−i3−1+i3−1−i32222222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1−1+i3−1+i3−1−i3−1−i3000000000000000000000000-1-1-1-11−i321+i321−i321+i32
χ162-2222-2-2-22-22-222-2-222222-2-2-2-2-2222222-2-2-2-2-2-2-112-22-2000000000000000000000000-1-111-1-111
χ172-2222-2-2-22-22-2−1−i3−1+i31+i31−i322222-2-2-2-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i3-11−1−i31+i3−1+i31−i3000000000000000000000000-1-1111+i321−i32−1−i32−1+i32
χ182-2222-2-2-22-22-2−1+i3−1−i31−i31+i322222-2-2-2-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i3-11−1+i31−i3−1−i31+i3000000000000000000000000-1-1111−i321+i32−1+i32−1−i32
χ19333-1-13-1-1-1-13333333-1-1-1-13-1-1-1-13-1-13-1-13-1-13-1-100-1-1-1-1111-1-11-1-111111-1-11-1-11-1-11-1-100000000
χ20333-1-13-1-1-1-13333333-1-1-1-13-1-1-1-13-1-13-1-13-1-13-1-100-1-1-1-1-1-1-111-111-1-1-1-1-111-111-111-11100000000
χ21333-1-13-1-1-1-133−3−3i32−3+3i32−3−3i32−3+3i323-1-1-1-13-1-1-1-1−3−3i321+i321+i32−3+3i321−i321−i32−3−3i321+i321+i32−3+3i321−i321−i32001+i321+i321−i321−i32111-1-11-1-1−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1+i321−i321−i32−1+i321−i321−i3200000000
χ22333-1-13-1-1-1-133−3−3i32−3+3i32−3−3i32−3+3i323-1-1-1-13-1-1-1-1−3−3i321+i321+i32−3+3i321−i321−i32−3−3i321+i321+i32−3+3i321−i321−i32001+i321+i321−i321−i32-1-1-111-1111+i321+i321−i321−i321+i32−1−i32−1−i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i32−1+i32−1+i3200000000
χ23333-1-13-1-1-1-133−3+3i32−3−3i32−3+3i32−3−3i323-1-1-1-13-1-1-1-1−3+3i321−i321−i32−3−3i321+i321+i32−3+3i321−i321−i32−3−3i321+i321+i32001−i321−i321+i321+i32111-1-11-1-1−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1−i321+i321+i32−1−i321+i321+i3200000000
χ24333-1-13-1-1-1-133−3+3i32−3−3i32−3+3i32−3−3i323-1-1-1-13-1-1-1-1−3+3i321−i321−i32−3−3i321+i321+i32−3+3i321−i321−i32−3−3i321+i321+i32001−i321−i321+i321+i32-1-1-111-1111−i321−i321+i321+i321−i32−1+i32−1+i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i32−1−i32−1−i3200000000
χ2533-13-1-13-1-1-1333333-13-1-1-1-13-1-1-1-13-1-13-1-13-1-13-100-1-1-1-111-11-1-11-11111-11-1-11-1-11-1-11-100000000
χ2633-13-1-13-1-1-1333333-13-1-1-1-13-1-1-1-13-1-13-1-13-1-13-100-1-1-1-1-1-11-111-11-1-1-1-11-111-111-111-1100000000
χ2733-13-1-13-1-1-133−3−3i32−3+3i32−3−3i32−3+3i32-13-1-1-1-13-1-1-11+i32−3−3i321+i321−i32−3+3i321−i321+i32−3−3i321+i321−i32−3+3i321−i32001+i321+i321−i321−i3211-11-1-11-1−1−i32−1−i32−1+i32−1+i321+i32−1−i321+i321+i32−1−i321+i321−i32−1+i321−i321−i32−1+i321−i3200000000
χ2833-13-1-13-1-1-133−3−3i32−3+3i32−3−3i32−3+3i32-13-1-1-1-13-1-1-11+i32−3−3i321+i321−i32−3+3i321−i321+i32−3−3i321+i321−i32−3+3i321−i32001+i321+i321−i321−i32-1-11-111-111+i321+i321−i321−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1+i321−i32−1+i32−1+i321−i32−1+i3200000000
χ2933-13-1-13-1-1-133−3+3i32−3−3i32−3+3i32−3−3i32-13-1-1-1-13-1-1-11−i32−3+3i321−i321+i32−3−3i321+i321−i32−3+3i321−i321+i32−3−3i321+i32001−i321−i321+i321+i3211-11-1-11-1−1+i32−1+i32−1−i32−1−i321−i32−1+i321−i321−i32−1+i321−i321+i32−1−i321+i321+i32−1−i321+i3200000000
χ3033-13-1-13-1-1-133−3+3i32−3−3i32−3+3i32−3−3i32-13-1-1-1-13-1-1-11−i32−3+3i321−i321+i32−3−3i321+i321−i32−3+3i321−i321+i32−3−3i321+i32001−i321−i321+i321+i32-1-11-111-111−i321−i321+i321+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1−i321+i32−1−i32−1−i321+i32−1−i3200000000
χ3133-1-13-1-13-1-1333333-1-13-1-1-1-13-1-1-1-13-1-13-1-13-1-1300-1-1-1-111-1-11-1-111111-1-11-1-11-1-11-1-1100000000
χ3233-1-13-1-13-1-1333333-1-13-1-1-1-13-1-1-1-13-1-13-1-13-1-1300-1-1-1-1-1-111-111-1-1-1-1-111-111-111-111-100000000
χ3333-1-13-1-13-1-133−3−3i32−3+3i32−3−3i32−3+3i32-1-13-1-1-1-13-1-11+i321+i32−3−3i321−i321−i32−3+3i321+i321+i32−3−3i321−i321−i32−3+3i32001+i321+i321−i321−i3211-1-11-1-11−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i321+i321+i32−1−i321−i321−i32−1+i321−i321−i32−1+i3200000000
χ3433-1-13-1-13-1-133−3−3i32−3+3i32−3−3i32−3+3i32-1-13-1-1-1-13-1-11+i321+i32−3−3i321−i321−i32−3+3i321+i321+i32−3−3i321−i321−i32−3+3i32001+i321+i321−i321−i32-1-111-111-11+i321+i321−i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i3200000000
χ3533-1-13-1-13-1-133−3+3i32−3−3i32−3+3i32−3−3i32-1-13-1-1-1-13-1-11−i321−i32−3+3i321+i321+i32−3−3i321−i321−i32−3+3i321+i321+i32−3−3i32001−i321−i321+i321+i3211-1-11-1-11−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i321−i321−i32−1+i321+i321+i32−1−i321+i321+i32−1−i3200000000
χ3633-1-13-1-13-1-133−3+3i32−3−3i32−3+3i32−3−3i32-1-13-1-1-1-13-1-11−i321−i32−3+3i321+i321+i32−3−3i321−i321−i32−3+3i321+i321+i32−3−3i32001−i321−i321+i321+i32-1-111-111-11−i321−i321+i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i3200000000
χ373-33-1-1-311-113-333-3-33-1-1-1-1-311113-1-13-1-1-311-31100-11-11i−ii−i−i−iiii−ii−ii−i−i−iiii−i−i−iii00000000
χ383-33-1-1-311-113-333-3-33-1-1-1-1-311113-1-13-1-1-311-31100-11-11−ii−iiii−i−i−ii−ii−iiii−i−i−iiii−i−i00000000
χ393-33-1-1-311-113-3−3−3i32−3+3i323+3i323−3i323-1-1-1-1-31111−3−3i321+i321+i32−3+3i321−i321−i323+3i32−1−i32−1−i323−3i32−1+i32−1+i32001+i32−1−i321−i32−1+i32i−ii−i−i−iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ7900000000
χ403-33-1-1-311-113-3−3−3i32−3+3i323+3i323−3i323-1-1-1-1-31111−3−3i321+i321+i32−3+3i321−i321−i323+3i32−1−i32−1−i323−3i32−1+i32−1+i32001+i32−1−i321−i32−1+i32−ii−iiii−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ7900000000
χ413-33-1-1-311-113-3−3+3i32−3−3i323−3i323+3i323-1-1-1-1-31111−3+3i321−i321−i32−3−3i321+i321+i323−3i32−1+i32−1+i323+3i32−1−i32−1−i32001−i32−1+i321+i32−1−i32i−ii−i−i−iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ8300000000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.