Finite Group Databasebeta

← Group #72340208

Character table — Group #72340208

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size111122222266666666666666666666666666666666666666661616161616161616323232323232323232323232111122222266666666666666666666666666666666666666661616161616161616323232323232323232323232
order124424888822222222224444444444888888888888888888883366121212126612122424242424242424224424888822222222224444444444888888888888888888886666121212126612122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111−1−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+i32−1+i32−1+i3211111111111111111111111111111111111111111111111111−1−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+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111−1+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−i32−1−i32−1−i3211111111111111111111111111111111111111111111111111−1+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−i32−1−i32−1−i32
χ4111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ5111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ6111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ71111-1-111-1-111111-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-111-1-111111-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ81111-1-111-1-111111-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321111-1-111-1-111111-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ91111-1-111-1-111111-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321111-1-111-1-111111-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ101111-1-1-1-11111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-11111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111-1-111
χ111111-1-1-1-11111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321111-1-1-1-11111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ121111-1-1-1-11111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321111-1-1-1-11111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-11-1i−ii−i111-1-1111-1-111-1-1-111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i1111-1-1-1-111-1-1i−ii−ii−ii−i11-1-11-1i−ii−i111-1-1111-1-111-1-1-111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i1111-1-1-1-111-1-1i−ii−ii−ii−i
χ1411-1-11-1i−ii−i111-1-1111-1-111-1-1-111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ711-1-11-1i−ii−i111-1-1111-1-111-1-1-111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ1511-1-11-1i−ii−i111-1-1111-1-111-1-1-111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ1111-1-11-1i−ii−i111-1-1111-1-111-1-1-111-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ1611-1-11-1−ii−ii111-1-1111-1-111-1-1-111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii1111-1-1-1-111-1-1−ii−ii−ii−ii11-1-11-1−ii−ii111-1-1111-1-111-1-1-111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii1111-1-1-1-111-1-1−ii−ii−ii−ii
χ1711-1-11-1−ii−ii111-1-1111-1-111-1-1-111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ711-1-11-1−ii−ii111-1-1111-1-111-1-1-111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ1811-1-11-1−ii−ii111-1-1111-1-111-1-1-111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ1111-1-11-1−ii−ii111-1-1111-1-111-1-1-111-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ1911-1-1-11i−i−ii111-1-1-1-1-11111-1-1-1-1-1111iiiii−i−i−i−i−i−i−i−i−i−iiiiii1111-1-1-1-1-1-111i−i−iii−i−ii11-1-1-11i−i−ii111-1-1-1-1-11111-1-1-1-1-1111iiiii−i−i−i−i−i−i−i−i−i−iiiiii1111-1-1-1-1-1-111i−i−iii−i−ii
χ2011-1-1-11i−i−ii111-1-1-1-1-11111-1-1-1-1-1111iiiii−i−i−i−i−i−i−i−i−i−iiiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ711-1-1-11i−i−ii111-1-1-1-1-11111-1-1-1-1-1111iiiii−i−i−i−i−i−i−i−i−i−iiiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ2111-1-1-11i−i−ii111-1-1-1-1-11111-1-1-1-1-1111iiiii−i−i−i−i−i−i−i−i−i−iiiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ1111-1-1-11i−i−ii111-1-1-1-1-11111-1-1-1-1-1111iiiii−i−i−i−i−i−i−i−i−i−iiiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ2211-1-1-11−iii−i111-1-1-1-1-11111-1-1-1-1-1111−i−i−i−i−iiiiiiiiiii−i−i−i−i−i1111-1-1-1-1-1-111−iii−i−iii−i11-1-1-11−iii−i111-1-1-1-1-11111-1-1-1-1-1111−i−i−i−i−iiiiiiiiiii−i−i−i−i−i1111-1-1-1-1-1-111−iii−i−iii−i
χ2311-1-1-11−iii−i111-1-1-1-1-11111-1-1-1-1-1111−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ711-1-1-11−iii−i111-1-1-1-1-11111-1-1-1-1-1111−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ2411-1-1-11−iii−i111-1-1-1-1-11111-1-1-1-1-1111−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ1111-1-1-11−iii−i111-1-1-1-1-11111-1-1-1-1-1111−i−i−i−i−iiiiiiiiiii−i−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ2533333333333-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-10000000000000000000033333333333-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-100000000000000000000
χ263333333333-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1000000000000000000003333333333-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-100000000000000000000
χ273333333333-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1000000000000000000003333333333-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-100000000000000000000
χ283333333333-1-1-13-1-1-1-13-13-1-1-1-13-1-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1000000000000000000003333333333-1-1-13-1-1-1-13-13-1-1-1-13-1-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-100000000000000000000
χ293333333333-1-1-1-13-1-1-1-13-13-1-1-1-13-1-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13000000000000000000003333333333-1-1-1-13-1-1-1-13-13-1-1-1-13-1-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-1300000000000000000000
χ30333333-3-3-3-33-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-31111-31111-31111-3111100000000000000000000333333-3-3-3-33-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-31111-31111-31111-3111100000000000000000000
χ31333333-3-3-3-3-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-11-31111-31111-31111-311100000000000000000000333333-3-3-3-3-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-11-31111-31111-31111-311100000000000000000000
χ32333333-3-3-3-3-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-1311-31111-31111-31111-31100000000000000000000333333-3-3-3-3-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-1311-31111-31111-31111-31100000000000000000000
χ33333333-3-3-3-3-1-1-13-1-1-1-13-13-1-1-1-13-1-1-1-1111-31111-31111-31111-3100000000000000000000333333-3-3-3-3-1-1-13-1-1-1-13-13-1-1-1-13-1-1-1-1111-31111-31111-31111-3100000000000000000000
χ34333333-3-3-3-3-1-1-1-13-1-1-1-13-13-1-1-1-13-1-1-11111-31111-31111-31111-300000000000000000000333333-3-3-3-3-1-1-1-13-1-1-1-13-13-1-1-1-13-1-1-11111-31111-31111-31111-300000000000000000000
χ353333-3-333-3-33-1-1-1-1-31111-1-13-1-111-3113-1-1-1-13-1-1-1-1-31111-31111000000000000000000003333-3-333-3-33-1-1-1-1-31111-1-13-1-111-3113-1-1-1-13-1-1-1-1-31111-3111100000000000000000000
χ363333-3-333-3-3-13-1-1-11-3111-1-1-13-1111-31-13-1-1-1-13-1-1-11-31111-3111000000000000000000003333-3-333-3-3-13-1-1-11-3111-1-1-13-1111-31-13-1-1-1-13-1-1-11-31111-311100000000000000000000
χ373333-3-333-3-3-1-13-1-111-311-1-1-1-131111-3-1-13-1-1-1-13-1-111-31111-311000000000000000000003333-3-333-3-3-1-13-1-111-311-1-1-1-131111-3-1-13-1-1-1-13-1-111-31111-31100000000000000000000
χ383333-3-333-3-3-1-1-13-1111-313-1-1-1-1-31111-1-1-13-1-1-1-13-1111-31111-31000000000000000000003333-3-333-3-3-1-1-13-1111-313-1-1-1-1-31111-1-1-13-1-1-1-13-1111-31111-3100000000000000000000
χ393333-3-333-3-3-1-1-1-131111-3-13-1-1-11-3111-1-1-1-13-1-1-1-131111-31111-3000000000000000000003333-3-333-3-3-1-1-1-131111-3-13-1-1-11-3111-1-1-1-13-1-1-1-131111-31111-300000000000000000000
χ403333-3-3-3-3333-1-1-1-1-31111-1-13-1-111-311-31111-311113-1-1-1-13-1-1-1-1000000000000000000003333-3-3-3-3333-1-1-1-1-31111-1-13-1-111-311-31111-311113-1-1-1-13-1-1-1-100000000000000000000
χ413333-3-3-3-333-13-1-1-11-3111-1-1-13-1111-311-31111-3111-13-1-1-1-13-1-1-1000000000000000000003333-3-3-3-333-13-1-1-11-3111-1-1-13-1111-311-31111-3111-13-1-1-1-13-1-1-100000000000000000000
χ423333-3-3-3-333-1-13-1-111-311-1-1-1-131111-311-31111-311-1-13-1-1-1-13-1-1000000000000000000003333-3-3-3-333-1-13-1-111-311-1-1-1-131111-311-31111-311-1-13-1-1-1-13-1-100000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.