Finite Group Databasebeta

← Group #72227329

Character table — Group #72227329

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size112226666666666666666666616161616323232323232112226666666666666666666616161616323232323232112226666666666666666666616161616323232323232112226666666666666666666616161616323232323232
order12224222222222224444444443366666612124444444444444444444444444121212121212121212122222422222222222444444444666666661212444444444444444444444444412121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32
χ31111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32
χ4111-1-1111111-1-1-1-1-11111-1-1-1-1-111111-11-1-1-1111-1-1111111-1-1-1-1-11111-1-1-1-1-111111-11-1-1-1111-1-1111111-1-1-1-1-11111-1-1-1-1-111111-11-1-1-1111-1-1111111-1-1-1-1-11111-1-1-1-1-111111-11-1-1-1
χ5111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32
χ6111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32
χ711-11-1111-1-1-1111-1-111-1-111-1-1-11111-11-11-1-111-11-1111-1-1-1111-1-111-1-111-1-1-11111-11-11-1-111-11-1111-1-1-1111-1-111-1-111-1-1-11111-11-11-1-111-11-1111-1-1-1111-1-111-1-111-1-1-11111-11-11-1-1
χ811-11-1111-1-1-1111-1-111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i3211-11-1111-1-1-1111-1-111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i3211-11-1111-1-1-1111-1-111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i3211-11-1111-1-1-1111-1-111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32
χ911-11-1111-1-1-1111-1-111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i3211-11-1111-1-1-1111-1-111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i3211-11-1111-1-1-1111-1-111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i3211-11-1111-1-1-1111-1-111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32
χ1011-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-111
χ1111-1-11111-1-1-1-1-1-11111-1-1-1-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3211-1-11111-1-1-1-1-1-11111-1-1-1-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3211-1-11111-1-1-1-1-1-11111-1-1-1-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3211-1-11111-1-1-1-1-1-11111-1-1-1-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32
χ1211-1-11111-1-1-1-1-1-11111-1-1-1-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3211-1-11111-1-1-1-1-1-11111-1-1-1-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3211-1-11111-1-1-1-1-1-11111-1-1-1-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3211-1-11111-1-1-1-1-1-11111-1-1-1-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32
χ13333333-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-10000000000333333-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-10000000000333333-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-10000000000333333-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-10000000000
χ1433333-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1000000000033333-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1000000000033333-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1000000000033333-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-10000000000
χ1533333-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13000000000033333-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13000000000033333-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13000000000033333-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-130000000000
χ1633333-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1000000000033333-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1000000000033333-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1000000000033333-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-10000000000
χ1733333-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1000000000033333-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1000000000033333-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1000000000033333-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-10000000000
χ18333-3-33-1-13-1-1-31111-1-1-1-111-3110000000000333-3-33-1-13-1-1-31111-1-1-1-111-3110000000000333-3-33-1-13-1-1-31111-1-1-1-111-3110000000000333-3-33-1-13-1-1-31111-1-1-1-111-3110000000000
χ19333-3-3-13-1-13-11-3111-1-1-1-1111-310000000000333-3-3-13-1-13-11-3111-1-1-1-1111-310000000000333-3-3-13-1-13-11-3111-1-1-1-1111-310000000000333-3-3-13-1-13-11-3111-1-1-1-1111-310000000000
χ20333-3-3-1-13-1-1311-311-1-1-1-11111-30000000000333-3-3-1-13-1-1311-311-1-1-1-11111-30000000000333-3-3-1-13-1-1311-311-1-1-1-11111-30000000000333-3-3-1-13-1-1311-311-1-1-1-11111-30000000000
χ21333-3-3-1-1-1-1-1-11111-3-13-131-31110000000000333-3-3-1-1-1-1-1-11111-3-13-131-31110000000000333-3-3-1-1-1-1-1-11111-3-13-131-31110000000000333-3-3-1-1-1-1-1-11111-3-13-131-31110000000000
χ22333-3-3-1-1-1-1-1-1111-313-13-1-311110000000000333-3-3-1-1-1-1-1-1111-313-13-1-311110000000000333-3-3-1-1-1-1-1-1111-313-13-1-311110000000000333-3-3-1-1-1-1-1-1111-313-13-1-311110000000000
χ2333-33-33-1-1-3113-1-111-1-111-1-1-311000000000033-33-33-1-1-3113-1-111-1-111-1-1-311000000000033-33-33-1-1-3113-1-111-1-111-1-1-311000000000033-33-33-1-1-3113-1-111-1-111-1-1-3110000000000
χ2433-33-3-13-11-31-13-111-1-111-1-11-31000000000033-33-3-13-11-31-13-111-1-111-1-11-31000000000033-33-3-13-11-31-13-111-1-111-1-11-31000000000033-33-3-13-11-31-13-111-1-111-1-11-310000000000
χ2533-33-3-1-1311-3-1-1311-1-111-1-111-3000000000033-33-3-1-1311-3-1-1311-1-111-1-111-3000000000033-33-3-1-1311-3-1-1311-1-111-1-111-3000000000033-33-3-1-1311-3-1-1311-1-111-1-111-30000000000
χ2633-33-3-1-1-1111-1-1-11-3-131-3-13111000000000033-33-3-1-1-1111-1-1-11-3-131-3-13111000000000033-33-3-1-1-1111-1-1-11-3-131-3-13111000000000033-33-3-1-1-1111-1-1-11-3-131-3-131110000000000
χ2733-33-3-1-1-1111-1-1-1-313-1-313-1111000000000033-33-3-1-1-1111-1-1-1-313-1-313-1111000000000033-33-3-1-1-1111-1-1-1-313-1-313-1111000000000033-33-3-1-1-1111-1-1-1-313-1-313-11110000000000
χ2833-3-333-1-1-311-311-1-1-1-111113-1-1000000000033-3-333-1-1-311-311-1-1-1-111113-1-1000000000033-3-333-1-1-311-311-1-1-1-111113-1-1000000000033-3-333-1-1-311-311-1-1-1-111113-1-10000000000
χ2933-3-33-13-11-311-31-1-1-1-11111-13-1000000000033-3-33-13-11-311-31-1-1-1-11111-13-1000000000033-3-33-13-11-311-31-1-1-1-11111-13-1000000000033-3-33-13-11-311-31-1-1-1-11111-13-10000000000
χ3033-3-33-1-1311-311-3-1-1-1-11111-1-13000000000033-3-33-1-1311-311-3-1-1-1-11111-1-13000000000033-3-33-1-1311-311-3-1-1-1-11111-1-13000000000033-3-33-1-1311-311-3-1-1-1-11111-1-130000000000
χ3133-3-33-1-1-11111113-13-1-31-31-1-1-1000000000033-3-33-1-1-11111113-13-1-31-31-1-1-1000000000033-3-33-1-1-11111113-13-1-31-31-1-1-1000000000033-3-33-1-1-11111113-13-1-31-31-1-1-10000000000
χ3233-3-33-1-1-1111111-13-131-31-3-1-1-1000000000033-3-33-1-1-1111111-13-131-31-3-1-1-1000000000033-3-33-1-1-1111111-13-131-31-3-1-1-1000000000033-3-33-1-1-1111111-13-131-31-3-1-1-10000000000
χ338-80000000000000000000000022-2-20000008-80000000000000000000000022-2-20000008-80000000000000000000000022-2-20000008-80000000000000000000000022-2-2000000
χ348-800000000000000000000000−1+i3−1−i31−i31+i30000008-800000000000000000000000−1+i3−1−i31−i31+i30000008-800000000000000000000000−1+i3−1−i31−i31+i30000008-800000000000000000000000−1+i3−1−i31−i31+i3000000
χ358-800000000000000000000000−1−i3−1+i31+i31−i30000008-800000000000000000000000−1−i3−1+i31+i31−i30000008-800000000000000000000000−1−i3−1+i31+i31−i30000008-800000000000000000000000−1−i3−1+i31+i31−i3000000
χ3611111111111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ371111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32iiiiiiiiiiiiiiiiiiiiiiiiiζ7ζ11ζ7ζ11ζ7ζ7ζ11ζ11ζ7ζ11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i321−i321+i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ7−ζ11−ζ11−ζ7−ζ11
χ381111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32iiiiiiiiiiiiiiiiiiiiiiiiiζ11ζ7ζ11ζ7ζ11ζ11ζ7ζ7ζ11ζ7-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i321+i321−i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ11−ζ7−ζ7−ζ11−ζ7
χ39111-1-1111111-1-1-1-1-11111-1-1-1-1-111111-11-1-1-1iii−i−iiiiiii−i−i−i−i−iiiii−i−i−i−i−iiiiii−ii−i−i−i-1-1-111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-11-1111−i−i−iii−i−i−i−i−i−iiiiii−i−i−i−iiiiii−i−i−i−i−ii−iiii
χ40111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32iii−i−iiiiiii−i−i−i−i−iiiii−i−i−i−i−iζ7ζ11ζ7ζ11ζ7−ζ7ζ11−ζ11−ζ7−ζ11-1-1-111-1-1-1-1-1-111111-1-1-1-1111111−i321+i321−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32−i−i−iii−i−i−i−i−i−iiiiii−i−i−i−iiiiii−ζ7−ζ11−ζ7−ζ11−ζ7ζ7−ζ11ζ11ζ7ζ11
χ41111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32iii−i−iiiiiii−i−i−i−i−iiiii−i−i−i−i−iζ11ζ7ζ11ζ7ζ11−ζ11ζ7−ζ7−ζ11−ζ7-1-1-111-1-1-1-1-1-111111-1-1-1-1111111+i321−i321+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32−i−i−iii−i−i−i−i−i−iiiiii−i−i−i−iiiiii−ζ11−ζ7−ζ11−ζ7−ζ11ζ11−ζ7ζ7ζ11ζ7
χ4211-11-1111-1-1-1111-1-111-1-111-1-1-11111-11-11-1-1ii−ii−iiii−i−i−iiii−i−iii−i−iii−i−i−iiiii−ii−ii−i−i-1-11-11-1-1-1111-1-1-111-1-111-1-1111-1-1-1-11-11-111−i−ii−ii−i−i−iiii−i−i−iii−i−iii−i−iiii−i−i−i−ii−ii−iii
χ4311-11-1111-1-1-1111-1-111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32ii−ii−iiii−i−i−iiii−i−iii−i−iii−i−i−iζ7ζ11ζ7ζ11−ζ7ζ7−ζ11ζ11−ζ7−ζ11-1-11-11-1-1-1111-1-1-111-1-111-1-11111−i321+i321−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−i−ii−ii−i−i−iiii−i−i−iii−i−iii−i−iiii−ζ7−ζ11−ζ7−ζ11ζ7−ζ7ζ11−ζ11ζ7ζ11
χ4411-11-1111-1-1-1111-1-111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32ii−ii−iiii−i−i−iiii−i−iii−i−iii−i−i−iζ11ζ7ζ11ζ7−ζ11ζ11−ζ7ζ7−ζ11−ζ7-1-11-11-1-1-1111-1-1-111-1-111-1-11111+i321−i321+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−i−ii−ii−i−i−iiii−i−i−iii−i−iii−i−iiii−ζ11−ζ7−ζ11−ζ7ζ11−ζ11ζ7−ζ7ζ11ζ7
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.