Finite Group Databasebeta

← Group #72344108

Character table — Group #72344108

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size111166666666661616161616161616111166666666661616161616161616111166666666661616161616161616111166666666661616161616161616111166666666661616161616161616111166666666661616161616161616111166666666661616161616161616111166666666661616161616161616
order12442222244444336612121212444444444444441212121212121212224422222444446666121212124444444444444412121212121212122244222224444466661212121244444444444444121212121212121222442222244444666612121212444444444444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ311111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ411-1-1111-1-111-1-1-11111-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-111-1-1111-1-111-1-1-11111-1-1-1-1
χ511-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ611-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ733333-1-1-1-1-1-13-1-10000000033333-1-1-1-1-1-13-1-10000000033333-1-1-1-1-1-13-1-10000000033333-1-1-1-1-1-13-1-10000000033333-1-1-1-1-1-13-1-10000000033333-1-1-1-1-1-13-1-10000000033333-1-1-1-1-1-13-1-10000000033333-1-1-1-1-1-13-1-100000000
χ83333-13-1-1-1-1-1-13-1000000003333-13-1-1-1-1-1-13-1000000003333-13-1-1-1-1-1-13-1000000003333-13-1-1-1-1-1-13-1000000003333-13-1-1-1-1-1-13-1000000003333-13-1-1-1-1-1-13-1000000003333-13-1-1-1-1-1-13-1000000003333-13-1-1-1-1-1-13-100000000
χ93333-1-13-1-1-1-1-1-13000000003333-1-13-1-1-1-1-1-13000000003333-1-13-1-1-1-1-1-13000000003333-1-13-1-1-1-1-1-13000000003333-1-13-1-1-1-1-1-13000000003333-1-13-1-1-1-1-1-13000000003333-1-13-1-1-1-1-1-13000000003333-1-13-1-1-1-1-1-1300000000
χ103333-1-1-13-13-1-1-1-1000000003333-1-1-13-13-1-1-1-1000000003333-1-1-13-13-1-1-1-1000000003333-1-1-13-13-1-1-1-1000000003333-1-1-13-13-1-1-1-1000000003333-1-1-13-13-1-1-1-1000000003333-1-1-13-13-1-1-1-1000000003333-1-1-13-13-1-1-1-100000000
χ113333-1-1-1-13-13-1-1-1000000003333-1-1-1-13-13-1-1-1000000003333-1-1-1-13-13-1-1-1000000003333-1-1-1-13-13-1-1-1000000003333-1-1-1-13-13-1-1-1000000003333-1-1-1-13-13-1-1-1000000003333-1-1-1-13-13-1-1-1000000003333-1-1-1-13-13-1-1-100000000
χ1233-3-33-1-111-1-1-3110000000033-3-33-1-111-1-1-3110000000033-3-33-1-111-1-1-3110000000033-3-33-1-111-1-1-3110000000033-3-33-1-111-1-1-3110000000033-3-33-1-111-1-1-3110000000033-3-33-1-111-1-1-3110000000033-3-33-1-111-1-1-31100000000
χ1333-3-3-13-111-1-11-310000000033-3-3-13-111-1-11-310000000033-3-3-13-111-1-11-310000000033-3-3-13-111-1-11-310000000033-3-3-13-111-1-11-310000000033-3-3-13-111-1-11-310000000033-3-3-13-111-1-11-310000000033-3-3-13-111-1-11-3100000000
χ1433-3-3-1-1311-1-111-30000000033-3-3-1-1311-1-111-30000000033-3-3-1-1311-1-111-30000000033-3-3-1-1311-1-111-30000000033-3-3-1-1311-1-111-30000000033-3-3-1-1311-1-111-30000000033-3-3-1-1311-1-111-30000000033-3-3-1-1311-1-111-300000000
χ1533-3-3-1-1-11-3-131110000000033-3-3-1-1-11-3-131110000000033-3-3-1-1-11-3-131110000000033-3-3-1-1-11-3-131110000000033-3-3-1-1-11-3-131110000000033-3-3-1-1-11-3-131110000000033-3-3-1-1-11-3-131110000000033-3-3-1-1-11-3-1311100000000
χ1633-3-3-1-1-1-313-11110000000033-3-3-1-1-1-313-11110000000033-3-3-1-1-1-313-11110000000033-3-3-1-1-1-313-11110000000033-3-3-1-1-1-313-11110000000033-3-3-1-1-1-313-11110000000033-3-3-1-1-1-313-11110000000033-3-3-1-1-1-313-111100000000
χ174-44i−4i000000000011-1-1i−ii−i4-44i−4i000000000011-1-1i−ii−i4-44i−4i000000000011-1-1i−ii−i4-44i−4i000000000011-1-1i−ii−i4-44i−4i000000000011-1-1i−ii−i4-44i−4i000000000011-1-1i−ii−i4-44i−4i000000000011-1-1i−ii−i4-44i−4i000000000011-1-1i−ii−i
χ184-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ74-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ74-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ74-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ74-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ74-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ74-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ74-44i−4i0000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7
χ194-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ114-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ114-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ114-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ114-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ114-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ114-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ114-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11
χ204-4−4i4i000000000011-1-1−ii−ii4-4−4i4i000000000011-1-1−ii−ii4-4−4i4i000000000011-1-1−ii−ii4-4−4i4i000000000011-1-1−ii−ii4-4−4i4i000000000011-1-1−ii−ii4-4−4i4i000000000011-1-1−ii−ii4-4−4i4i000000000011-1-1−ii−ii4-4−4i4i000000000011-1-1−ii−ii
χ214-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ74-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ74-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ74-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ74-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ74-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ74-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ74-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7
χ224-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ114-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ114-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ114-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ114-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ114-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ114-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ114-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11
χ231111111111111111111111iiiiiiiiiiiiiiiiiiiiii-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−i1111111111111111111111iiiiiiiiiiiiiiiiiiiiii-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
χ2411111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32iiiiiiiiiiiiiiζ11ζ7ζ11ζ7ζ11ζ11ζ7ζ7-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ11−ζ7−ζ711111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32iiiiiiiiiiiiiiζ11ζ7ζ11ζ7ζ11ζ11ζ7ζ7-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ11−ζ7−ζ7
χ2511111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32iiiiiiiiiiiiiiζ7ζ11ζ7ζ11ζ7ζ7ζ11ζ11-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ7−ζ11−ζ1111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32iiiiiiiiiiiiiiζ7ζ11ζ7ζ11ζ7ζ7ζ11ζ11-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ7−ζ11−ζ11
χ2611-1-1111-1-111-1-1-11111-1-1-1-1ii−i−iiii−i−iii−i−i−iiiii−i−i−i−i-1-111-1-1-111-1-1111-1-1-1-11111−i−iii−i−i−iii−i−iiii−i−i−i−iiiii11-1-1111-1-111-1-1-11111-1-1-1-1ii−i−iiii−i−iii−i−i−iiiii−i−i−i−i-1-111-1-1-111-1-1111-1-1-1-11111−i−iii−i−i−iii−i−iiii−i−i−i−iiiii
χ2711-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ii−i−iiii−i−iii−i−i−iζ11ζ7ζ11ζ7−ζ11−ζ11−ζ7−ζ7-1-111-1-1-111-1-11111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−i−iii−i−i−iii−i−iiii−ζ11−ζ7−ζ11−ζ7ζ11ζ11ζ7ζ711-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ii−i−iiii−i−iii−i−i−iζ11ζ7ζ11ζ7−ζ11−ζ11−ζ7−ζ7-1-111-1-1-111-1-11111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−i−iii−i−i−iii−i−iiii−ζ11−ζ7−ζ11−ζ7ζ11ζ11ζ7ζ7
χ2811-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ii−i−iiii−i−iii−i−i−iζ7ζ11ζ7ζ11−ζ7−ζ7−ζ11−ζ11-1-111-1-1-111-1-11111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−i−iii−i−i−iii−i−iiii−ζ7−ζ11−ζ7−ζ11ζ7ζ7ζ11ζ1111-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ii−i−iiii−i−iii−i−i−iζ7ζ11ζ7ζ11−ζ7−ζ7−ζ11−ζ11-1-111-1-1-111-1-11111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−i−iii−i−i−iii−i−iiii−ζ7−ζ11−ζ7−ζ11ζ7ζ7ζ11ζ11
χ2933333-1-1-1-1-1-13-1-1000000003i3i3i3i3i−i−i−i−i−i−i3i−i−i00000000-3-3-3-3-3111111-31100000000−3i−3i−3i−3i−3iiiiiii−3iii0000000033333-1-1-1-1-1-13-1-1000000003i3i3i3i3i−i−i−i−i−i−i3i−i−i00000000-3-3-3-3-3111111-31100000000−3i−3i−3i−3i−3iiiiiii−3iii00000000
χ303333-13-1-1-1-1-1-13-1000000003i3i3i3i−i3i−i−i−i−i−i−i3i−i00000000-3-3-3-31-3111111-3100000000−3i−3i−3i−3ii−3iiiiiii−3ii000000003333-13-1-1-1-1-1-13-1000000003i3i3i3i−i3i−i−i−i−i−i−i3i−i00000000-3-3-3-31-3111111-3100000000−3i−3i−3i−3ii−3iiiiiii−3ii00000000
χ313333-1-13-1-1-1-1-1-13000000003i3i3i3i−i−i3i−i−i−i−i−i−i3i00000000-3-3-3-311-3111111-300000000−3i−3i−3i−3iii−3iiiiiii−3i000000003333-1-13-1-1-1-1-1-13000000003i3i3i3i−i−i3i−i−i−i−i−i−i3i00000000-3-3-3-311-3111111-300000000−3i−3i−3i−3iii−3iiiiiii−3i00000000
χ323333-1-1-13-13-1-1-1-1000000003i3i3i3i−i−i−i3i−i3i−i−i−i−i00000000-3-3-3-3111-31-3111100000000−3i−3i−3i−3iiii−3ii−3iiiii000000003333-1-1-13-13-1-1-1-1000000003i3i3i3i−i−i−i3i−i3i−i−i−i−i00000000-3-3-3-3111-31-3111100000000−3i−3i−3i−3iiii−3ii−3iiiii00000000
χ333333-1-1-1-13-13-1-1-1000000003i3i3i3i−i−i−i−i3i−i3i−i−i−i00000000-3-3-3-31111-31-311100000000−3i−3i−3i−3iiiii−3ii−3iiii000000003333-1-1-1-13-13-1-1-1000000003i3i3i3i−i−i−i−i3i−i3i−i−i−i00000000-3-3-3-31111-31-311100000000−3i−3i−3i−3iiiii−3ii−3iiii00000000
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χ1734-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11−4i4i4-40000000000−ζ7−ζ11ζ7ζ11−1+i321−i32−1−i321+i32-44−4i4i00000000001−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ114i−4i-440000000000ζ7ζ11−ζ7−ζ111−i32−1+i321+i32−1−i32-44−4i4i00000000001−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ114i−4i-440000000000ζ7ζ11−ζ7−ζ111−i32−1+i321+i32−1−i324-44i−4i0000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11−4i4i4-40000000000−ζ7−ζ11ζ7ζ11−1+i321−i32−1−i321+i32
χ1744-4−4i4i000000000011-1-1−ii−ii−4i4i-440000000000−i−iii-11-11-444i−4i0000000000-1-111i−ii−i4i−4i4-40000000000ii−i−i1-11-1-444i−4i0000000000-1-111i−ii−i4i−4i4-40000000000ii−i−i1-11-14-4−4i4i000000000011-1-1−ii−ii−4i4i-440000000000−i−iii-11-11
χ1754-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7−4i4i-440000000000−ζ11−ζ7ζ11ζ71+i32−1−i321−i32−1+i32-444i−4i00000000001+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ74i−4i4-40000000000ζ11ζ7−ζ11−ζ7−1−i321+i32−1+i321−i32-444i−4i00000000001+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ74i−4i4-40000000000ζ11ζ7−ζ11−ζ7−1−i321+i32−1+i321−i324-4−4i4i0000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7−4i4i-440000000000−ζ11−ζ7ζ11ζ71+i32−1−i321−i32−1+i32
χ1764-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11−4i4i-440000000000−ζ7−ζ11ζ7ζ111−i32−1+i321+i32−1−i32-444i−4i00000000001−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ114i−4i4-40000000000ζ7ζ11−ζ7−ζ11−1+i321−i32−1−i321+i32-444i−4i00000000001−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ114i−4i4-40000000000ζ7ζ11−ζ7−ζ11−1+i321−i32−1−i321+i324-4−4i4i0000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11−4i4i-440000000000−ζ7−ζ11ζ7ζ111−i32−1+i321+i32−1−i32

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