Finite Group Databasebeta

← Group #12110566

Character table — Group #12110566

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size111111112222222222222222222222222222222222222222222244444444444444444444444444444444444444444444444444444444888888888888888888888888888888888888888840404040404040404040404040404040
order1222222244444444444455101010101010101010101010101020202020202020202020202020202020224444441010101010101010202020202020202020202020202020202020202020202020202020202020202020202020202020202244444410101010101010102020202020202020202020202020202020202020202020202244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ1711-1-111-1-111-1-1ii−i−i11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1i−ii−ii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11-1i−i1-1i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-11-1i−ii−i1-11-1i−ii−i
χ1811-1-111-1-111-1-1ii−i−i11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1i−ii−ii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11-1i−i1-1i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11-11−ii−ii-11-11−ii−ii
χ1911-1-111-1-111-1-1ii−i−i11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1i−ii−ii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-11−ii-11−ii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-11-1i−ii−i-11-11−ii−ii
χ2011-1-111-1-111-1-1ii−i−i11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1i−ii−ii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-11−ii-11−ii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-11-11−ii−ii1-11-1i−ii−i
χ2111-1-111-1-111-1-1−i−iii11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1−ii−ii−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11-1−ii1-1−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-11-1−ii−ii1-11-1−ii−ii
χ2211-1-111-1-111-1-1−i−iii11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1−ii−ii−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11-1−ii1-1−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-11-11i−ii−i-11-11i−ii−i
χ2311-1-111-1-111-1-1−i−iii11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1−ii−ii−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-11i−i-11i−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-11-1−ii−ii-11-11i−ii−i
χ2411-1-111-1-111-1-1−i−iii11-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1−ii−ii−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-11i−i-11i−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-11-11i−ii−i1-11-1−ii−ii
χ2511-1-111-1-1-1-111ii−i−i11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11i−i−ii−ii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11-1−ii-11i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1-11i−i−ii1-1-11i−i−ii
χ2611-1-111-1-1-1-111ii−i−i11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11i−i−ii−ii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11-1−ii-11i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-111-1−iii−i-111-1−iii−i
χ2711-1-111-1-1-1-111ii−i−i11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11i−i−ii−ii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-11i−i1-1−ii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11-1-11i−i−ii-111-1−iii−i
χ2811-1-111-1-1-1-111ii−i−i11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11i−i−ii−ii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-11i−i1-1−ii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-111-1−iii−i1-1-11i−i−ii
χ2911-1-111-1-1-1-111−i−iii11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11−iii−ii−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11-1i−i-11−ii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1-11−iii−i1-1-11−iii−i
χ3011-1-111-1-1-1-111−i−iii11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11−iii−ii−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11-1i−i-11−ii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-111-1i−i−ii-111-1i−i−ii
χ3111-1-111-1-1-1-111−i−iii11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11−iii−ii−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-11−ii1-1i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11-1-11−iii−i-111-1i−i−ii
χ3211-1-111-1-1-1-111−i−iii11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11−iii−ii−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-11−ii1-1i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-111-1i−i−ii1-1-11−iii−i
χ3322222222222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ3422222222222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ3522222222222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ3622222222222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ372222222222222222-2-2-2-222222222222222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-222-2-222-2-222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
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χ1614-4-4-4-44440000-444-40000−1+5−1−51−5−1+51+5−1−51−5−1+51−5−1+51+5−1−51+5−1−51−51+5−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ700000000000000001−5−1+5001+5−1−500−1+51−500−1−51+5002ζ11−2ζ19−2ζ11+2ζ19002ζ3−2ζ7−2ζ3+2ζ700−2ζ11+2ζ192ζ11−2ζ1900−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000000000000000000000000000000000000000
χ1624-4-4-4-44440000-444-40000−1+5−1−51−5−1+51+5−1−51−5−1+51−5−1+51+5−1−51+5−1−51−51+52ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ700000000000000001−5−1+5001+5−1−500−1+51−500−1−51+500−2ζ11+2ζ192ζ11−2ζ1900−2ζ3+2ζ72ζ3−2ζ7002ζ11−2ζ19−2ζ11+2ζ19002ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000000000000000000000000000000000000000
χ1634-4-4-4-44440000-444-40000−1−5−1+51+5−1−51−5−1+51+5−1−51+5−1−51−5−1+51−5−1+51+51−52ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ1900000000000000001+5−1−5001−5−1+500−1−51+500−1+51−500−2ζ3+2ζ72ζ3−2ζ7002ζ11−2ζ19−2ζ11+2ζ19002ζ3−2ζ7−2ζ3+2ζ700−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000000000000000000000000000000000000000
χ1644-4-4-4-44440000-444-40000−1−5−1+51+5−1−51−5−1+51+5−1−51+5−1−51−5−1+51−5−1+51+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ1900000000000000001+5−1−5001−5−1+500−1−51+500−1+51−5002ζ3−2ζ7−2ζ3+2ζ700−2ζ11+2ζ192ζ11−2ζ1900−2ζ3+2ζ72ζ3−2ζ7002ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.