Finite Group Databasebeta

← Group #72342743

Character table — Group #72342743

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222244446666666688888812121212121212121212121212121212161616161616161616161616161616162424242424242424323232323232323232323232323232323232323232323232
order12442488888888224488882244882222444488888888336612121212242424242424242444448888666666121212121212242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111−1−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+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−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111−1+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−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+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ41111111111-1-1-1-111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-11-1-11111-1-11111-1-1
χ51111111111-1-1-1-111111111-1-1-1-1-1-11111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1-1-1-1-1−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ61111111111-1-1-1-111111111-1-1-1-1-1-11111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1-1-1-1-1−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ7111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-1-11-1-11-1-11-1-1-1-1-1-111-1-1-1-111
χ8111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11111−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32
χ9111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11111−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32
χ10111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321111-1-1-1-1−1−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−i321−i321−i321−i321−i32
χ12111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321111-1-1-1-1−1+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+i321+i321+i321+i321+i32
χ131111-1-111-1-11111-11-1111-1-11-11-1-1-111-1-111-1-11111-1-1-1-1111111111111111111-1-111-1-1-11-1-11-1-11-1-11-111-1-1-1-111-1-1-1-1
χ141111-1-111-1-11111-11-1111-1-11-11-1-1-111-1-111-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211-1-111-1-11+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32
χ151111-1-111-1-11111-11-1111-1-11-11-1-1-111-1-111-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211-1-111-1-11−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32
χ161111-1-111-1-1-1-1-1-1-11-1111-1-1-11-111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-11-1-11-1-1111-1-11111-1-111
χ171111-1-111-1-1-1-1-1-1-11-1111-1-1-11-111111-1-111-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-111-1-1111+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ181111-1-111-1-1-1-1-1-1-11-1111-1-1-11-111111-1-111-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-111-1-1111−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ191111-1-1-1-1111111-11-11-1-111-11-11-1-111-1-111-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-11-1-11-1-11-1-11-1-111-1-1-1-111-1-1
χ201111-1-1-1-1111111-11-11-1-111-11-11-1-111-1-111-1-1-1-1-1-11111−1−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+i32-1-11111-1-11+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32
χ211111-1-1-1-1111111-11-11-1-111-11-11-1-111-1-111-1-1-1-1-1-11111−1+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−i32-1-11111-1-11−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32
χ221111-1-1-1-111-1-1-1-1-11-11-1-1111-11-11111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-11-1-11-1-11-1-11-1-1-11111-1-11111
χ231111-1-1-1-111-1-1-1-1-11-11-1-1111-11-11111-1-111-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-1-1111+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ241111-1-1-1-111-1-1-1-1-11-11-1-1111-11-11111-1-111-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-1-1111−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ2511-1-11-1i−ii−iii−i−i11-1-1i−ii−i1-1-11i−i1-11-11-11-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-11-1i−ii−i11-111-1-1-11-1-11i−ii−ii−ii−ii−ii−i
χ2611-1-11-1i−ii−iii−i−i11-1-1i−ii−i1-1-11i−i1-11-11-11-1ii−i−iii−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ141-11-1i−ii−i−1−i32−1−i321+i32−1+i32−1+i321−i321+i321+i32−1−i321−i321−i32−1+i32ζ22−ζ22ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ14ζ14−ζ14
χ2711-1-11-1i−ii−iii−i−i11-1-1i−ii−i1-1-11i−i1-11-11-11-1ii−i−iii−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ221-11-1i−ii−i−1+i32−1+i321−i32−1−i32−1−i321+i321−i321−i32−1+i321+i321+i32−1−i32ζ14−ζ14ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ22ζ22−ζ22
χ2811-1-11-1i−ii−i−i−iii11-1-1i−ii−i-111-1−ii1-11-11-11-1ii−i−iii−i−i1111-1-1-1-1−i−iii−i−iii-11-11−ii−ii1-111-11-11-1-11-1i−ii−i−iii−ii−i−ii
χ2911-1-11-1i−ii−i−i−iii11-1-1i−ii−i-111-1−ii1-11-11-11-1ii−i−iii−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14-11-11−ii−ii−1−i321+i32−1−i32−1+i321−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32ζ22−ζ22ζ22−ζ22−ζ22ζ22ζ14−ζ14ζ14−ζ14−ζ14ζ14
χ3011-1-11-1i−ii−i−i−iii11-1-1i−ii−i-111-1−ii1-11-11-11-1ii−i−iii−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22-11-11−ii−ii−1+i321−i32−1+i32−1−i321+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32ζ14−ζ14ζ14−ζ14−ζ14ζ14ζ22−ζ22ζ22−ζ22−ζ22ζ22
χ3111-1-11-1−ii−iiii−i−i11-1-1−ii−ii-111-1i−i1-11-11-11-1−i−iii−i−iii1111-1-1-1-1ii−i−iii−i−i-11-11i−ii−i1-111-11-11-1-11-1−ii−iii−i−ii−iii−i
χ3211-1-11-1−ii−iiii−i−i11-1-1−ii−ii-111-1i−i1-11-11-11-1−i−iii−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14-11-11i−ii−i−1−i321+i32−1−i32−1+i321−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−ζ22ζ22−ζ22ζ22ζ22−ζ22−ζ14ζ14−ζ14ζ14ζ14−ζ14
χ3311-1-11-1−ii−iiii−i−i11-1-1−ii−ii-111-1i−i1-11-11-11-1−i−iii−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22-11-11i−ii−i−1+i321−i32−1+i32−1−i321+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−ζ14ζ14−ζ14ζ14ζ14−ζ14−ζ22ζ22−ζ22ζ22ζ22−ζ22
χ3411-1-11-1−ii−ii−i−iii11-1-1−ii−ii1-1-11−ii1-11-11-11-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-11-1−ii−ii11-111-1-1-11-1-11−ii−ii−ii−ii−ii−ii
χ3511-1-11-1−ii−ii−i−iii11-1-1−ii−ii1-1-11−ii1-11-11-11-1−i−iii−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ141-11-1−ii−ii−1−i32−1−i321+i32−1+i32−1+i321−i321+i321+i32−1−i321−i321−i32−1+i32−ζ22ζ22−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ14−ζ14ζ14
χ3611-1-11-1−ii−ii−i−iii11-1-1−ii−ii1-1-11−ii1-11-11-11-1−i−iii−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ221-11-1−ii−ii−1+i32−1+i321−i32−1−i32−1−i321+i321−i321−i32−1+i321+i321+i32−1−i32−ζ14ζ14−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ22−ζ22ζ22
χ3711-1-1-11i−i−iiii−i−i-111-1i−i−ii11-1-1−ii1-1-111-1-11ii−i−i−i−iii1111-1-1-1-1ii−i−iii−i−i1-1-11i−i−ii-111-1111-1-11-1-1i−i−ii−iii−i−ii−ii
χ3811-1-1-11i−i−iiii−i−i-111-1i−i−ii11-1-1−ii1-1-111-1-11ii−i−i−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ141-1-11i−i−ii1+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i32ζ22−ζ22−ζ22ζ22−ζ22ζ22ζ14−ζ14−ζ14ζ14−ζ14ζ14
χ3911-1-1-11i−i−iiii−i−i-111-1i−i−ii11-1-1−ii1-1-111-1-11ii−i−i−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ221-1-11i−i−ii1−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i32ζ14−ζ14−ζ14ζ14−ζ14ζ14ζ22−ζ22−ζ22ζ22−ζ22ζ22
χ4011-1-1-11i−i−ii−i−iii-111-1i−i−ii-1-111i−i1-1-111-1-11ii−i−i−i−iii1111-1-1-1-1−i−iii−i−iii-111-1−iii−i-1-1-1-1-1-1111111i−i−iii−ii−i−iii−i
χ4111-1-1-11i−i−ii−i−iii-111-1i−i−ii-1-111i−i1-1-111-1-11ii−i−i−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14-111-1−iii−i1+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ22−ζ22−ζ22ζ22ζ22−ζ22ζ14−ζ14−ζ14ζ14ζ14−ζ14
χ4211-1-1-11i−i−ii−i−iii-111-1i−i−ii-1-111i−i1-1-111-1-11ii−i−i−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22-111-1−iii−i1−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ14−ζ14−ζ14ζ14ζ14−ζ14ζ22−ζ22−ζ22ζ22ζ22−ζ22
χ4311-1-1-11−iii−iii−i−i-111-1−iii−i-1-111−ii1-1-111-1-11−i−iiiii−i−i1111-1-1-1-1ii−i−iii−i−i-111-1i−i−ii-1-1-1-1-1-1111111−iii−i−ii−iii−i−ii
χ4411-1-1-11−iii−iii−i−i-111-1−iii−i-1-111−ii1-1-111-1-11−i−iiiii−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14-111-1i−i−ii1+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−ζ22ζ22ζ22−ζ22−ζ22ζ22−ζ14ζ14ζ14−ζ14−ζ14ζ14
χ4511-1-1-11−iii−iii−i−i-111-1−iii−i-1-111−ii1-1-111-1-11−i−iiiii−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22-111-1i−i−ii1−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−ζ14ζ14ζ14−ζ14−ζ14ζ14−ζ22ζ22ζ22−ζ22−ζ22ζ22
χ4611-1-1-11−iii−i−i−iii-111-1−iii−i11-1-1i−i1-1-111-1-11−i−iiiii−i−i1111-1-1-1-1−i−iii−i−iii1-1-11−iii−i-111-1111-1-11-1-1−iii−ii−i−iii−ii−i
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.