Finite Group Databasebeta

← Group #72342783

Character table — Group #72342783

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136
size112222244444444488888888881616161616161616336666612121212121212121224242424242424242424484848484848484844888881616161616161616163232323232323232323264646464646464644488888161616161616161616323232323232323232326464646464646464
order1224488448881616161616163232323232323232222444882224488448881616161616163232323232323232222444883661212242412122424244848484848489696969696969696666121212242436612122424121224242448484848484896969696969696966661212122424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1
χ61111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111
χ71111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111
χ81111111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-11111111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-11111111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-11111111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-1
χ911-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i1-11-1i−ii−i11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i1-11-1i−ii−i11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i1-11-1i−ii−i11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i1-11-1i−ii−i
χ1011-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i-11-11−ii−ii11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i-11-11−ii−ii11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i-11-11−ii−ii11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i-11-11−ii−ii
χ1111-11-111i−ii−i-111-1-1i−i-1-111−i−iii1-1-11i−i−ii11-11-111i−ii−i-111-1-1i−i-1-111−i−iii1-1-11i−i−ii11-11-111i−ii−i-111-1-1i−i-1-111−i−iii1-1-11i−i−ii11-11-111i−ii−i-111-1-1i−i-1-111−i−iii1-1-11i−i−ii
χ1211-11-111i−ii−i-111-1-1i−i-1-111−i−iii-111-1−iii−i11-11-111i−ii−i-111-1-1i−i-1-111−i−iii-111-1−iii−i11-11-111i−ii−i-111-1-1i−i-1-111−i−iii-111-1−iii−i11-11-111i−ii−i-111-1-1i−i-1-111−i−iii-111-1−iii−i
χ1311-11-111−ii−ii-111-1-1−ii11-1-1−i−iii1-11-1−ii−ii11-11-111−ii−ii-111-1-1−ii11-1-1−i−iii1-11-1−ii−ii11-11-111−ii−ii-111-1-1−ii11-1-1−i−iii1-11-1−ii−ii11-11-111−ii−ii-111-1-1−ii11-1-1−i−iii1-11-1−ii−ii
χ1411-11-111−ii−ii-111-1-1−ii11-1-1−i−iii-11-11i−ii−i11-11-111−ii−ii-111-1-1−ii11-1-1−i−iii-11-11i−ii−i11-11-111−ii−ii-111-1-1−ii11-1-1−i−iii-11-11i−ii−i11-11-111−ii−ii-111-1-1−ii11-1-1−i−iii-11-11i−ii−i
χ1511-11-111−ii−ii-111-1-1−ii-1-111ii−i−i1-1-11−iii−i11-11-111−ii−ii-111-1-1−ii-1-111ii−i−i1-1-11−iii−i11-11-111−ii−ii-111-1-1−ii-1-111ii−i−i1-1-11−iii−i11-11-111−ii−ii-111-1-1−ii-1-111ii−i−i1-1-11−iii−i
χ1611-11-111−ii−ii-111-1-1−ii-1-111ii−i−i-111-1i−i−ii11-11-111−ii−ii-111-1-1−ii-1-111ii−i−i-111-1i−i−ii11-11-111−ii−ii-111-1-1−ii-1-111ii−i−i-111-1i−i−ii11-11-111−ii−ii-111-1-1−ii-1-111ii−i−i-111-1i−i−ii
χ17222222222222-2-2-2-2-2-20000000000000000222222222222-2-2-2-2-2-20000000000000000222222222222-2-2-2-2-2-20000000000000000222222222222-2-2-2-2-2-20000000000000000
χ182222222-2-2-2-22-2-2-2-22200000000000000002222222-2-2-2-22-2-2-2-22200000000000000002222222-2-2-2-22-2-2-2-22200000000000000002222222-2-2-2-22-2-2-2-2220000000000000000
χ1922222-2-222-2-2-20000002−22−22−22−20000000022222-2-222-2-2-20000002−22−22−22−20000000022222-2-222-2-2-20000002−22−22−22−20000000022222-2-222-2-2-20000002−22−22−22−200000000
χ2022222-2-222-2-2-2000000−22−22−22−220000000022222-2-222-2-2-2000000−22−22−22−220000000022222-2-222-2-2-2000000−22−22−22−220000000022222-2-222-2-2-2000000−22−22−22−2200000000
χ2122222-2-2-2-222-20000002−22−2−22−220000000022222-2-2-2-222-20000002−22−2−22−220000000022222-2-2-2-222-20000002−22−2−22−220000000022222-2-2-2-222-20000002−22−2−22−2200000000
χ2222222-2-2-2-222-2000000−22−222−22−20000000022222-2-2-2-222-2000000−22−222−22−20000000022222-2-2-2-222-2000000−22−222−22−20000000022222-2-2-2-222-2000000−22−222−22−200000000
χ2322-22-2222i−2i2i−2i-2-2-222−2i2i000000000000000022-22-2222i−2i2i−2i-2-2-222−2i2i000000000000000022-22-2222i−2i2i−2i-2-2-222−2i2i000000000000000022-22-2222i−2i2i−2i-2-2-222−2i2i0000000000000000
χ2422-22-222−2i2i−2i2i-2-2-2222i−2i000000000000000022-22-222−2i2i−2i2i-2-2-2222i−2i000000000000000022-22-222−2i2i−2i2i-2-2-2222i−2i000000000000000022-22-222−2i2i−2i2i-2-2-2222i−2i0000000000000000
χ2522-22-2-2-22i−2i−2i2i20000002−2−22i2−i2−i2i20000000022-22-2-2-22i−2i−2i2i20000002−2−22i2−i2−i2i20000000022-22-2-2-22i−2i−2i2i20000002−2−22i2−i2−i2i20000000022-22-2-2-22i−2i−2i2i20000002−2−22i2−i2−i2i200000000
χ2622-22-2-2-22i−2i−2i2i2000000−222−2−i2i2i2−i20000000022-22-2-2-22i−2i−2i2i2000000−222−2−i2i2i2−i20000000022-22-2-2-22i−2i−2i2i2000000−222−2−i2i2i2−i20000000022-22-2-2-22i−2i−2i2i2000000−222−2−i2i2i2−i200000000
χ2722-22-2-2-2−2i2i2i−2i20000002−2−22−i2i2i2−i20000000022-22-2-2-2−2i2i2i−2i20000002−2−22−i2i2i2−i20000000022-22-2-2-2−2i2i2i−2i20000002−2−22−i2i2i2−i20000000022-22-2-2-2−2i2i2i−2i20000002−2−22−i2i2i2−i200000000
χ2822-22-2-2-2−2i2i2i−2i2000000−222−2i2−i2−i2i20000000022-22-2-2-2−2i2i2i−2i2000000−222−2i2−i2−i2i20000000022-22-2-2-2−2i2i2i−2i2000000−222−2i2−i2−i2i20000000022-22-2-2-2−2i2i2i−2i2000000−222−2i2−i2−i2i200000000
χ29444-4-4000000022−2222−22000000000000000000444-4-4000000022−2222−22000000000000000000444-4-4000000022−2222−22000000000000000000444-4-4000000022−2222−22000000000000000000
χ30444-4-40000000−2222−2222000000000000000000444-4-40000000−2222−2222000000000000000000444-4-40000000−2222−2222000000000000000000444-4-40000000−2222−2222000000000000000000
χ3144-4-44000000022−22−222200000000000000000044-4-44000000022−22−222200000000000000000044-4-44000000022−22−222200000000000000000044-4-44000000022−22−2222000000000000000000
χ3244-4-440000000−222222−2200000000000000000044-4-440000000−222222−2200000000000000000044-4-440000000−222222−2200000000000000000044-4-440000000−222222−22000000000000000000
χ338-800042−420000000000000000000000000008-800042−420000000000000000000000000008-800042−420000000000000000000000000008-800042−42000000000000000000000000000
χ348-8000−42420000000000000000000000000008-8000−42420000000000000000000000000008-8000−42420000000000000000000000000008-8000−4242000000000000000000000000000
χ3511111111111111111111111111111111111111111111111111111111111111111111−1+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+i32−1+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−i32−1−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
χ3611111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1−1+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+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−i32−1−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ37111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1−1+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+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ38111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ391111111-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-11111111-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ401111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−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+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ421111111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-11111111-1-1-1-111111-1-1-1-1-1-11111-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ4311-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i1-11-1i−ii−i11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i1-11-1i−ii−i−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32ζ14−ζ14ζ14−ζ141−i32−1+i32−1+i321−i321−i32ζ14−ζ14−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ14−1+i321−i32−1+i321−i32ζ14−ζ14ζ14−ζ14−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32ζ22−ζ22ζ22−ζ221+i32−1−i32−1−i321+i321+i32ζ22−ζ22−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ22−1−i321+i32−1−i321+i32ζ22−ζ22ζ22−ζ22
χ4411-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i-11-11−ii−ii11-11-111i−ii−i-111-1-1i−i11-1-1ii−i−i-11-11−ii−ii−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32ζ14−ζ14ζ14−ζ141−i32−1+i32−1+i321−i321−i32ζ14−ζ14−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ141−i32−1+i321−i32−1+i32−ζ14ζ14−ζ14ζ14−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32ζ22−ζ22ζ22−ζ221+i32−1−i32−1−i321+i321+i32ζ22−ζ22−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ221+i32−1−i321+i32−1−i32−ζ22ζ22−ζ22ζ22
χ4511-11-111i−ii−i-111-1-1i−i-1-111−i−iii1-1-11i−i−ii11-11-111i−ii−i-111-1-1i−i-1-111−i−iii1-1-11i−i−ii−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32ζ14−ζ14ζ14−ζ141−i32−1+i32−1+i321−i321−i32ζ14−ζ141−i321−i32−1+i32−1+i32−ζ14−ζ14ζ14ζ14−1+i321−i321−i32−1+i32ζ14−ζ14−ζ14ζ14−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32ζ22−ζ22ζ22−ζ221+i32−1−i32−1−i321+i321+i32ζ22−ζ221+i321+i32−1−i32−1−i32−ζ22−ζ22ζ22ζ22−1−i321+i321+i32−1−i32ζ22−ζ22−ζ22ζ22
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χ119666666666666-6-6-6-6-6-60000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1206666666-6-6-6-66-6-6-6-6660000000000000000-2-2-2-2-2-2-22222-22222-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ131121212-12-12000000062−6262−62000000000000000000-4-4-4440000000−2222−222200000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ132121212-12-120000000−6262−6262000000000000000000-4-4-444000000022−2222−2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1331212-12-1212000000062−62−6262000000000000000000-4-444-40000000−222222−2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1341212-12-12120000000−626262−62000000000000000000-4-444-4000000022−22−222200000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13524-24000122−122000000000000000000000000000-88000−424200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13624-24000−122122000000000000000000000000000-8800042−4200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.