Finite Group Databasebeta

← Group #13164497

Character table — Group #13164497

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111166666666661212121212121818181818181818181818182424242424242424242424243636363636361111111111116666666666121212121212181818181818181818181818242424242424242424242424363636363636
order12334466121212122346661212121266612121288882424242424242424333666121212121212246612122266446612121212264666121212126661212128888242424242424242466666612121212121224661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ31111-1-111-1-1-1-1-111-1-11-1-111-1-1-111111-1-11111-1-1-1-1111111-1-1-1-1-1-11-111-1-11111-1-111-1-1-1-1-111-1-11-1-111-1-1-111111-1-11111-1-1-1-1111111-1-1-1-1-1-11-111-1-1
χ41111-1-111-1-1-1-1-111-1-11-1-111-1-1-1111-1-111-1-1-1-11111111111-1-1-1-1-1-1-11-1-1111111-1-111-1-1-1-1-111-1-11-1-111-1-1-1111-1-111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111
χ52222222222222222222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000002222222222222222222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000
χ62222222222222-1222-1-1-122-1-1-1-1-1-10000000000002-1-12-1-122-1-1-1-10000002222222222222-1222-1-1-122-1-1-1-1-1-10000000000002-1-12-1-122-1-1-1-1000000
χ72222222222222-1222-1-1-122-1-1-1-1-1-1000000000000-12-1-12-1-1-122-1-10000002222222222222-1222-1-1-122-1-1-1-1-1-1000000000000-12-1-12-1-1-122-1-1000000
χ82222222222222-1222-1-1-122-1-1-1-1-1-1000000000000-1-12-1-12-1-1-1-1220000002222222222222-1222-1-1-122-1-1-1-1-1-1000000000000-1-12-1-12-1-1-1-122000000
χ92222-2-222-2-2-2-2-222-2-22-2-222-2-2-2222000000000000-1-1-1-1-1-11111110000002222-2-222-2-2-2-2-222-2-22-2-222-2-2-2222000000000000-1-1-1-1-1-1111111000000
χ102222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-10000000000002-1-12-1-1-2-211110000002222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-10000000000002-1-12-1-1-2-21111000000
χ112222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-1000000000000-12-1-12-111-2-2110000002222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-1000000000000-12-1-12-111-2-211000000
χ122222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-1000000000000-1-12-1-121111-2-20000002222-2-222-2-2-2-2-2-12-2-2-11122111-1-1-1000000000000-1-12-1-121111-2-2000000
χ132-2222i−2i-2-22i2i−2i−2i02000-22i−2i00000000−i2i22−2−i2−i2i2i222−2−2-1-1-1111i−ii−ii−i0000002-2222i−2i-2-22i2i−2i−2i02000-22i−2i00000000−i2i22−2−i2−i2i2i222−2−2-1-1-1111i−ii−ii−i000000
χ142-2222i−2i-2-22i2i−2i−2i02000-22i−2i00000000i2−i2−22i2i2−i2−i2−2−222-1-1-1111i−ii−ii−i0000002-2222i−2i-2-22i2i−2i−2i02000-22i−2i00000000i2−i2−22i2i2−i2−i2−2−222-1-1-1111i−ii−ii−i000000
χ152-222−2i2i-2-2−2i−2i2i2i02000-2−2i2i00000000−i2i2−22−i2−i2i2i2−2−222-1-1-1111−ii−ii−ii0000002-222−2i2i-2-2−2i−2i2i2i02000-2−2i2i00000000−i2i2−22−i2−i2i2i2−2−222-1-1-1111−ii−ii−ii000000
χ162-222−2i2i-2-2−2i−2i2i2i02000-2−2i2i00000000i2−i22−2i2i2−i2−i222−2−2-1-1-1111−ii−ii−ii0000002-222−2i2i-2-2−2i−2i2i2i02000-2−2i2i00000000i2−i22−2i2i2−i2−i222−2−2-1-1-1111−ii−ii−ii000000
χ17333333333333-13-1-1-1333-1-1-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-1333333333333-13-1-1-1333-1-1-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-1
χ18333333333333-13-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111333333333333-13-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111
χ193333-3-333-3-3-3-313-1113-3-3-1-1111-1-1-111-1-11111-1-1-1-1000000000000-11-1-1113333-3-333-3-3-3-313-1113-3-3-1-1111-1-1-111-1-11111-1-1-1-1000000000000-11-1-111
χ203333-3-333-3-3-3-313-1113-3-3-1-1111-1-1-1-1-111-1-1-1-111110000000000001-111-1-13333-3-333-3-3-3-313-1113-3-3-1-1111-1-1-1-1-111-1-1-1-111110000000000001-111-1-1
χ2133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i320000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i320000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000011−1−i32−1+i32−1−i32−1+i32
χ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i32000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i32000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000-1-11+i321−i321+i321−i32
χ2333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i31111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000-1-11+i321−i321+i321−i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i31111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000-1-11+i321−i321+i321−i32
χ2433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i3-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000011−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i3-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000011−1−i32−1+i32−1−i32−1+i32
χ2533−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i311-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32000000000000-111+i321−i32−1−i32−1+i3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i311-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32000000000000-111+i321−i32−1−i32−1+i32
χ2633−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i3-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000001-1−1−i32−1+i321+i321−i3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i3-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000001-1−1−i32−1+i321+i321−i32
χ2733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i3200000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000001-1−1−i32−1+i321+i321−i3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i3200000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000001-1−1−i32−1+i321+i321−i32
χ2833−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i32000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000-111+i321−i32−1−i32−1+i3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i32000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000-111+i321−i32−1−i32−1+i32
χ2933−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i320000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i320000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000000011−1+i32−1−i32−1+i32−1−i32
χ3033−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i32000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i32000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000-1-11−i321+i321−i321+i32
χ3133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i31111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000-1-11−i321+i321−i321+i3233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i31111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000-1-11−i321+i321−i321+i32
χ3233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i3-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000011−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i3-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000011−1+i32−1−i32−1+i32−1−i32
χ3333−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i311-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32000000000000-111−i321+i32−1+i32−1−i3233−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i311-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32000000000000-111−i321+i32−1+i32−1−i32
χ3433−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i3-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i320000000000001-1−1+i32−1−i321−i321+i3233−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i3-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i320000000000001-1−1+i32−1−i321−i321+i32
χ3533−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i3200000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i320000000000001-1−1+i32−1−i321−i321+i3233−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i3200000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i320000000000001-1−1+i32−1−i321−i321+i32
χ3633−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i32000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32000000000000-111−i321+i32−1+i32−1−i3233−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i32000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32000000000000-111−i321+i32−1+i32−1−i32
χ374-4444i−4i-4-44i4i−4i−4i04000-44i−4i00000000000000000000111-1-1-1−ii−ii−ii0000004-4444i−4i-4-44i4i−4i−4i04000-44i−4i00000000000000000000111-1-1-1−ii−ii−ii000000
χ384-4444i−4i-4-44i4i−4i−4i0-20002−2i2i0000000000000000000011-2-1-12−ii−ii2i−2i0000004-4444i−4i-4-44i4i−4i−4i0-20002−2i2i0000000000000000000011-2-1-12−ii−ii2i−2i000000
χ394-4444i−4i-4-44i4i−4i−4i0-20002−2i2i000000000000000000001-21-12-1−ii2i−2i−ii0000004-4444i−4i-4-44i4i−4i−4i0-20002−2i2i000000000000000000001-21-12-1−ii2i−2i−ii000000
χ404-4444i−4i-4-44i4i−4i−4i0-20002−2i2i00000000000000000000-2112-1-12i−2i−ii−ii0000004-4444i−4i-4-44i4i−4i−4i0-20002−2i2i00000000000000000000-2112-1-12i−2i−ii−ii000000
χ414-444−4i4i-4-4−4i−4i4i4i04000-4−4i4i00000000000000000000111-1-1-1i−ii−ii−i0000004-444−4i4i-4-4−4i−4i4i4i04000-4−4i4i00000000000000000000111-1-1-1i−ii−ii−i000000
χ424-444−4i4i-4-4−4i−4i4i4i0-200022i−2i0000000000000000000011-2-1-12i−ii−i−2i2i0000004-444−4i4i-4-4−4i−4i4i4i0-200022i−2i0000000000000000000011-2-1-12i−ii−i−2i2i000000
χ434-444−4i4i-4-4−4i−4i4i4i0-200022i−2i000000000000000000001-21-12-1i−i−2i2ii−i0000004-444−4i4i-4-4−4i−4i4i4i0-200022i−2i000000000000000000001-21-12-1i−i−2i2ii−i000000
χ444-444−4i4i-4-4−4i−4i4i4i0-200022i−2i00000000000000000000-2112-1-1−2i2ii−ii−i0000004-444−4i4i-4-4−4i−4i4i4i0-200022i−2i00000000000000000000-2112-1-1−2i2ii−ii−i000000
χ45666666666666-2-3-2-2-2-3-3-3-2-2111111000000000000000000000000000000666666666666-2-3-2-2-2-3-3-3-2-2111111000000000000000000000000000000
χ466666-6-666-6-6-6-62-3-222-333-2-2-1-1-11110000000000000000000000000000006666-6-666-6-6-6-62-3-222-333-2-2-1-1-1111000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.