Finite Group Databasebeta

← Group #11784367

Character table — Group #11784367

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size11111111222222222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444488888888888888888888888888888888999999991818181818181818181818183636363636363636
order1222444422344666888888889991212121218181818181818181836363636363636363636363644444444661212181818181818242424242424242436363636363672727272727272727272727272727272727272727272727212121212121212123636363636363636363636363636363636363636363636368888888844444444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ91111-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1-1111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ141111-1-1-1-1-1-1111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−iiiii−i−i
χ151111-1-1-1-1-1-1111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ161111-1-1-1-1-1-1111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−i−iii
χ1711-1-111-1-1-111-111-1-111-1-111-1-111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−ii−i1-1-11111-1-1-111-1-111-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−ii−iiii−i−i−iiii−i−i−iiii−i−i−iiii−i−i−i11-1-111-1-111-1-111-1-11-11-1i−ii−ii−ii−i
χ1811-1-111-1-1-111-111-1-111-1-111-1-111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−ii−i1-1-11111-1-1-111-1-111-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−ii−iiii−i−i−iiii−i−i−iiii−i−i−iiii−i−i−i-1-111-1-111-1-111-1-111-11-11−ii−ii−ii−ii
χ1911-1-111-1-1-111-111-1-111-1-111-1-111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii−ii1-1-11111-1-1-111-1-111-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii−ii−i−i−iiii−i−i−iiii−i−i−iiii−i−i−iiii11-1-111-1-111-1-111-1-11-11-1−ii−ii−ii−ii
χ2011-1-111-1-1-111-111-1-111-1-111-1-111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii−ii1-1-11111-1-1-111-1-111-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii−ii−i−i−iiii−i−i−iiii−i−i−iiii−i−i−iiii-1-111-1-111-1-111-1-111-11-11i−ii−ii−ii−i
χ2111-1-111-1-1-111-111-1-1-1-111-1-11111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i−ii−ii1-1-11111-1-1-1-1-111-1-111-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1111111i−ii−i−ii−iiiii−i−i−iiii−i−i−i−i−i−iiii−i−i−iiii11-1-111-1-1-1-111-1-1111-11-1i−ii−i−ii−ii
χ2211-1-111-1-1-111-111-1-1-1-111-1-11111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i−ii−ii1-1-11111-1-1-1-1-111-1-111-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1111111i−ii−i−ii−iiiii−i−i−iiii−i−i−i−i−i−iiii−i−i−iiii-1-111-1-11111-1-111-1-1-11-11−ii−iii−ii−i
χ2311-1-111-1-1-111-111-1-1-1-111-1-11111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−iii−ii−i1-1-11111-1-1-1-1-111-1-111-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1111111−ii−iii−ii−i−i−i−iiii−i−i−iiiiiii−i−i−iiii−i−i−i11-1-111-1-1-1-111-1-1111-11-1−ii−iii−ii−i
χ2411-1-111-1-1-111-111-1-1-1-111-1-11111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−iii−ii−i1-1-11111-1-1-1-1-111-1-111-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1111111−ii−iii−ii−i−i−i−iiii−i−i−iiiiiii−i−i−iiii−i−i−i-1-111-1-11111-1-111-1-1-11-11i−ii−i−ii−ii
χ2511-1-1-1-1111-11-111-1-111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−ii-11-11-1-1-111111-1-1-1-111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−iiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiii−i−i−i−iiiii−i−i−i−iiii−i−ii-111-1-111-1
χ2611-1-1-1-1111-11-111-1-111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−ii-11-11-1-1-111111-1-1-1-111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−iiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiii−i−iiiii−i−i−i−iiiii−i−i−iii−i1-1-111-1-11
χ2711-1-1-1-1111-11-111-1-111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i-11-11-1-1-111111-1-1-1-111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−iii−i−i−i−iiiii−i−i−i−iiii−i−ii1-1-111-1-11
χ2811-1-1-1-1111-11-111-1-111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i-11-11-1-1-111111-1-1-1-111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−iiiii−i−i−i−iiiii−i−i−iii−i-111-1-111-1
χ2911-1-1-1-1111-11-111-1-1-1-11111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−ii−iii−i-11-11-1-1-1111-1-11111-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1i−i−ii−iii−iiii−i−i−i−i−i−iiii−i−i−iiiiiii−i−i−iii−i−i−i−iii−i−iiiii−i−ii−i−ii-111-11-1-11
χ3011-1-1-1-1111-11-111-1-1-1-11111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−ii−iii−i-11-11-1-1-1111-1-11111-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1i−i−ii−iii−iiii−i−i−i−i−i−iiii−i−i−iiiiiii−i−i−i−i−iiiii−i−iii−i−i−i−iii−iii−i1-1-11-111-1
χ3111-1-1-1-1111-11-111-1-1-1-11111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−ii−i−ii-11-11-1-1-1111-1-11111-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1−iii−ii−i−ii−i−i−iiiiiii−i−i−iiii−i−i−i−i−i−iiiiii−i−i−i−iii−i−iiiii−i−ii−i−ii1-1-11-111-1
χ3211-1-1-1-1111-11-111-1-1-1-11111-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−ii−i−ii-11-11-1-1-1111-1-11111-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1−iii−ii−i−ii−i−i−iiiiiii−i−i−iiii−i−i−i−i−i−iiii−i−iiiii−i−iii−i−i−i−iii−iii−i-111-11-1-11
χ33222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ34222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111111111110000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111111111111111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
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χ1684-4-44−4i4i4i−4i00-20022-2−222222−22−2i22i22i2−2i2−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ522i−2i−2i2i2ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ4−2ζ68−2ζ44+2ζ52−2ζ682ζ44−2ζ52+2ζ68−2ζ4+2ζ44−2ζ522ζ4−2ζ44+2ζ522ζ14+2ζ22−2ζ14−2ζ22−2ζ14−2ζ62+2ζ702ζ14+2ζ62−2ζ70−2ζ22+2ζ62−2ζ702ζ22−2ζ62+2ζ70−2ζ14−2ζ222ζ14+2ζ222ζ14+2ζ62−2ζ70−2ζ14−2ζ62+2ζ702ζ22−2ζ62+2ζ70−2ζ22+2ζ62−2ζ700000000000000000002−2−22i2−i2−i2i2000000ζ5+ζ13−ζ23−ζ31−ζ5−ζ13+ζ23+ζ31−ζ5−ζ7+ζ23−ζ53+ζ61+ζ71ζ5+ζ7−ζ23+ζ53−ζ61−ζ71ζ7−ζ13+ζ31+ζ53−ζ61−ζ71−ζ7+ζ13−ζ31−ζ53+ζ61+ζ71−ζ5−ζ13+ζ23+ζ31ζ5+ζ13−ζ23−ζ31ζ5+ζ7−ζ23+ζ53−ζ61−ζ71−ζ5−ζ7+ζ23−ζ53+ζ61+ζ71−ζ7+ζ13−ζ31−ζ53+ζ61+ζ71ζ7−ζ13+ζ31+ζ53−ζ61−ζ71ζ5+ζ13+ζ23+ζ31−ζ5−ζ13−ζ23−ζ31−ζ5+ζ7−ζ23−ζ53+ζ61−ζ71ζ5−ζ7+ζ23+ζ53−ζ61+ζ71−ζ7−ζ13−ζ31+ζ53−ζ61+ζ71ζ7+ζ13+ζ31−ζ53+ζ61−ζ71−ζ5−ζ13−ζ23−ζ31ζ5+ζ13+ζ23+ζ31ζ5−ζ7+ζ23+ζ53−ζ61+ζ71−ζ5+ζ7−ζ23−ζ53+ζ61−ζ71ζ7+ζ13+ζ31−ζ53+ζ61−ζ71−ζ7−ζ13−ζ31+ζ53−ζ61+ζ71000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.