Finite Group Databasebeta

← Group #11721869

Character table — Group #11721869

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111111111112222222222222222226666666666666666999999999999121212121212121212121212121212121212121212121212181818181818181818181818181818181818
order123344661212121222244466666612121212121233336666121212121212121288882424242424242424666666666666121212121212121212121212888888242424242424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111-1-11-1-111-1-1-1-111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111-1-11-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ5111111111111-11-1-11-1-1-111-1-1-1-111-1-11111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111-11-1-11-1-1-111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-11111
χ7111111111111-1-11-1-11-1-1-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111-1-11-1-11-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ91111-1-111-1-1-1-111-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−ii−iii−i−iii−i−iii−i−i
χ101111-1-111-1-1-1-111-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-1-1-1-11111−ii−ii−ii−i−iii−i−iii−i−iii
χ111111-1-111-1-1-1-11-11-11-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1i−i−ii−iiii−i−i−i−iii−i−iii
χ121111-1-111-1-1-1-11-11-11-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−iii−ii−i−i−iiiii−i−iii−i−i
χ131111-1-111-1-1-1-1-1111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1111111111111-1-1-1-1-1-1-1-1−iii−i−ii−i−iiiii−i−i−i−iii
χ141111-1-111-1-1-1-1-1111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1111111111111-1-1-1-1-1-1-1-1i−i−iii−iii−i−i−i−iiiii−i−i
χ151111-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1111111111111−ii−iii−i−i−iii−i−iiiii−i−i
χ161111-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1111111111111i−ii−i−iiii−i−iii−i−i−i−iii
χ172222222222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-10000000000002-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1000000000000000000
χ18222222222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1000000000000-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1000000000000000000
χ19222222222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1000000000000-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1000000000000000000
χ20222222222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122000000000000-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12000000000000000000
χ212222222222222-2-22-2-222-2-2-2-222-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-10000000000002-1-1-1-2111-21112-1-1-1-2111-2111000000000000000000
χ222222222222222-2-22-2-222-2-2-2-222-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1000000000000-12-1-11-2111-211-12-1-11-2111-211000000000000000000
χ232222222222222-2-22-2-222-2-2-2-222-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1000000000000-1-12-111-2111-21-1-12-111-2111-21000000000000000000
χ242222222222222-2-22-2-222-2-2-2-222-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122000000000000-1-1-12111-2111-2-1-1-12111-2111-2000000000000000000
χ25222222222222-22-2-22-2-2-222-2-2-2-222-2-22-1-1-12-1-1-122-1-1-1-1-1-1000000000000-21112-1-1-1-2111-21112-1-1-1-2111000000000000000000
χ26222222222222-22-2-22-2-2-222-2-2-2-222-2-2-12-1-1-12-1-1-1-122-1-1-1-10000000000001-211-12-1-11-2111-211-12-1-11-211000000000000000000
χ27222222222222-22-2-22-2-2-222-2-2-2-222-2-2-1-12-1-1-12-1-1-1-1-122-1-100000000000011-21-1-12-111-2111-21-1-12-111-21000000000000000000
χ28222222222222-22-2-22-2-2-222-2-2-2-222-2-2-1-1-12-1-1-12-1-1-1-1-1-122000000000000111-2-1-1-12111-2111-2-1-1-12111-2000000000000000000
χ29222222222222-2-22-2-22-2-2-2-222-2-2-2-2222-1-1-12-1-1-122-1-1-1-1-1-1000000000000-2111-21112-1-1-1-2111-21112-1-1-1000000000000000000
χ30222222222222-2-22-2-22-2-2-2-222-2-2-2-222-12-1-1-12-1-1-1-122-1-1-1-10000000000001-2111-211-12-1-11-2111-211-12-1-1000000000000000000
χ31222222222222-2-22-2-22-2-2-2-222-2-2-2-222-1-12-1-1-12-1-1-1-1-122-1-100000000000011-2111-21-1-12-111-2111-21-1-12-1000000000000000000
χ32222222222222-2-22-2-22-2-2-2-222-2-2-2-222-1-1-12-1-1-12-1-1-1-1-1-122000000000000111-2111-2-1-1-12111-2111-2-1-1-12000000000000000000
χ332222-2-222-2-2-2-222-2-2-222222-2-2-2-2-2-2222-1-1-12-1-1-1-2-21111110000000000002-1-1-12-1-1-1-2111-2111-21112-1-1-1000000000000000000
χ342222-2-222-2-2-2-222-2-2-222222-2-2-2-2-2-222-12-1-1-12-1-111-2-21111000000000000-12-1-1-12-1-11-2111-2111-211-12-1-1000000000000000000
χ352222-2-222-2-2-2-222-2-2-222222-2-2-2-2-2-222-1-12-1-1-12-11111-2-211000000000000-1-12-1-1-12-111-2111-2111-21-1-12-1000000000000000000
χ362222-2-222-2-2-2-222-2-2-222222-2-2-2-2-2-222-1-1-12-1-1-12111111-2-2000000000000-1-1-12-1-1-12111-2111-2111-2-1-1-12000000000000000000
χ372222-2-222-2-2-2-22-22-22-222-2-222-2-222-2-22-1-1-12-1-1-1-2-21111110000000000002-1-1-1-21112-1-1-1-21112-1-1-1-2111000000000000000000
χ382222-2-222-2-2-2-22-22-22-222-2-222-2-222-2-2-12-1-1-12-1-111-2-21111000000000000-12-1-11-211-12-1-11-211-12-1-11-211000000000000000000
χ392222-2-222-2-2-2-22-22-22-222-2-222-2-222-2-2-1-12-1-1-12-11111-2-211000000000000-1-12-111-21-1-12-111-21-1-12-111-21000000000000000000
χ402222-2-222-2-2-2-22-22-22-222-2-222-2-222-2-2-1-1-12-1-1-12111111-2-2000000000000-1-1-12111-2-1-1-12111-2-1-1-12111-2000000000000000000
χ412222-2-222-2-2-2-2-2222-2-2-2-2222222-2-2-2-22-1-1-12-1-1-1-2-2111111000000000000-21112-1-1-12-1-1-12-1-1-1-2111-2111000000000000000000
χ422222-2-222-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-12-1-1-12-1-111-2-211110000000000001-211-12-1-1-12-1-1-12-1-11-2111-211000000000000000000
χ432222-2-222-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-1-12-1-1-12-11111-2-21100000000000011-21-1-12-1-1-12-1-1-12-111-2111-21000000000000000000
χ442222-2-222-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-1-1-12-1-1-12111111-2-2000000000000111-2-1-1-12-1-1-12-1-1-12111-2111-2000000000000000000
χ452222-2-222-2-2-2-2-2-2-2222-2-2-2-2-2-22222222-1-1-12-1-1-1-2-2111111000000000000-2111-2111-21112-1-1-12-1-1-12-1-1-1000000000000000000
χ462222-2-222-2-2-2-2-2-2-2222-2-2-2-2-2-2222222-12-1-1-12-1-111-2-211110000000000001-2111-2111-211-12-1-1-12-1-1-12-1-1000000000000000000
χ472222-2-222-2-2-2-2-2-2-2222-2-2-2-2-2-2222222-1-12-1-1-12-11111-2-21100000000000011-2111-2111-21-1-12-1-1-12-1-1-12-1000000000000000000
χ482222-2-222-2-2-2-2-2-2-2222-2-2-2-2-2-2222222-1-1-12-1-1-12111111-2-2000000000000111-2111-2111-2-1-1-12-1-1-12-1-1-12000000000000000000
χ492-2222i−2i-2-22i2i−2i−2i0000000000000000002222-2-2-2-22i−2i2i−2i2i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000000000000000000000
χ502-2222i−2i-2-22i2i−2i−2i0000000000000000002222-2-2-2-22i−2i2i−2i2i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000000000000000000000
χ512-222−2i2i-2-2−2i−2i2i2i0000000000000000002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000000000000000000000
χ522-222−2i2i-2-2−2i−2i2i2i0000000000000000002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000000000000000000000
χ5333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ5433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ5533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323-3-33-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i3200000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000011-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ5633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323-3-33-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i320000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000-1-111111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ5733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-33-3-33-33+3i323−3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i3200000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000-1-111-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ5833−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-33-3-33-33+3i323−3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i320000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000011-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ5933−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33-3-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i3200000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000-1-1-1-1111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ6033−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33-3-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i320000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000000000001111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ6133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3233-3-3-33−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i320000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14000000000000000000000000i−ii−ii−iζ22ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14
χ6233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3233-3-3-33−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i320000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14000000000000000000000000−ii−ii−ii−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ22ζ14
χ6333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-33-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i320000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14000000000000000000000000i−i−ii−iiζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ22ζ14
χ6433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-33-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i320000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14000000000000000000000000−iii−ii−i−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14
χ6533−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3333-3-33+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i320000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14000000000000000000000000−iii−i−ii−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14
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χ6733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-3-3-33333+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14000000000000000000000000−ii−iii−i−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14
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χ1006-6−3+3i3−3−3i3−6i6i3−3i33+3i3−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ52ζ132ζ232ζ7−2ζ23−2ζ7000000000000000000000000000000000000000000

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