Finite Group Databasebeta

← Group #13135924

Character table — Group #13135924

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113
size111111111111222222222222444666666666666666688888812121212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636363636363636363636363636
order122233666666444412121212121212124121233336666666666664412121212121212121212121212121212121212121212121212121212121212121212121212121212121212128888888824242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ92222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000
χ102222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000000000000000
χ11222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1222222-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000
χ12222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000000000000000
χ13222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1222222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000
χ14222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-211000000000000000000000000
χ15222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000
χ16222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2000000000000000000000000
χ172222222222222-22-222-2-222-2-2-2-2-22222222222222222000000-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ182222222222222-22-222-2-222-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1000000-2-211111122-1-1-1-1-1-1-2-211111100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000000
χ192222222222222-22-222-2-222-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1000000-2-211111122-1-1-1-1-1-1-2-211111100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000000
χ202222222222222-22-222-2-222-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-100000011-2-21111-1-122-1-1-1-111-2-21111−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000000000
χ212222222222222-22-222-2-222-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-100000011-2-21111-1-122-1-1-1-111-2-21111i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000000000
χ222222222222222-22-222-2-222-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-10000001111-2-211-1-1-1-122-1-11111-2-211−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000000000
χ232222222222222-22-222-2-222-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-10000001111-2-211-1-1-1-122-1-11111-2-211i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000000000000
χ242222222222222-22-222-2-222-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000111111-2-2-1-1-1-1-1-122111111-2-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000000000000
χ252222222222222-22-222-2-222-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000111111-2-2-1-1-1-1-1-122111111-2-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000000000000
χ26222222222222-22-22-2-222-2-222-2-2-22222222222222222000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ27222222222222-22-22-2-222-2-222-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1000000-2-2111111-2-211111122-1-1-1-1-1-100−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000000000000000000000
χ28222222222222-22-22-2-222-2-222-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1000000-2-2111111-2-211111122-1-1-1-1-1-100i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000000000000000000000
χ29222222222222-22-22-2-222-2-222-2-2-2-12-1-1-1-122-1-1-1-1-12-1-100000011-2-2111111-2-21111-1-122-1-1-1-1−i3i300−i3i3i3−i3i3−i300i3−i3−i3i3000000000000000000000000
χ30222222222222-22-22-2-222-2-222-2-2-2-12-1-1-1-122-1-1-1-1-12-1-100000011-2-2111111-2-21111-1-122-1-1-1-1i3−i300i3−i3−i3i3−i3i300−i3i3i3−i3000000000000000000000000
χ31222222222222-22-22-2-222-2-222-2-2-2-1-12-1-1-1-1-122-1-1-1-12-10000001111-2-2111111-2-211-1-1-1-122-1-1−i3i3i3−i300−i3i3i3−i3−i3i300i3−i3000000000000000000000000
χ32222222222222-22-22-2-222-2-222-2-2-2-1-12-1-1-1-1-122-1-1-1-12-10000001111-2-2111111-2-211-1-1-1-122-1-1i3−i3−i3i300i3−i3−i3i3i3−i300−i3i3000000000000000000000000
χ33222222222222-22-22-2-222-2-222-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000111111-2-2111111-2-2-1-1-1-1-1-122−i3i3−i3i3i3−i300i3−i3i3−i3−i3i300000000000000000000000000
χ34222222222222-22-22-2-222-2-222-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000111111-2-2111111-2-2-1-1-1-1-1-122i3−i3i3−i3−i3i300−i3i3−i3i3i3−i300000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-122-1-1-1-1-1-12-1-1-12-222-2-222-1-1-1-1-1-1-2-2111111-2-211111122-1-1-1-1-1-1-2-2111111000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-122-1-1-1-1-1-12-1-1-1-22-2-22222-1-1-1-1-1-1-2-2111111-2-2111111-2-211111122-1-1-1-1-1-1000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-12-1-1-1-122-1-1-1-1-12-1-12-222-2-2-1-122-1-1-1-111-2-2111111-2-21111-1-122-1-1-1-111-2-21111000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-12-1-1-1-122-1-1-1-1-12-1-1-22-2-222-1-122-1-1-1-111-2-2111111-2-2111111-2-21111-1-122-1-1-1-1000000000000000000000000
χ39222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-1-12-1-1-1-1-122-1-1-1-12-12-222-2-2-1-1-1-122-1-11111-2-2111111-2-211-1-1-1-122-1-11111-2-211000000000000000000000000
χ40222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-1-12-1-1-1-1-122-1-1-1-12-1-22-2-222-1-1-1-122-1-11111-2-2111111-2-2111111-2-211-1-1-1-122-1-1000000000000000000000000
χ41222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-1-1-12-1-1-1-1-1-122-1-1-122-222-2-2-1-1-1-1-1-122111111-2-2111111-2-2-1-1-1-1-1-122111111-2-2000000000000000000000000
χ42222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-1-1-12-1-1-1-1-1-122-1-1-12-22-2-222-1-1-1-1-1-122111111-2-2111111-2-2111111-2-2-1-1-1-1-1-122000000000000000000000000
χ4322-2-22222-2-2-2-220-202200-2-20000022222-22-22-22-2-2-2-2-2000000000000002-22-22-22-200000000000000000000000000002−22−20000000022−2−222−2−2
χ4422-2-22222-2-2-2-220-202200-2-20000022222-22-22-22-2-2-2-2-2000000000000002-22-22-22-20000000000000000000000000000−22−2200000000−2−222−2−222
χ4522-2-22222-2-2-2-2-2020-2-200220000022222-22-22-22-2-2-2-2-200000000000000-22-22-22-220000000000000000000000000000−i2i2i2−i200000000−i2−i2i2i2i2i2−i2−i2
χ4622-2-22222-2-2-2-2-2020-2-200220000022222-22-22-22-2-2-2-2-200000000000000-22-22-22-220000000000000000000000000000i2−i2−i2i200000000i2i2−i2−i2−i2−i2i2i2
χ472-2-2222-2-2-2-222020-2002200-2-20002222-2-2-2-2-2-2-2-2222200000000000000000000002-22-22-22-20000000000000000−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i200000000
χ482-2-2222-2-2-2-222020-2002200-2-20002222-2-2-2-2-2-2-2-2222200000000000000000000002-22-22-22-20000000000000000i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i200000000
χ492-2-2222-2-2-2-2220-20200-2-200220002222-2-2-2-2-2-2-2-222220000000000000000000000-22-22-22-2200000000000000002−2−22000022−2−2−2−22200000000
χ502-2-2222-2-2-2-2220-20200-2-200220002222-2-2-2-2-2-2-2-222220000000000000000000000-22-22-22-220000000000000000−222−20000−2−22222−2−200000000
χ513333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32000000000000000033−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000000011111111−1−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
χ523333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32000000000000000033−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ533333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i320000000000000000-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ543333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i320000000000000000-3-33+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ553333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323−3−3i32−3+3i3200000000000000003-3−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000000000ii−i−iii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14
χ563333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323−3−3i32−3+3i3200000000000000003-3−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000000000−i−iii−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14
χ573333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323−3−3i32−3+3i320000000000000000-333+3i323−3i32−3−3i32−3+3i320000000000000000000000000000000000000000ii−i−i−i−iiiζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14
χ583333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323−3−3i32−3+3i320000000000000000-333+3i323−3i32−3−3i32−3+3i320000000000000000000000000000000000000000−i−iiiii−i−i−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14
χ593333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32000000000000000033−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000000011111111−1+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
χ603333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32000000000000000033−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ613333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-3-33−3i323+3i323−3i323+3i3200000000000000000000000000000000000000001111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ623333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-3-33−3i323+3i323−3i323+3i320000000000000000000000000000000000000000-1-1-1-111111−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
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χ643333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3+3i32−3−3i3200000000000000003-3−3+3i32−3−3i323−3i323+3i320000000000000000000000000000000000000000−i−iii−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.