Finite Group Databasebeta

← Group #13147354

Character table — Group #13147354

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111112222222222222222229999999999991212121212121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1233446612121212246688881212242424242424242422446666121212123366666612121212121212122424242424242424242424242424242424668888121224242424242424244444444412121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-1-1-11-11-11-11-111-1-111-1-111-1-111-1-1
χ101111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-1-1-1-11-11-11-11-1-111-1-111-1-111-1-111
χ111111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ121111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ131111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-1-1-111111-1-111-1-1111-1-1-1-11111-1-1-1-111
χ141111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-1-1-11111-111-1-111-1-1-11111-1-1-1-11111-1-1
χ151111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-11111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ161111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-11111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-20000-2-20000000022222222222222-2-2-2-2222222-2-2-2-20000000000000000-2-2-2-20000-2-200000000000000000000000000000000
χ18222222222222-2-2-2-20000-2-200000000-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-20000000000000000222200002200000000000000000000000000000000
χ192222-2-222-2-2-2-22-2220000-2-20000000022-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000002-2220000-2-200000000000000000000000000000000
χ202222-2-222-2-2-2-22-2220000-2-200000000-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-20000000000000000-22-2-200002200000000000000000000000000000000
χ212-2222i−2i-2-22i2i−2i−2i00002−2−i2i20022−2−2−i2−i2i2i22-22i−2i22-2-22i2i−2i−2i220000-2-22i2i−2i−2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i200002−2−i2i20022−2−2−i2−i2i2i2000000000000000000000000
χ222-2222i−2i-2-22i2i−2i−2i00002−2−i2i20022−2−2−i2−i2i2i2-22−2i2i-2-222−2i−2i2i2i220000-2-22i2i−2i−2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i20000−22i2−i200−2−222i2i2−i2−i2000000000000000000000000
χ232-2222i−2i-2-22i2i−2i−2i0000−22i2−i200−2−222i2i2−i2−i22-22i−2i22-2-22i2i−2i−2i220000-2-22i2i−2i−2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i20000−22i2−i200−2−222i2i2−i2−i2000000000000000000000000
χ242-2222i−2i-2-22i2i−2i−2i0000−22i2−i200−2−222i2i2−i2−i2-22−2i2i-2-222−2i−2i2i2i220000-2-22i2i−2i−2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i200002−2−i2i20022−2−2−i2−i2i2i2000000000000000000000000
χ252-222−2i2i-2-2−2i−2i2i2i00002−2i2−i20022−2−2i2i2−i2−i22-2−2i2i22-2-2−2i−2i2i2i220000-2-2−2i−2i2i2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i200002−2i2−i20022−2−2i2i2−i2−i2000000000000000000000000
χ262-222−2i2i-2-2−2i−2i2i2i00002−2i2−i20022−2−2i2i2−i2−i2-222i−2i-2-2222i2i−2i−2i220000-2-2−2i−2i2i2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i20000−22−i2i200−2−222−i2−i2i2i2000000000000000000000000
χ272-222−2i2i-2-2−2i−2i2i2i0000−22−i2i200−2−222−i2−i2i2i22-2−2i2i22-2-2−2i−2i2i2i220000-2-2−2i−2i2i2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i20000−22−i2i200−2−222−i2−i2i2i2000000000000000000000000
χ282-222−2i2i-2-2−2i−2i2i2i0000−22−i2i200−2−222−i2−i2i2i2-222i−2i-2-2222i2i−2i−2i220000-2-2−2i−2i2i2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i200002−2i2−i20022−2−2i2i2−i2−i2000000000000000000000000
χ2933−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000000000000000000011−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32iiii−i−i−i−iζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22
χ3033−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000000000000000000011−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−i−i−i−iiiii−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22
χ3133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-11+i321−i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i3211111111−1+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
χ3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-11+i321−i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ3333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000000000000000000011−1−i32−1+i32-1-1-1-1−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32ii−i−i−i−iiiζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
χ3433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000000000000000000011−1−i32−1+i32-1-1-1-1−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32−i−iiiii−i−i−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
χ3533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-11+i321−i3211111+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ3633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-11+i321−i3211111+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ3733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3200000000000000000000000000000000-111+i321−i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32i−ii−i−ii−iiζ14ζ22−ζ14−ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22−ζ14−ζ22ζ14ζ22
χ3833−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3200000000000000000000000000000000-111+i321−i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−ii−iii−ii−i−ζ14−ζ22ζ14ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22ζ14ζ22−ζ14−ζ22
χ3933−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000000000001-1−1−i32−1+i32-1-1111+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-11-11-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ4033−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000000000001-1−1−i32−1+i32-1-1111+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-11-11-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ4133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32-3-333−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3200000000000000000000000000000000-111+i321−i32-1-111−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32i−i−ii−iii−iζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22
χ4233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32-3-333−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3200000000000000000000000000000000-111+i321−i32-1-111−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−iii−ii−i−ii−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22
χ4333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32-3-333−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000000000001-1−1−i32−1+i3211-1-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1-111-1-11−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
χ4433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32-3-333−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000000000001-1−1−i32−1+i3211-1-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-111-1-111-11−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.