Finite Group Databasebeta

← Group #13161981

Character table — Group #13161981

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size111122222222222222444444444444444444444444448888888888888888888888888888888888888181836363636363636363636363636363636363636363672727272727272
order1222333446666666663333366666666666666612121212121226666666666666666666666666612121212121212121212222222466888812122424242424242424466661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-111-1-1
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-11-1-11111
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χ13222222-122222-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-1222-1-2-2-2-2-211-2-2-2-2111111111111111122-1-1-1-1-1-1-1-100002200000-2-20000001111000-1-100
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χ382-22-22-12-22-211-2-2-122-2-12-1-1-111-2-2111111-12-1-1-112-22-1-2000i3−i300i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i31-1-221-111-1-100-2200000000000−i3−i3i3i3000001-10000
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χ774-44-44-2-2-44-42222-2-24-4-2-21112222-1-1-1-1-1-1-2-21112-2-44-220002i3−2i3002i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i32-22-2-11-1-111000000000000000000000000000000
χ784-44-4-2444-42-4-4-4-444-22-2-24-2-22222-4-42222-2-24-2-24-4-22-44000000000000000000000000000-22-224-4-2-222000000000000000000000000000000
χ794-44-4-244-442-4-4-4-444-22-2-24-2-22222-4-42222-2-24-2-2-442-24-40000000000000000000000000002-22-2-4422-2-2000000000000000000000000000000
χ804-44-4-24-24-42-4-4224-2-22-21-21122-1-122-1-1-1-1-21-21142-22-4-200000−2i32i30000i3−i3i3−i3−2i3−2i32i32i3i3i3−i3−i3i3i3−i3−i3-221-1-2211-1-1000000000000000000000000000000
χ814-44-4-24-24-42-4-4224-2-22-21-21122-1-122-1-1-1-1-21-21142-22-4-2000002i3−2i30000−i3i3−i3i32i32i3−2i3−2i3−i3−i3i3i3−i3−i3i3i3-221-1-2211-1-1000000000000000000000000000000
χ824-44-4-24-2-442-4-4224-2-22-21-21122-1-122-1-1-1-1-21-211-4-22-242000000000003-3-33000033-3-3-3-3332-2-112-2-1-111000000000000000000000000000000
χ834-44-4-24-2-442-4-4224-2-22-21-21122-1-122-1-1-1-1-21-211-4-22-24200000000000-333-30000-3-33333-3-32-2-112-2-1-111000000000000000000000000000000
χ844-44-4-2-244-4222-4-4-24-221-2-211-1-12222-1-1-1-11-2-211-2-4-222400000003-3-33000000003-33-3-33-331-1-22-2211-1-1000000000000000000000000000000
χ854-44-4-2-244-4222-4-4-24-221-2-211-1-12222-1-1-1-11-2-211-2-4-22240000000-333-300000000-33-333-33-31-1-22-2211-1-1000000000000000000000000000000
χ864-44-4-2-24-44222-4-4-24-221-2-211-1-12222-1-1-1-11-2-211242-2-2-4000−2i32i300i3−i3i3−i30000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i3-112-22-2-1-111000000000000000000000000000000
χ874-44-4-2-24-44222-4-4-24-221-2-211-1-12222-1-1-1-11-2-211242-2-2-40002i3−2i300−i3i3−i3i300002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i3-112-22-2-1-111000000000000000000000000000000
χ884-44-4-2-2-24-422222-2-2-22111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-22-222-200000−2i32i33-3-33i3−i3i3−i3i3i3−i3−i3−3−i323−i32−3+i323+i323−i32−3−i323+i32−3+i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000000
χ894-44-4-2-2-24-422222-2-2-22111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-22-222-2000002i3−2i3-333-3−i3i3−i3i3−i3−i3i3i33+i32−3+i323−i32−3−i32−3+i323+i32−3−i323−i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000000
χ904-44-4-2-2-24-422222-2-2-22111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-22-222-200000−2i32i3-333-3i3−i3i3−i3i3i3−i3−i33−i32−3−i323+i32−3+i32−3−i323−i32−3+i323+i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000
χ914-44-4-2-2-24-422222-2-2-22111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-22-222-2000002i3−2i33-3-33−i3i3−i3i3−i3−i3i3i3−3+i323+i32−3−i323−i323+i32−3+i323−i32−3−i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000
χ924-44-4-2-2-2-4422222-2-2-22111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-22-2-22000−2i32i300i3−i3i3−i33-3-33i3−i3i3−i3−3−i32−3+i323−i323+i323−i323+i32−3−i32−3+i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000
χ934-44-4-2-2-2-4422222-2-2-22111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-22-2-220002i3−2i300−i3i3−i3i3-333-3−i3i3−i3i33+i323−i32−3+i32−3−i32−3+i32−3−i323+i323−i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000
χ944-44-4-2-2-2-4422222-2-2-22111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-22-2-22000−2i32i300i3−i3i3−i3-333-3i3−i3i3−i33−i323+i32−3−i32−3+i32−3−i32−3+i323−i323+i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000
χ954-44-4-2-2-2-4422222-2-2-22111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-22-2-220002i3−2i300−i3i3−i3i33-3-33−i3i3−i3i3−3+i32−3−i323+i323−i323+i323−i32−3+i32−3−i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000
χ964-4-4444-200-44-4-22-42-444-2-2-2-24-4-22-22-2-222-4222200000000000000000000000000000000000000000000000000000022−22000000−22−220000000
χ974-4-4444-200-44-4-22-42-444-2-2-2-24-4-22-22-2-222-42222000000000000000000000000000000000000000000000000000000−22220000002−22−20000000
χ984-4-444-2400-4-224-42-4-44-24-2-2-2-224-4-22-2-2222-4222000000000000000000000000000000000000000000000000000022−220000−22−2200000000000
χ994-4-444-2400-4-224-42-4-44-24-2-2-2-224-4-22-2-2222-42220000000000000000000000000000000000000000000000000000−222200002−22−200000000000
χ1004-4-44-2440024-44-4-4-42-2-2-24-2-2-22-224-4-2-22222-42200000000000000000000000000000000000000000004-400000-22000000000000000000000
χ1014-4-44-2440024-44-4-4-42-2-2-24-2-2-22-224-4-2-22222-4220000000000000000000000000000000000000000000-44000002-2000000000000000000000
χ10288-8-88-4-40084-44-444-8-8-4-42224-44-4-22-2-22244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-400-4-884-4-8444-42-4224-4-224-4-2-2224-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4800-44-4-884-8442-4-422-224-44-4-2-222-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-44-44-44444222−1−3i3−1+3i3-22-22-221+3i31−3i3−1−3i3−1+3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-400-44-44-44444222−1+3i3−1−3i3-22-22-221−3i31+3i3−1+3i3−1−3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-400-8-44-4444-88-4-4222-44-442-222-2-244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-40048-8-44-844-4-42-422-442-2-4422-2-24-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48004-448-84-84-42-4-4222-2-44-4422-2-2-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4004-44-44444-4222−1−3i3−1+3i32-22-22-2−1−3i3−1+3i31+3i31−3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4004-44-44444-4222−1+3i3−1−3i32-22-22-2−1+3i3−1−3i31−3i31+3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).