Finite Group Databasebeta

← Group #13161984

Character table — Group #13161984

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222222244444444444444444444444444448888888888888888888888888888888888888363636363636363636363636727272727272727272727272
order12233344666663333366666666666666666121212121212266666666666666666666666666121212121212121212122222444412121212666688121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11-11-1-1-1-1-1-1-11-1-1-11-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-1-11-1-1-11-11-1-111
χ511111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ611111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-11-11111111-1-1-1-111-1-1-111
χ811111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-11111111-11-1-11-1-1111-1-1
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χ10222222-2-2222222222222222222222222222-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-2-22000000000000-2200000000
χ1122222-122-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-1222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122000022-1-1-1-100-1-100000000
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χ1322222-122-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-12222-2-2-2-2-211-2-2-2-2111111111111111122-1-1-1-1-1-1-1-1220000-2-2111100-1-100000000
χ1422222-122-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-12222-2-2-2-2-211-2-2-2-2111111111111111122-1-1-1-1-1-1-1-1-2-2000022-1-1-1-1001100000000
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χ59444-2-2-2-4-4-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32222222000002i3−2i3-333-3−i3−i3−i3−i33+i32−3+i32−3+i323+i32i3i3i3i33−i32−3−i32−3−i323−i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
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χ7744-4-2-2-24-4-222-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32-22-222-20002i3−2i300−i3−i3i3i33-3−i3i3−3+i323+i32−3−i323−i32-33−i3i33+i32−3+i323−i32−3−i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000
χ7844-4-2-2-24-4-222-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32-22-222-2000−2i32i300i3i3−i3−i3-33i3−i33−i32−3−i323+i32−3+i323-3i3−i3−3−i323−i32−3+i323+i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000
χ7944-4-2-2-24-4-222-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32-22-222-20002i3−2i300−i3−i3i3i3-33−i3i33+i32−3+i323−i32−3−i323-3−i3i3−3+i323+i32−3−i323−i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000
χ8044-4-2-2-24-4-222-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32-22-222-2000−2i32i300i3i3−i3−i33-3i3−i3−3−i323−i32−3+i323+i32-33i3−i33−i32−3−i323+i32−3+i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000
χ8144-4-2-2-2-44-222-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i322-22-2-2202i3−2i30000−i3i3−i3i3−i3i33-3−3+i32−3−i323+i323−i32−i3i3-333+i323−i32−3+i32−3−i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000
χ8244-4-2-2-2-44-222-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i322-22-2-220−2i32i30000i3−i3i3−i3i3−i3-333−i323+i32−3−i32−3+i32i3−i33-3−3−i32−3+i323−i323+i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000
χ8344-4-2-2-2-44-222-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i322-22-2-2202i3−2i30000−i3i3−i3i3−i3i3-333+i323−i32−3+i32−3−i32−i3i33-3−3+i32−3−i323+i323−i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000
χ8444-4-2-2-2-44-222-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i322-22-2-220−2i32i30000i3−i3i3−i3i3−i33-3−3−i32−3+i323−i323+i32i3−i3-333−i323+i32−3−i32−3+i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000
χ854-4044400-400-4-444444000000000000-4-4-4-4-400000000000000000000000000000000000000000000000002-22-22-2000000000000
χ864-4044400-400-4-444444000000000000-4-4-4-4-40000000000000000000000000000000000000000000000000-22-22-22000000000000
χ874-4044-20022i3−2i3-4-44-2-2-2-200002i3−2i32i3−2i32i3−2i32i3−2i3-4222200000000000000000000000000000000000000000000000002-2−1+i31−i3−1−i31+i3000000000000
χ884-4044-20022i3−2i3-4-44-2-2-2-200002i3−2i32i3−2i32i3−2i32i3−2i3-422220000000000000000000000000000000000000000000000000-221−i3−1+i31+i3−1−i3000000000000
χ894-4044-2002−2i32i3-4-44-2-2-2-20000−2i32i3−2i32i3−2i32i3−2i32i3-4222200000000000000000000000000000000000000000000000002-2−1−i31+i3−1+i31−i3000000000000
χ904-4044-2002−2i32i3-4-44-2-2-2-20000−2i32i3−2i32i3−2i32i3−2i32i3-422220000000000000000000000000000000000000000000000000-221+i3−1−i31−i3−1+i3000000000000
χ918-808-4800-800-84-48-4-4-40000000000004-84440000000000000000000000000000000000000000000000000000000000000000000
χ928-808-4-40044i3−4i3-84-4-422200004i3−4i3−2i32i3−2i32i3−2i32i344-2-2-20000000000000000000000000000000000000000000000000000000000000000000
χ938-808-4-4004−4i34i3-84-4-42220000−4i34i32i3−2i32i3−2i32i3−2i344-2-2-20000000000000000000000000000000000000000000000000000000000000000000
χ948-80-48800-8004-8-4-48-4-400000000000044-8440000000000000000000000000000000000000000000000000000000000000000000
χ958-80-48-40044i3−4i34-8-42-4220000−2i32i34i3−4i3−2i32i3−2i32i34-24-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-80-48-4004−4i34i34-8-42-42200002i3−2i3−4i34i32i3−2i32i3−2i34-24-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-80-4-4800-800442-4-422006-600006-6-66-244-2-20000000000000000000000000000000000000000000000000000000000000000000
χ988-80-4-4800-800442-4-42200-660000-666-6-244-2-20000000000000000000000000000000000000000000000000000000000000000000
χ998-80-4-4-40044i3−4i344222−1+3i3−1−3i3006-6−2i32i3−2i32i3−3+i33−i33+i3−3−i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000
χ1008-80-4-4-40044i3−4i344222−1−3i3−1+3i300-66−2i32i3−2i32i33+i3−3−i3−3+i33−i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000
χ1018-80-4-4-4004−4i34i344222−1+3i3−1−3i300-662i3−2i32i3−2i33−i3−3+i3−3−i33+i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-4004−4i34i344222−1−3i3−1+3i3006-62i3−2i32i3−2i3−3−i33+i33−i3−3+i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000

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