Finite Group Databasebeta

← Group #13156980

Character table — Group #13156980

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222222222444444444444444444448888888888888899121212121212121212121212121218181818181818242424242424242424242424242424242424242436363636363672727272108108
order1222233366666333666666666666666663666666666666644224444666612121212444121212126666661212121212121212121212121212444412121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111-1-11-11-11111-1-111-1-1-1-1-1-1-1-1-11-111-1-11-111-1-11111111111-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-11-11-1-1-111-1-111-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111111111111111111111-1-1-11-1111-1-111-1-111-1-1-1-1-1-1-1-11-1-111-11-1-11111111111-1-111-1-1-1-111-1-1
χ811111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-111-11-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ9111-1-11111111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-1111-1-11i−i11-1-1-1-1111-1-111111-111-1-1-11-1-111iiii−i−i−i−ii−ii−i-1-1i−ii−ii−i
χ10111-1-11111111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-1111-1-11−ii11-1-1-1-1111-1-111111-111-1-1-11-1-111−i−i−i−iiiii−ii−ii-1-1−ii−ii−ii
χ11111-1-11111111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-111-111-1i−i-1-11111-1-11-1-11111-11-1-1111-111-1-1iiii−i−i−i−i−ii−ii-1-1−ii−iii−i
χ12111-1-11111111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-111-111-1−ii-1-11111-1-11-1-11111-11-1-1111-111-1-1−i−i−i−iiiiii−ii−i-1-1i−ii−i−ii
χ13111-1-11111111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-1-1-111-1-1i−i1111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−ii−i−ii11i−i−ii−ii
χ14111-1-11111111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-1-1-111-1-1−ii1111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii−iii−i11−iii−ii−i
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χ192222222-1-1-122-12-1-122-1-12-1-1-1-12222-1-122-122-1-1-1-1-1-1-1-1-1-1-1-2-22-22-200-1-111-1-111-2-2-211112-2-1-1112-2-1-11100000000000011000000
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χ4122-22-2222-2-2222222-2-22-22-2-2-2-2-2-2-2-222222-222-22-22-2-222-2-22200000000000000-22-222-2-20000000000000000000000002-2000000
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χ958-8000-48-4−4i34i34-84-42-4000042i3−2i3−4i34i30000-24002000000-22i3−2i300000000000000000000000000000000000000000000000000000000000
χ968-8000-48-44i3−4i34-84-42-400004−2i32i34i3−4i30000-24002000000-2−2i32i300000000000000000000000000000000000000000000000000000000000
χ978-8000-4-480044-82-4-40000-20000006-644002000000-200006-60000000000000000000000000000000000000000000000000000000
χ988-8000-4-480044-82-4-40000-2000000-6644002000000-20000-660000000000000000000000000000000000000000000000000000000
χ998-8000-4-4-4−4i34i34442220000-22i3−2i32i3−2i3006-6-2-200-10000001−i3i3−3i33i3-330000000000000000000000000000000000000000000000000000000
χ1008-8000-4-4-4−4i34i34442220000-22i3−2i32i3−2i300-66-2-200-10000001−i3i33i3−3i33-30000000000000000000000000000000000000000000000000000000
χ1018-8000-4-4-44i3−4i34442220000-2−2i32i3−2i32i3006-6-2-200-10000001i3−i33i3−3i3-330000000000000000000000000000000000000000000000000000000
χ1028-8000-4-4-44i3−4i34442220000-2−2i32i3−2i32i300-66-2-200-10000001i3−i3−3i33i33-30000000000000000000000000000000000000000000000000000000

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