Finite Group Databasebeta

← Group #72221321

Character table — Group #72221321

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111224444444444444444448888888888888888888888888888888888888888202020202020202025252525404040404040404040404040404040405050100100200200200200200200200200
order1222444455101010101010202020202020202055101010101010202020202020202020202020202020202020202020202020202020202020202088888888222240404040404040404040404040404040444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1i−iiii−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−i−iiii
χ51111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1i−ii−i−iii−i
χ61111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−ii−iii−i−ii
χ71111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11
χ81111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1
χ9111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-111-11-11-1-1
χ10111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11-11-111
χ11111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111i−i−ii−i−iii
χ12111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−iii−iii−i−i
χ13111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111i−i−i−iii−ii
χ14111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111−iiii−i−ii−i
χ15111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1111111-1-111-1-11-11-1
χ16111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-11-11
χ172222-2-22-222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000022220000000000000000-2-22-200000000
χ182222-2-22-222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-2000000000000000022-2200000000
χ192222-2-2-2222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000022220000000000000000-2-2-2200000000
χ202222-2-2-2222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000-2-2-2-20000000000000000222-200000000
χ2122-2-22-2002222-2-2-2-22222-2-2-2-22222-2-2-2-2000000002222-2-2-2-20000000000000000002-2002-222-2-2000022-2-2000022-2-22-20000000000
χ2222-2-22-2002222-2-2-2-22222-2-2-2-22222-2-2-2-2000000002222-2-2-2-20000000000000000002-200-22-2-222000022-2-20000-2-222-220000000000
χ2322-2-22-2002222-2-2-2-22222-2-2-2-22222-2-2-2-2000000002222-2-2-2-2000000000000000000-22002-2-2-2220000-2-222000022-2-2-220000000000
χ2422-2-22-2002222-2-2-2-22222-2-2-2-22222-2-2-2-2000000002222-2-2-2-2000000000000000000-2200-2222-2-20000-2-2220000-2-2222-20000000000
χ2522-2-2-22002222-2-2-2-2-2-2-2-222222222-2-2-2-200000000-2-2-2-2222200000000000000002-2002-20022-2-222-2-2000022-2-20000-220000000000
χ2622-2-2-22002222-2-2-2-2-2-2-2-222222222-2-2-2-200000000-2-2-2-2222200000000000000002-200-2200-2-22222-2-20000-2-22200002-20000000000
χ2722-2-2-22002222-2-2-2-2-2-2-2-222222222-2-2-2-200000000-2-2-2-222220000000000000000-22002-200-2-222-2-222000022-2-200002-20000000000
χ2822-2-2-22002222-2-2-2-2-2-2-2-222222222-2-2-2-200000000-2-2-2-222220000000000000000-2200-220022-2-2-2-2220000-2-2220000-220000000000
χ29444444444-14-144-1-144-1-144-1-1-1-1-1-1-1-1-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100004444000000000000-1-1-1-1-1-1-1-1000000000000
χ30444444444-14-144-1-144-1-144-1-1-1-1-1-1-1-1-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-4-4-400000000000011111111000000000000
χ3144444444-14-14-1-144-1-144-1-144-1-1-1-1-1-1-1-1-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444400000000-1-1-1-1-1-1-1-100000000000000000000
χ3244444444-14-14-1-144-1-144-1-144-1-1-1-1-1-1-1-1-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4000000001111111100000000000000000000
χ33444444-4-44-14-144-1-144-1-144-1-1-1-1-1-1-1-1-1-1-4-411-4-411-1-1-1-1-1-1-1-11111111111111111000044-4-4000000000000-1-1-1-11111000000000000
χ34444444-4-44-14-144-1-144-1-144-1-1-1-1-1-1-1-1-1-1-4-411-4-411-1-1-1-1-1-1-1-111111111111111110000-4-4440000000000001111-1-1-1-1000000000000
χ35444444-4-4-14-14-1-144-1-144-1-144-1-1-1-1-1-1-1-111-4-411-4-4-1-1-1-1-1-1-1-1111111111111111144-4-400000000-1-1-1-1111100000000000000000000
χ36444444-4-4-14-14-1-144-1-144-1-144-1-1-1-1-1-1-1-111-4-411-4-4-1-1-1-1-1-1-1-11111111111111111-4-444000000001111-1-1-1-100000000000000000000
χ374444-4-44-44-14-144-1-1-4-411-4-411-1-1-1-1-1-1-1-144-1-1-4-41111111111-1-1-1-1-1-1-1-11111111100000000000000000000i5−i5i5−i5i5−i5i5−i5000000000000
χ384444-4-44-44-14-144-1-1-4-411-4-411-1-1-1-1-1-1-1-144-1-1-4-41111111111-1-1-1-1-1-1-1-11111111100000000000000000000−i5i5−i5i5−i5i5−i5i5000000000000
χ394444-4-44-4-14-14-1-14411-4-411-4-4-1-1-1-1-1-1-1-1-1-14411-4-411111111-1-1-1-1-1-1-1-111111111000000000000i5−i5i5−i5i5−i5i5−i500000000000000000000
χ404444-4-44-4-14-14-1-14411-4-411-4-4-1-1-1-1-1-1-1-1-1-14411-4-411111111-1-1-1-1-1-1-1-111111111000000000000−i5i5−i5i5−i5i5−i5i500000000000000000000
χ414444-4-4-444-14-144-1-1-4-411-4-411-1-1-1-1-1-1-1-1-4-41144-1-11111111111111111-1-1-1-1-1-1-1-100000000000000000000i5−i5i5−i5−i5i5−i5i5000000000000
χ424444-4-4-444-14-144-1-1-4-411-4-411-1-1-1-1-1-1-1-1-4-41144-1-11111111111111111-1-1-1-1-1-1-1-100000000000000000000−i5i5−i5i5i5−i5i5−i5000000000000
χ434444-4-4-44-14-14-1-14411-4-411-4-4-1-1-1-1-1-1-1-111-4-4-1-1441111111111111111-1-1-1-1-1-1-1-1000000000000i5−i5i5−i5−i5i5−i5i500000000000000000000
χ444444-4-4-44-14-14-1-14411-4-411-4-4-1-1-1-1-1-1-1-111-4-4-1-1441111111111111111-1-1-1-1-1-1-1-1000000000000−i5i5−i5i5i5−i5i5−i500000000000000000000
χ4544-4-44-4004-14-1-4-41144-1-1-4-411-1-1-1-1111100i5−i500i5−i5-1-1-1-11111i5i5i5i5−i5−i5−i5−i5i5i5i5i5−i5−i5−i5−i50000004-4000000000000i5−i5−i5i5-1-111000000000000
χ4644-4-44-4004-14-1-4-41144-1-1-4-411-1-1-1-1111100i5−i500i5−i5-1-1-1-11111i5i5i5i5−i5−i5−i5−i5i5i5i5i5−i5−i5−i5−i5000000-44000000000000−i5i5i5−i511-1-1000000000000
χ4744-4-44-4004-14-1-4-41144-1-1-4-411-1-1-1-1111100−i5i500−i5i5-1-1-1-11111−i5−i5−i5−i5i5i5i5i5−i5−i5−i5−i5i5i5i5i50000004-4000000000000−i5i5i5−i5-1-111000000000000
χ4844-4-44-4004-14-1-4-41144-1-1-4-411-1-1-1-1111100−i5i500−i5i5-1-1-1-11111−i5−i5−i5−i5i5i5i5i5−i5−i5−i5−i5i5i5i5i5000000-44000000000000i5−i5−i5i511-1-1000000000000
χ4944-4-44-400-14-1411-4-4-1-14411-4-4-1-1-1-11111i5−i500i5−i500-1-1-1-11111i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5004-400000000i5−i5−i5i5-1-11100000000000000000000
χ5044-4-44-400-14-1411-4-4-1-14411-4-4-1-1-1-11111i5−i500i5−i500-1-1-1-11111i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i500-4400000000−i5i5i5−i511-1-100000000000000000000
χ5144-4-44-400-14-1411-4-4-1-14411-4-4-1-1-1-11111−i5i500−i5i500-1-1-1-11111−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5004-400000000−i5i5i5−i5-1-11100000000000000000000
χ5244-4-44-400-14-1411-4-4-1-14411-4-4-1-1-1-11111−i5i500−i5i500-1-1-1-11111−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i500-4400000000i5−i5−i5i511-1-100000000000000000000
χ5344-4-4-44004-14-1-4-411-4-41144-1-1-1-1-1-1111100i5−i500−i5i51111-1-1-1-1i5i5i5i5−i5−i5−i5−i5−i5−i5−i5−i5i5i5i5i500004-400000000000000-1-111−i5i5i5−i5000000000000
χ5444-4-4-44004-14-1-4-411-4-41144-1-1-1-1-1-1111100i5−i500−i5i51111-1-1-1-1i5i5i5i5−i5−i5−i5−i5−i5−i5−i5−i5i5i5i5i50000-440000000000000011-1-1i5−i5−i5i5000000000000
χ5544-4-4-44004-14-1-4-411-4-41144-1-1-1-1-1-1111100−i5i500i5−i51111-1-1-1-1−i5−i5−i5−i5i5i5i5i5i5i5i5i5−i5−i5−i5−i500004-400000000000000-1-111i5−i5−i5i5000000000000
χ5644-4-4-44004-14-1-4-411-4-41144-1-1-1-1-1-1111100−i5i500i5−i51111-1-1-1-1−i5−i5−i5−i5i5i5i5i5i5i5i5i5−i5−i5−i5−i50000-440000000000000011-1-1−i5i5i5−i5000000000000
χ5744-4-4-4400-14-1411-4-411-4-4-1-144-1-1-1-11111i5−i500−i5i5001111-1-1-1-1i5i5−i5−i5i5i5−i5−i5−i5−i5i5i5−i5−i5i5i54-40000000000-1-111−i5i5i5−i500000000000000000000
χ5844-4-4-4400-14-1411-4-411-4-4-1-144-1-1-1-11111i5−i500−i5i5001111-1-1-1-1i5i5−i5−i5i5i5−i5−i5−i5−i5i5i5−i5−i5i5i5-44000000000011-1-1i5−i5−i5i500000000000000000000
χ5944-4-4-4400-14-1411-4-411-4-4-1-144-1-1-1-11111−i5i500i5−i5001111-1-1-1-1−i5−i5i5i5−i5−i5i5i5i5i5−i5−i5i5i5−i5−i54-40000000000-1-111i5−i5−i5i500000000000000000000
χ6044-4-4-4400-14-1411-4-411-4-4-1-144-1-1-1-11111−i5i500i5−i5001111-1-1-1-1−i5−i5i5i5−i5−i5i5i5i5i5−i5−i5i5i5−i5−i5-44000000000011-1-1−i5i5i5−i500000000000000000000
χ614-44-4000044-4-44-44-40000000044-4-444-4-400000000000000000000000000000000000000004-44-40000000000000000000000000000
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χ6588888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2-2-2-2-2-233-2-233-2-233-2-2-2-23333-2-2-2-2330000000000000000000000000000000000000000
χ6688888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2-2-2-2-2-2-233-2-233-2-23333-2-2-2-23333-2-20000000000000000000000000000000000000000
χ67888888-8-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-23-23-23-22222222233-2-233-2-2-3-32222-3-3-3-32222-3-30000000000000000000000000000000000000000
χ68888888-8-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-23-23-2322222222-2-233-2-23322-3-3-3-32222-3-3-3-3220000000000000000000000000000000000000000
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χ7588-8-88-800-2-2-2-22222-2-2-2-22222-23-232-32-32i5−2i5−2i52i52i5−2i5−2i52i5-2-23322-3-300i5i5−i5−i50000i5i5−i5−i5000000000000000000000000000000000000000000
χ7688-8-88-800-2-2-2-22222-2-2-2-22222-23-232-32-3−2i52i52i5−2i5−2i52i52i5−2i5-2-23322-3-300−i5−i5i5i50000−i5−i5i5i5000000000000000000000000000000000000000000
χ7788-8-8-8800-2-2-2-222222222-2-2-2-23-23-2-32-322i5−2i52i5−2i5−2i52i5−2i52i5-3-32233-2-2−i5−i50000i5i5i5i50000−i5−i50000000000000000000000000000000000000000
χ7888-8-8-8800-2-2-2-222222222-2-2-2-23-23-2-32-32−2i52i5−2i52i52i5−2i52i5−2i5-3-32233-2-2i5i50000−i5−i5−i5−i50000i5i50000000000000000000000000000000000000000
χ7988-8-8-8800-2-2-2-222222222-2-2-2-2-23-232-32-32i5−2i5−2i52i5−2i52i52i5−2i522-3-3-2-23300i5i5−i5−i50000−i5−i5i5i5000000000000000000000000000000000000000000
χ8088-8-8-8800-2-2-2-222222222-2-2-2-2-23-232-32-3−2i52i52i5−2i52i5−2i5−2i52i522-3-3-2-23300−i5−i5i5i50000i5i5−i5−i5000000000000000000000000000000000000000000
χ818-88-800008-2-828-8-22002i5−2i5002i5−2i5-2-222-2-222000000002i5−2i52i5−2i52i5−2i52i5−2i500000000000000000000000000000000000000000000000000000000
χ828-88-800008-2-828-8-2200−2i52i500−2i52i5-2-222-2-22200000000−2i52i5−2i52i5−2i52i5−2i52i500000000000000000000000000000000000000000000000000000000
χ838-88-80000-282-8-228-82i5−2i5002i5−2i500-2-222-2-222000000002i5−2i5−2i52i52i5−2i5−2i52i500000000000000000000000000000000000000000000000000000000
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χ868-88-80000-2-222-22-222i5−2i52i5−2i52i5−2i52i5−2i53-2-323-2-3200000000−i5i500−i5i500-550000-55−i5i5−2i52i5−2i52i5−i5i50000000000000000000000000000000000000000
χ878-88-80000-2-222-22-222i5−2i5−2i52i52i5−2i5−2i52i5-232-3-232-30000000000i5−i500i5−i5005-55-5002i5−2i5−i5i5−i5i52i5−2i50000000000000000000000000000000000000000
χ888-88-80000-2-222-22-222i5−2i5−2i52i52i5−2i5−2i52i5-232-3-232-30000000000i5−i500i5−i500-55-5500−2i52i5i5−i5i5−i5−2i52i50000000000000000000000000000000000000000
χ898-88-80000-2-222-22-22−2i52i52i5−2i5−2i52i52i5−2i5-232-3-232-30000000000−i5i500−i5i5005-55-500−2i52i5i5−i5i5−i5−2i52i50000000000000000000000000000000000000000
χ908-88-80000-2-222-22-22−2i52i52i5−2i5−2i52i52i5−2i5-232-3-232-30000000000−i5i500−i5i500-55-55002i5−2i5−i5i5−i5i52i5−2i50000000000000000000000000000000000000000
χ918-88-80000-2-222-22-22−2i52i5−2i52i5−2i52i5−2i52i53-2-323-2-3200000000i5−i500i5−i5005-500005-5−i5i5−2i52i5−2i52i5−i5i50000000000000000000000000000000000000000
χ928-88-80000-2-222-22-22−2i52i5−2i52i5−2i52i5−2i52i53-2-323-2-3200000000i5−i500i5−i500-550000-55i5−i52i5−2i52i5−2i5i5−i50000000000000000000000000000000000000000
χ938-8-8800008-2-82-882-2002i5−2i500−2i52i5-2-22222-2-2000000002i5−2i52i5−2i5−2i52i5−2i52i500000000000000000000000000000000000000000000000000000000
χ948-8-8800008-2-82-882-200−2i52i5002i5−2i5-2-22222-2-200000000−2i52i5−2i52i52i5−2i52i5−2i500000000000000000000000000000000000000000000000000000000
χ958-8-880000-282-82-2-882i5−2i500−2i52i500-2-22222-2-2000000002i5−2i5−2i52i5−2i52i52i5−2i500000000000000000000000000000000000000000000000000000000
χ968-8-880000-282-82-2-88−2i52i5002i5−2i500-2-22222-2-200000000−2i52i52i5−2i52i5−2i5−2i52i500000000000000000000000000000000000000000000000000000000
χ978-8-880000-2-2222-22-22i5−2i52i5−2i5−2i52i5−2i52i53-2-32-323-200000000−i5i500i5−i500i5−i52i5−2i5−2i52i5−i5i5-5500005-50000000000000000000000000000000000000000
χ988-8-880000-2-2222-22-22i5−2i52i5−2i5−2i52i5−2i52i53-2-32-323-200000000−i5i500i5−i500−i5i5−2i52i52i5−2i5i5−i55-50000-550000000000000000000000000000000000000000
χ998-8-880000-2-2222-22-22i5−2i5−2i52i5−2i52i52i5−2i5-232-32-3-230000000000i5−i500−i5i52i5−2i5−i5i5i5−i5−2i52i500-555-5000000000000000000000000000000000000000000
χ1008-8-880000-2-2222-22-22i5−2i5−2i52i5−2i52i52i5−2i5-232-32-3-230000000000i5−i500−i5i5−2i52i5i5−i5−i5i52i5−2i5005-5-55000000000000000000000000000000000000000000
χ1018-8-880000-2-2222-22-2−2i52i52i5−2i52i5−2i5−2i52i5-232-32-3-230000000000−i5i500i5−i52i5−2i5−i5i5i5−i5−2i52i5005-5-55000000000000000000000000000000000000000000
χ1028-8-880000-2-2222-22-2−2i52i52i5−2i52i5−2i5−2i52i5-232-32-3-230000000000−i5i500i5−i5−2i52i5i5−i5−i5i52i5−2i500-555-5000000000000000000000000000000000000000000
χ1038-8-880000-2-2222-22-2−2i52i5−2i52i52i5−2i52i5−2i53-2-32-323-200000000i5−i500−i5i500i5−i52i5−2i5−2i52i5−i5i55-50000-550000000000000000000000000000000000000000
χ1048-8-880000-2-2222-22-2−2i52i5−2i52i52i5−2i52i5−2i53-2-32-323-200000000i5−i500−i5i500−i5i5−2i52i52i5−2i5i5−i5-5500005-50000000000000000000000000000000000000000

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