Finite Group Databasebeta

← Group #72221285

Character table — Group #72221285

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122244444444448888888888888888888888888888888888888888888820202020252540405050508080808080808080100100100100100100100100100100200200200200
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χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111111111111111111111111111111111111111111-1-111-1-1-11-1-1-1-1-1-1-11111-1-1ii−i−iii−i−ii−ii−i
χ611111111111111111111111111111111111111111111111111111111111-1-111-1-1-11-1-1-1-1-1-1-11111-1-1−i−iii−i−iii−ii−ii
χ711111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11
χ811111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1
χ911111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-111-1-1-1-111111111-1-1-1-1
χ1011111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
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χ1211111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-111-1-1-1-11111−i−i−i−iiiiiii−i−i
χ1311111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-111ii−i−iii−i−i−ii−ii
χ1411111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-111−i−iii−i−iiii−ii−i
χ1511111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111-1-111-1-1-1-111-111-1
χ1611111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111-1-1-1-11111-1-11-1-11
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χ2722-2-22002222-2-2-2-22222-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000-2-20022-200000000002i−2i0000−2i2i0000
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χ3344444-4-44-14-144-1-1-1-1-1-1-1-1-1-14-14-1-4-4-4-41111-1-1-1-1-1-1-1-111111111111111110044000-40000000-1-11100000000000000
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χ43444-4-400-14-14-1-144-1-1-1-1-1-1-1-11-41-4−5−555000011111111−5−5−5−55555−5−5−5−555554-4000000000-11−55000000000000000000
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χ464-40002-244-4-4000044-4-4000000002-22-22-22-20000000022-2-222-2-222-2-222-2-20000-440000000000000-22000000000000
χ474-4000-2244-4-4000044-4-400000000-22-22-22-2200000000-2-222-2-222-2-222-2-22200004-40000000000000-22000000000000
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χ498888888-2-2-2-2-2-2-2-23-23-233-2-2-2-2-2-2-2-2-2-2-2-2-2-233-2-233-2-23333-2-2-2-2-2-2-2-23333000000000000000000000000000000000
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χ5188888-8-8-2-2-2-2-2-2-2-23-23-233-2-2-2-2-2-22222222233-2-233-2-2-3-3-3-322222222-3-3-3-3000000000000000000000000000000000
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χ6688-8-8800-2-2-2-222223-23-2-3-32222-2-200000000-3-32233-2-2−i5i5−i5i5−2i52i5−2i52i52i5−2i52i5−2i5i5−i5i5−i5000000000000000000000000000000000
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χ698-80004-48-2-820025−25-2-22225−2525−2500004-44-4−1+51−5−1−51+500000000−1+5−1+51−51−5−1+5−1+51−51−5−1−5−1−51+51+5−1−5−1−51+51+5000000000000000000000000000000000
χ708-80004-48-2-8200−2525-2-222−2525−252500004-44-4−1−51+5−1+51−500000000−1−5−1−51+51+5−1−5−1−51+51+5−1+5−1+51−51−5−1+5−1+51−51−5000000000000000000000000000000000
χ718-80004-4-282-825−2500-2-22225−25−25250000−1+51−5−1−51+54-44-400000000−1+5−1+51−51−5−1−5−1−51+51+5−1+5−1+51−51−5−1−5−1−51+51+5000000000000000000000000000000000
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χ738-80004-4-2-22225−2525−253-2-32−55000000−1+51−5−1−51+5−1+51−5−1−51+5i5−i52i5−2i55i−5i00ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−1+i5−1−i51−i51+i5−1−i5−1+i51+i51−i52ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19000000000000000000000000000000000
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χ798-80004-4-2-222−2525−25253-2-325−5000000−1−51+5−1+51−5−1−51+5−1+51−5i5−i52i5−2i5−5i5i002ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−1+i5−1−i51−i51+i5−1−i5−1+i51+i51−i5ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19000000000000000000000000000000000
χ808-80004-4-2-222−2525−25253-2-325−5000000−1−51+5−1+51−5−1−51+5−1+51−5−i5i5−2i52i55i−5i002ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−1−i5−1+i51+i51−i5−1+i5−1−i51−i51+i5ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19000000000000000000000000000000000
χ818-8000-448-2-820025−25-2-22225−2525−250000-44-441−5−1+51+5−1−5000000001−51−5−1+5−1+51−51−5−1+5−1+51+51+5−1−5−1−51+51+5−1−5−1−5000000000000000000000000000000000
χ828-8000-448-2-8200−2525-2-222−2525−25250000-44-441+5−1−51−5−1+5000000001+51+5−1−5−1−51+51+5−1−5−1−51−51−5−1+5−1+51−51−5−1+5−1+5000000000000000000000000000000000
χ838-8000-44-282-825−2500-2-22225−25−252500001−5−1+51+5−1−5-44-44000000001−51−5−1+5−1+51+51+5−1−5−1−51−51−5−1+5−1+51+51+5−1−5−1−5000000000000000000000000000000000
χ848-8000-44-282-8−252500-2-222−252525−2500001+5−1−51−5−1+5-44-44000000001+51+5−1−5−1−51−51−5−1+5−1+51+51+5−1−5−1−51−51−5−1+5−1+5000000000000000000000000000000000
χ858-8000-44-2-22225−2525−253-2-32−550000001−5−1+51+5−1−51−5−1+51+5−1−5i5−i52i5−2i55i−5i00−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ191−i51+i5−1+i5−1−i51+i51−i5−1−i5−1+i5−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19000000000000000000000000000000000
χ868-8000-44-2-22225−2525−253-2-32−550000001−5−1+51+5−1−51−5−1+51+5−1−5−i5i5−2i52i5−5i5i00−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ191+i51−i5−1−i5−1+i51−i51+i5−1+i5−1−i5−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19000000000000000000000000000000000
χ878-8000-44-2-22225−25−2525-232-3005−500001−5−1+51+5−1−51+5−1−51−5−1+52i5−2i5−i5i5005i−5i1−i51+i5−1+i5−1−i5−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ191+i51−i5−1−i5−1+i5000000000000000000000000000000000
χ888-8000-44-2-22225−25−2525-232-3005−500001−5−1+51+5−1−51+5−1−51−5−1+5−2i52i5i5−i500−5i5i1+i51−i5−1−i5−1+i5−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ191−i51+i5−1+i5−1−i5000000000000000000000000000000000
χ898-8000-44-2-222−252525−25-232-300−5500001+5−1−51−5−1+51−5−1+51+5−1−52i5−2i5−i5i500−5i5i1−i51+i5−1+i5−1−i5−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ191+i51−i5−1−i5−1+i5000000000000000000000000000000000
χ908-8000-44-2-222−252525−25-232-300−5500001+5−1−51−5−1+51−5−1+51+5−1−5−2i52i5i5−i5005i−5i1+i51−i5−1−i5−1+i5−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ191−i51+i5−1+i5−1−i5000000000000000000000000000000000
χ918-8000-44-2-222−2525−25253-2-325−50000001+5−1−51−5−1+51+5−1−51−5−1+5i5−i52i5−2i5−5i5i00−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ191−i51+i5−1+i5−1−i51+i51−i5−1−i5−1+i5−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19000000000000000000000000000000000
χ928-8000-44-2-222−2525−25253-2-325−50000001+5−1−51−5−1+51+5−1−51−5−1+5−i5i5−2i52i55i−5i00−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ191+i51−i5−1−i5−1+i51−i51+i5−1+i5−1−i5−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.