Finite Group Databasebeta

← Group #72221253

Character table — Group #72221253

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122244444444448888888888888888888888888888888888888888888820202020252540405050508080808080808080100100100100100100100100100100200200200200
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χ4111111111111111111111111111111111111111111111111111111111111-11-1-1-11-1-1-1-11-11-111-1-1-1-1−ii−i−i−iiii−ii−ii
χ511111111111111111111111111111111111111111111111111111111111-11-11-1-1-11-1-1-1-11-11-1-111-1-1i−ii−i−iii−i−iii−i
χ611111111111111111111111111111111111111111111111111111111111-11-11-1-1-11-1-1-1-11-11-1-111-1-1−ii−iii−i−iii−i−ii
χ711111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-11-1-111
χ811111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111-1-1-11111-111-1-1
χ911111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-1-1-111111111-1-1-1-1
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χ788-80004-4-2-222−2i52i52i5−2i5-23002-3−25255−500005i−5i00−i5i5−1−i51+i5−1+i51−i5−1+i51−i5−1−i51+i5−1+5−1−51−51+5ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−1+5−1−51−51+5000000000000000000000000000000000
χ798-80004-4-2-222−2i52i5−2i52i53-200-325−525−2500−5i5i00i5−i500−1−i51+i5−1+i51−i5−1−i51+i5−1+i51−i5ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−1−5−1+51+51−5−1−5−1+51+51−5ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19000000000000000000000000000000000
χ808-80004-4-2-222−2i52i5−2i52i53-200-32−55−2525005i−5i00i5−i500−1−i51+i5−1+i51−i5−1−i51+i5−1+i51−i52ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−1+5−1−51−51+5−1+5−1−51−51+52ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19000000000000000000000000000000000
χ818-8000-448-2-82002i5−2i5-2-2002200000000002i5−2i52i5−2i5-44-441−i5−1+i51+i5−1−i51−i51−i5−1+i5−1+i51−i51−i5−1+i5−1+i51+i51+i5−1−i5−1−i51+i51+i5−1−i5−1−i5000000000000000000000000000000000
χ828-8000-448-2-8200−2i52i5-2-200220000000000−2i52i5−2i52i5-44-441+i5−1−i51−i5−1+i51+i51+i5−1−i5−1−i51+i51+i5−1−i5−1−i51−i51−i5−1+i5−1+i51−i51−i5−1+i5−1+i5000000000000000000000000000000000
χ838-8000-44-282-82i5−2i500-2-2002200000000002i5−2i5−2i52i51−i5−1+i51+i5−1−i5-44-441−i51−i5−1+i5−1+i51+i51+i5−1−i5−1−i51−i51−i5−1+i5−1+i51+i51+i5−1−i5−1−i5000000000000000000000000000000000
χ848-8000-44-282-8−2i52i500-2-200220000000000−2i52i52i5−2i51+i5−1−i51−i5−1+i5-44-441+i51+i5−1−i5−1−i51−i51−i5−1+i5−1+i51+i51+i5−1−i5−1−i51−i51−i5−1+i5−1+i5000000000000000000000000000000000
χ858-8000-44-2-2222i5−2i52i5−2i53-200-325−525−25005i−5i00−i5i5001−i5−1+i51+i5−1−i51−i5−1+i51+i5−1−i5−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ191+51−5−1−5−1+51+51−5−1−5−1+5−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19000000000000000000000000000000000
χ868-8000-44-2-2222i5−2i52i5−2i53-200-32−55−252500−5i5i00−i5i5001−i5−1+i51+i5−1−i51−i5−1+i51+i5−1−i5−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ191−51+5−1+5−1−51−51+5−1+5−1−5−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19000000000000000000000000000000000
χ878-8000-44-2-2222i5−2i5−2i52i5-23002-325−25−5500005i−5i00i5−i51−i5−1+i51+i5−1−i51+i5−1−i51−i5−1+i51+51−5−1−5−1+5−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ191+51−5−1−5−1+5000000000000000000000000000000000
χ888-8000-44-2-2222i5−2i5−2i52i5-23002-3−25255−50000−5i5i00i5−i51−i5−1+i51+i5−1−i51+i5−1−i51−i5−1+i51−51+5−1+5−1−5−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ191−51+5−1+5−1−5000000000000000000000000000000000
χ898-8000-44-2-222−2i52i52i5−2i5-23002-325−25−550000−5i5i00−i5i51+i5−1−i51−i5−1+i51−i5−1+i51+i5−1−i51+51−5−1−5−1+5−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ191+51−5−1−5−1+5000000000000000000000000000000000
χ908-8000-44-2-222−2i52i52i5−2i5-23002-3−25255−500005i−5i00−i5i51+i5−1−i51−i5−1+i51−i5−1+i51+i5−1−i51−51+5−1+5−1−5−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ191−51+5−1+5−1−5000000000000000000000000000000000
χ918-8000-44-2-222−2i52i5−2i52i53-200-325−525−2500−5i5i00i5−i5001+i5−1−i51−i5−1+i51+i5−1−i51−i5−1+i5−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ19−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ191+51−5−1−5−1+51+51−5−1−5−1+5−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ19−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19000000000000000000000000000000000
χ928-8000-44-2-222−2i52i5−2i52i53-200-32−55−2525005i−5i00i5−i5001+i5−1−i51−i5−1+i51+i5−1−i51−i5−1+i5−2ζ2−3ζ3−ζ6−3ζ7−2ζ11−ζ14−2ζ18−2ζ19−ζ2+2ζ3−2ζ6+2ζ7+3ζ11−2ζ14−ζ18+3ζ192ζ2+3ζ3+ζ6+3ζ7+2ζ11+ζ14+2ζ18+2ζ19ζ2−2ζ3+2ζ6−2ζ7−3ζ11+2ζ14+ζ18−3ζ191−51+5−1+5−1−51−51+5−1+5−1−5−2ζ2+3ζ3−ζ6+3ζ7+2ζ11−ζ14−2ζ18+2ζ19−ζ2−2ζ3−2ζ6−2ζ7−3ζ11−2ζ14−ζ18−3ζ192ζ2−3ζ3+ζ6−3ζ7−2ζ11+ζ14+2ζ18−2ζ19ζ2+2ζ3+2ζ6+2ζ7+3ζ11+2ζ14+ζ18+3ζ19000000000000000000000000000000000

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