Finite Group Databasebeta

← Group #13022372

Character table — Group #13022372

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222224444444444448888888888888888101010101010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12442224445888810101020202020244410102020202020202020202022224444101020204040404044444444888888888888244488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i
χ911111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111
χ1111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii-1-111ii−i−i−i−iii
χ1211111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i-1-111−i−iiiii−i−i
χ1311111111111-1-1-1-11111111-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ1411111111111-1-1-1-11111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1
χ1511111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ1611111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1711-1-11-1-111-11ii−i−i111-1-1-1-11-1i−i-1-111iiii−i−i−i−i11-1-1-111-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-11-1i−ii−i1-1i−i1-1
χ1811-1-11-1-111-11ii−i−i111-1-1-1-11-1i−i-1-111iiii−i−i−i−i11-1-1-111-111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-111-1-1111-1i−i−ii-11−ii-11
χ1911-1-11-1-111-11ii−i−i111-1-1-1-11-1i−i-1-111iiii−i−i−i−i-1-1111-1-1111-1-1ii−i−i11-1-1-1-111−i−iii−i−iiiii−i−i-11−ii1-1−ii-11i−i
χ2011-1-11-1-111-11ii−i−i111-1-1-1-11-1i−i-1-111iiii−i−i−i−i-1-1111-1-1111-1-1ii−i−i-1-11111-1-1−i−iiiii−i−i−i−iii-11−ii-11i−i1-1−ii
χ2111-1-11-1-111-11ii−i−i111-1-1-1-1-11−ii-1-111−i−i−i−iiiii11-1-1-111-1-1-111ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1-11−ii−ii-11−ii-11
χ2211-1-11-1-111-11ii−i−i111-1-1-1-1-11−ii-1-111−i−i−i−iiiii11-1-1-111-1-1-111ii−i−i−i−iii−i−iiiii−i−i-1-111-1-111-11−iii−i1-1i−i1-1
χ2311-1-11-1-111-11ii−i−i111-1-1-1-1-11−ii-1-111−i−i−i−iiiii-1-1111-1-11-1-111ii−i−i11-1-1-1-111−i−iii−i−iiiii−i−i1-1i−i-11i−i1-1−ii
χ2411-1-11-1-111-11ii−i−i111-1-1-1-1-11−ii-1-111−i−i−i−iiiii-1-1111-1-11-1-111ii−i−i-1-11111-1-1−i−iiiii−i−i−i−iii1-1i−i1-1−ii-11i−i
χ2511-1-11-1-111-11−i−iii111-1-1-1-11-1−ii-1-111−i−i−i−iiiii11-1-1-111-111-1-1−i−iiiii−i−iii−i−i−i−iii-1-111-1-1111-1−iii−i-11i−i-11
χ2611-1-11-1-111-11−i−iii111-1-1-1-11-1−ii-1-111−i−i−i−iiiii11-1-1-111-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-11-1−ii−ii1-1−ii1-1
χ2711-1-11-1-111-11−i−iii111-1-1-1-11-1−ii-1-111−i−i−i−iiiii-1-1111-1-1111-1-1−i−iii11-1-1-1-111ii−i−iii−i−i−i−iii-11i−i1-1i−i-11−ii
χ2811-1-11-1-111-11−i−iii111-1-1-1-11-1−ii-1-111−i−i−i−iiiii-1-1111-1-1111-1-1−i−iii-1-11111-1-1ii−i−i−i−iiiii−i−i-11i−i-11−ii1-1i−i
χ2911-1-11-1-111-11−i−iii111-1-1-1-1-11i−i-1-111iiii−i−i−i−i11-1-1-111-1-1-111−i−iiiii−i−iii−i−i−i−iii-1-111-1-111-11i−i−ii1-1−ii1-1
χ3011-1-11-1-111-11−i−iii111-1-1-1-1-11i−i-1-111iiii−i−i−i−i11-1-1-111-1-1-111−i−iii−i−iii−i−iii−i−iii11-1-111-1-1-11i−ii−i-11i−i-11
χ3111-1-11-1-111-11−i−iii111-1-1-1-1-11i−i-1-111iiii−i−i−i−i-1-1111-1-11-1-111−i−iii11-1-1-1-111ii−i−iii−i−i−i−iii1-1−ii-11−ii1-1i−i
χ3211-1-11-1-111-11−i−iii111-1-1-1-1-11i−i-1-111iiii−i−i−i−i-1-1111-1-11-1-111−i−iii-1-11111-1-1ii−i−i−i−iiiii−i−i1-1−ii1-1i−i-11−ii
χ3322222-2-2-2-222000022222220000-2-2-2-20000000022-2-22-2-22000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ3422222-2-2-2-222000022222220000-2-2-2-20000000022-2-22-2-2200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ3522222-2-2-2-222000022222220000-2-2-2-200000000-2-222-222-2000000000000000000002-22-2-22-22000000000000
χ3622222-2-2-2-222000022222220000-2-2-2-200000000-2-222-222-200000000000000000000-22-222-22-2000000000000
χ372222-22-22-2-220000-2-22-2-22200002-22-2000000002-22-222-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ382222-22-22-2-220000-2-22-2-22200002-22-2000000002-22-222-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ392222-22-22-2-220000-2-22-2-22200002-22-200000000-22-22-2-222000000002-22-2-22-22000000000000000000000000
χ402222-22-22-2-220000-2-22-2-22200002-22-200000000-22-22-2-22200000000-22-222-22-2000000000000000000000000
χ412222-2-22-22-222-22-2-2-22-2-2220000-22-22000000002-2-222-22-200002-22-2000000002-22-200000000000000000000
χ422222-2-22-22-222-22-2-2-22-2-2220000-22-2200000000-222-2-22-2200002-22-200000000-22-2200000000000000000000
χ432222-2-22-22-22-22-22-2-22-2-2220000-22-22000000002-2-222-22-20000-22-2200000000-22-2200000000000000000000
χ442222-2-22-22-22-22-22-2-22-2-2220000-22-2200000000-222-2-22-220000-22-22000000002-22-200000000000000000000
χ4522-2-2222-2-2-220000222-2-2-2-2000022-2-2000000002222-2-2-2-2000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ4622-2-2222-2-2-220000222-2-2-2-2000022-2-2000000002222-2-2-2-200000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ4722-2-2222-2-2-220000222-2-2-2-2000022-2-200000000-2-2-2-22222000000000000000000002-2-22-222-2000000000000
χ4822-2-2222-2-2-220000222-2-2-2-2000022-2-200000000-2-2-2-2222200000000000000000000-222-22-2-22000000000000
χ4922-2-2-22-2-22222i−2i−2i2i-2-2222-2-200002-2-22000000002-22-2-2-22200002i−2i−2i2i000000002i−2i−2i2i00000000000000000000
χ5022-2-2-22-2-22222i−2i−2i2i-2-2222-2-200002-2-2200000000-22-2222-2-200002i−2i−2i2i00000000−2i2i2i−2i00000000000000000000
χ5122-2-2-22-2-2222−2i2i2i−2i-2-2222-2-200002-2-22000000002-22-2-2-2220000−2i2i2i−2i00000000−2i2i2i−2i00000000000000000000
χ5222-2-2-22-2-2222−2i2i2i−2i-2-2222-2-200002-2-2200000000-22-2222-2-20000−2i2i2i−2i000000002i−2i−2i2i00000000000000000000
χ5322-2-2-2-222-2220000-2-2222-2-20000-222-2000000002-2-22-22-22000000002-2-222-2-22000000000000000000000000
χ5422-2-2-2-222-2220000-2-2222-2-20000-222-2000000002-2-22-22-2200000000-222-2-222-2000000000000000000000000
χ5522-2-2-2-222-2220000-2-2222-2-20000-222-200000000-222-22-22-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5622-2-2-2-222-2220000-2-2222-2-20000-222-200000000-222-22-22-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ574444444444-14444-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ584444444444-14444-1-1-1-1-1-1-1-4-4-4-4-1-1-1-111111111000000001111-1-1-1-100000000000000000000000000000000
χ594444444444-1-4-4-4-4-1-1-1-1-1-1-144-4-4-1-1-1-11111111100000000-1-1-1-1111100000000000000000000000000000000
χ604444444444-1-4-4-4-4-1-1-1-1-1-1-1-4-444-1-1-1-1-1-1-1-1-1-1-1-1000000001111111100000000000000000000000000000000
χ614444-4-44-44-4-14-44-411-111-1-100001-11-155−5−555−5−5000000005−55−5-11-1100000000000000000000000000000000
χ624444-4-44-44-4-14-44-411-111-1-100001-11-1−5−555−5−55500000000−55−55-11-1100000000000000000000000000000000
χ634444-4-44-44-4-1-44-4411-111-1-100001-11-155−5−555−5−500000000−55−551-11-100000000000000000000000000000000
χ644444-4-44-44-4-1-44-4411-111-1-100001-11-1−5−555−5−555000000005−55−51-11-100000000000000000000000000000000
χ6544-4-44-4-444-4-14i4i−4i−4i-1-1-111114-44i−4i11-1-1−i−i−i−iiiii00000000-1-111−i−iii00000000000000000000000000000000
χ6644-4-44-4-444-4-14i4i−4i−4i-1-1-11111-44−4i4i11-1-1iiii−i−i−i−i0000000011-1-1−i−iii00000000000000000000000000000000
χ6744-4-44-4-444-4-1−4i−4i4i4i-1-1-111114-4−4i4i11-1-1iiii−i−i−i−i00000000-1-111ii−i−i00000000000000000000000000000000
χ6844-4-44-4-444-4-1−4i−4i4i4i-1-1-11111-444i−4i11-1-1−i−i−i−iiiii0000000011-1-1ii−i−i00000000000000000000000000000000
χ6944-4-4-44-4-444-14i−4i−4i4i11-1-1-1110000-111-1i5i5−i5−i5−i5−i5i5i5000000005−5−55−iii−i00000000000000000000000000000000
χ7044-4-4-44-4-444-14i−4i−4i4i11-1-1-1110000-111-1−i5−i5i5i5i5i5−i5−i500000000−555−5−iii−i00000000000000000000000000000000
χ7144-4-4-44-4-444-1−4i4i4i−4i11-1-1-1110000-111-1i5i5−i5−i5−i5−i5i5i500000000−555−5i−i−ii00000000000000000000000000000000
χ7244-4-4-44-4-444-1−4i4i4i−4i11-1-1-1110000-111-1−i5−i5i5i5i5i5−i5−i5000000005−5−55i−i−ii00000000000000000000000000000000
χ7388888-8-8-8-88-20000-2-2-2-2-2-2-20000222200000000000000000000000000000000000000000000000000000000
χ748888-88-88-8-8-2000022-222-2-20000-22-2200000000000000000000000000000000000000000000000000000000
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χ778-88i−8i0000008000000-8008i−8i0000000000000000000000000000000000000000000000000000000000000000
χ788-88i−8i000000-2000025−2522i5−2i5−2i2i00000000−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19000000000000000000000000000000000000000000000000
χ798-88i−8i000000-2000025−2522i5−2i5−2i2i00000000ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19000000000000000000000000000000000000000000000000
χ808-88i−8i000000-20000−25252−2i52i5−2i2i00000000−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19000000000000000000000000000000000000000000000000
χ818-88i−8i000000-20000−25252−2i52i5−2i2i00000000ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19000000000000000000000000000000000000000000000000
χ828-8−8i8i0000008000000-800−8i8i0000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000000-2000025−252−2i52i52i−2i00000000−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19000000000000000000000000000000000000000000000000
χ848-8−8i8i000000-2000025−252−2i52i52i−2i00000000ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19000000000000000000000000000000000000000000000000
χ858-8−8i8i000000-20000−252522i5−2i52i−2i00000000−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19000000000000000000000000000000000000000000000000
χ868-8−8i8i000000-20000−252522i5−2i52i−2i00000000ζ2+ζ3−ζ6−ζ7+ζ11+ζ14−ζ18−ζ19−ζ2−ζ3+ζ6+ζ7−ζ11−ζ14+ζ18+ζ19−ζ2−ζ3−ζ6+ζ7+ζ11+ζ14+ζ18−ζ19ζ2+ζ3+ζ6−ζ7−ζ11−ζ14−ζ18+ζ19ζ2−ζ3−ζ6+ζ7−ζ11+ζ14−ζ18+ζ19−ζ2+ζ3+ζ6−ζ7+ζ11−ζ14+ζ18−ζ19−ζ2+ζ3−ζ6−ζ7−ζ11+ζ14+ζ18+ζ19ζ2−ζ3+ζ6+ζ7+ζ11−ζ14−ζ18−ζ19000000000000000000000000000000000000000000000000

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