Finite Group Databasebeta

← Group #13014446

Character table — Group #13014446

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112244444488888888161616161616161616161616161620202020404040404040404040404040404080808080
order12222244510101044101020202020882020202040404040404040404444224444888888884444
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ911-1-1-111-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i11-1-1-11ii−i−iii−i−iii−i−i1-11-1
χ1011-1-1-111-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i11-1-1-11ii−i−i−i−iii−i−iii-11-11
χ1111-1-1-111-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i-1-1111-1−i−iii11-1-1-1-111−iii−i
χ1211-1-1-111-11-1-111-11-111-1-1i−i11-1-1iiii−i−i−i−i-1-1111-1−i−iii-1-11111-1-1i−i−ii
χ1311-1-1-111-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii11-1-1-11−i−iiiii−i−iii−i−i-11-11
χ1411-1-1-111-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii11-1-1-11−i−iii−i−iii−i−iii1-11-1
χ1511-1-1-111-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii-1-1111-1ii−i−i11-1-1-1-111i−i−ii
χ1611-1-1-111-11-1-111-11-111-1-1−ii11-1-1−i−i−i−iiiii-1-1111-1ii−i−i-1-11111-1-1−iii−i
χ17222222222222-2-222222200-2-2-2-2000000002222-2-20000000000000000
χ18222222222222-2-222222200-2-2-2-200000000-2-2-2-2220000000000000000
χ1922-2-2-222-22-2-22-222-222-2-200-2-2220000000022-2-22-20000000000000000
χ2022-2-2-222-22-2-22-222-222-2-200-2-22200000000-2-222-220000000000000000
χ2144444444-1-1-1-144-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ2244444444-1-1-1-144-1-1-1-1-1-1-4-4-1-1-1-1111111110000000000000000000000
χ2344444444-1-1-1-1-4-4-1-1-1-1-1-100111155−5−555−5−50000000000000000000000
χ2444444444-1-1-1-1-4-4-1-1-1-1-1-1001111−5−555−5−5550000000000000000000000
χ25444444-4-444440044-4-4-4-4000000000000000000000000000000000000
χ26444444-4-4-1-1-1-100-1-11111005−55−5−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ190000000000000000000000
χ27444444-4-4-1-1-1-100-1-11111005−55−5ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ190000000000000000000000
χ28444444-4-4-1-1-1-100-1-1111100−55−55ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ190000000000000000000000
χ29444444-4-4-1-1-1-100-1-1111100−55−55−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ190000000000000000000000
χ304444-4-400444400-4-40000000000000000000000002-22-2000000000000
χ314444-4-400444400-4-4000000000000000000000000-22-22000000000000
χ3244-4-44-4004-4-4400-440000000000000000000000002i−2i−2i2i000000000000
χ3344-4-44-4004-4-4400-44000000000000000000000000−2i2i2i−2i000000000000
χ3444-4-4-444-4-111-14-4-11-1-1114i−4i-1-111−i−i−i−iiiii0000000000000000000000
χ3544-4-4-444-4-111-14-4-11-1-111−4i4i-1-111iiii−i−i−i−i0000000000000000000000
χ3644-4-4-444-4-111-1-44-11-1-1110011-1-1i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ3744-4-4-444-4-111-1-44-11-1-1110011-1-1−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ3844-4-4-44-444-4-44004-4-4-444000000000000000000000000000000000000
χ3944-4-4-44-44-111-100-1111-1-1005−5−55−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000000
χ4044-4-4-44-44-111-100-1111-1-1005−5−55ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000000
χ4144-4-4-44-44-111-100-1111-1-100−555−5−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000000
χ4244-4-4-44-44-111-100-1111-1-100−555−5ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000000
χ434-44-4000044-4-400000000000000000000002i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ444-44-4000044-4-400000000000000000000002i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ454-44-4000044-4-40000000000000000000000−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ464-44-4000044-4-40000000000000000000000−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ474-4-4400004-44-400000000000000000000002i−2i−2i2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ484-4-4400004-44-400000000000000000000002i−2i−2i2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ494-4-4400004-44-40000000000000000000000−2i2i2i−2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ504-4-4400004-44-40000000000000000000000−2i2i2i−2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ518888-8-800-2-2-2-2002225−2525−25000000000000000000000000000000000000
χ528888-8-800-2-2-2-20022−2525−2525000000000000000000000000000000000000
χ5388-8-88-800-222-2002-225−25−2525000000000000000000000000000000000000
χ5488-8-88-800-222-2002-2−252525−25000000000000000000000000000000000000
χ5516-1616-160000-4-44400000000000000000000000000000000000000000000
χ5616-16-16160000-44-4400000000000000000000000000000000000000000000

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