Finite Group Databasebeta

← Group #13013891

Character table — Group #13013891

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224444444488888888888888161616161616161616162020202020202020404040404040404040404040404040408080
order124422244451010102020202044101020202020202020202020884040404040404040888888881616161616161616161616161616161688
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−i11-1-1ii−i−ii−i
χ1011-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1i−iiiii−i−i−i−i11-1-111-1-1-1-111−i−iii-1-111−i−iiii−i
χ1111-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1i−iiiii−i−i−i−i-1-111-1-111ii−i−i-1-111−i−iii11-1-1−ii
χ1211-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1i−iiiii−i−i−i−i-1-111-1-111−i−iii11-1-1ii−i−i-1-111−ii
χ1311-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1−ii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii11-1-1−i−iii−ii
χ1411-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1−ii−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i-1-111ii−i−i−ii
χ1511-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1−ii−i−i−i−iiiii-1-111-1-111ii−i−i11-1-1−i−iii-1-111i−i
χ1611-1-1-1-1111-11111-1-1-1-11-1-1-1111111-1-1-1-1−ii−i−i−i−iiiii-1-111-1-111−i−iii-1-111ii−i−i11-1-1i−i
χ17222222222222222222-2-22222-2-2-2-2-2-2-2-2000000000022-2-2-2-222000000000000000000
χ18222222222222222222-2-22222-2-2-2-2-2-2-2-20000000000-2-22222-2-2000000000000000000
χ1922222-2-22-2-222-2-2-2-222002-22-2000000000000000000002i−2i2i−2i0000001+i−1−i1+i−1−i00001−i−1+i1−i−1+i00
χ2022222-2-22-2-222-2-2-2-222002-22-2000000000000000000002i−2i2i−2i000000−1−i1+i−1−i1+i0000−1+i1−i−1+i1−i00
χ2122222-2-22-2-222-2-2-2-222002-22-200000000000000000000−2i2i−2i2i0000001−i−1+i1−i−1+i00001+i−1−i1+i−1−i00
χ2222222-2-22-2-222-2-2-2-222002-22-200000000000000000000−2i2i−2i2i000000−1+i1−i−1+i1−i0000−1−i1+i−1−i1+i00
χ232222-22-2-22-222-2-2-2-22200-22-220000000000000000002i−2i00002i−2i1+i−1−i1+i−1−i00001−i−1+i1−i−1+i000000
χ242222-22-2-22-222-2-2-2-22200-22-220000000000000000002i−2i00002i−2i−1−i1+i−1−i1+i0000−1+i1−i−1+i1−i000000
χ252222-22-2-22-222-2-2-2-22200-22-22000000000000000000−2i2i0000−2i2i1−i−1+i1−i−1+i00001+i−1−i1+i−1−i000000
χ262222-22-2-22-222-2-2-2-22200-22-22000000000000000000−2i2i0000−2i2i−1+i1−i−1+i1−i0000−1−i1+i−1−i1+i000000
χ2722-2-22-2-2-22222-2-222-2-2002-2-220000000000000000002i−2i0000−2i2i1+i−1−i−1−i1+i00001−i−1+i−1+i1−i000000
χ2822-2-22-2-2-22222-2-222-2-2002-2-220000000000000000002i−2i0000−2i2i−1−i1+i1+i−1−i0000−1+i1−i1−i−1+i000000
χ2922-2-22-2-2-22222-2-222-2-2002-2-22000000000000000000−2i2i00002i−2i1−i−1+i−1+i1−i00001+i−1−i−1−i1+i000000
χ3022-2-22-2-2-22222-2-222-2-2002-2-22000000000000000000−2i2i00002i−2i−1+i1−i1−i−1+i0000−1−i1+i1+i−1−i000000
χ3122-2-2-22-22-2222-2-222-2-200-222-2000000000000000000002i−2i−2i2i0000001+i−1−i−1−i1+i0000−1+i1−i1−i−1+i00
χ3222-2-2-22-22-2222-2-222-2-200-222-2000000000000000000002i−2i−2i2i000000−1−i1+i1+i−1−i00001−i−1+i−1+i1−i00
χ3322-2-2-22-22-2222-2-222-2-200-222-200000000000000000000−2i2i2i−2i0000001−i−1+i−1+i1−i0000−1−i1+i1+i−1−i00
χ3422-2-2-22-22-2222-2-222-2-200-222-200000000000000000000−2i2i2i−2i000000−1+i1−i1−i−1+i00001+i−1−i−1−i1+i00
χ3522-2-2-2-2222-22222-2-2-2-2-22-2-222-2-2-2-2222200000000002222-2-2-2-2000000000000000000
χ3622-2-2-2-2222-22222-2-2-2-2-22-2-222-2-2-2-222220000000000-2-2-2-22222000000000000000000
χ374444444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-4-41111111100000000000000000000000000
χ394444444444-1-1-1-1-1-1-1-1-4-4-1-1-1-1111111110055−5−555−5−500000000000000000000000000
χ404444444444-1-1-1-1-1-1-1-1-4-4-1-1-1-11111111100−5−555−5−55500000000000000000000000000
χ414444-4-44-4-444444444400-4-4-4-400000000000000000000000000000000000000000000
χ424444-4-44-4-44-1-1-1-1-1-1-1-100111155−5−555−5−500−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ1800000000000000000000000000
χ434444-4-44-4-44-1-1-1-1-1-1-1-100111155−5−555−5−500ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000000000000000000
χ444444-4-44-4-44-1-1-1-1-1-1-1-1001111−5−555−5−55500−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ1800000000000000000000000000
χ454444-4-44-4-44-1-1-1-1-1-1-1-1001111−5−555−5−55500ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ1800000000000000000000000000
χ4644-4-4444-4-4-44444-4-4-4-40044-4-400000000000000000000000000000000000000000000
χ4744-4-4444-4-4-4-1-1-1-1111100-1-11155−5−5−5−55500−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ1900000000000000000000000000
χ4844-4-4444-4-4-4-1-1-1-1111100-1-11155−5−5−5−55500ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ1900000000000000000000000000
χ4944-4-4444-4-4-4-1-1-1-1111100-1-111−5−55555−5−500ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ1900000000000000000000000000
χ5044-4-4444-4-4-4-1-1-1-1111100-1-111−5−55555−5−500−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ1900000000000000000000000000
χ5144-4-4-4-4444-4-1-1-1-111114-411-1-1-1-1-1-111114i−4i−i−i−i−iiiii00000000000000000000000000
χ5244-4-4-4-4444-4-1-1-1-111114-411-1-1-1-1-1-11111−4i4iiiii−i−i−i−i00000000000000000000000000
χ5344-4-4-4-4444-4-1-1-1-11111-4411-1-11111-1-1-1-100i5i5−i5−i5−i5−i5i5i500000000000000000000000000
χ5444-4-4-4-4444-4-1-1-1-11111-4411-1-11111-1-1-1-100−i5−i5i5i5i5i5−i5−i500000000000000000000000000
χ5588888-8-88-8-8-2-22222-2-200-22-2200000000000000000000000000000000000000000000
χ568888-88-8-88-8-2-22222-2-2002-22-200000000000000000000000000000000000000000000
χ5788-8-88-8-8-888-2-222-2-22200-222-200000000000000000000000000000000000000000000
χ5888-8-8-88-88-88-2-222-2-222002-2-2200000000000000000000000000000000000000000000
χ598-88i−8i0000008-800008i−8i00000000000000000000000000000000000000000000000000
χ608-88i−8i000000-2225−252i5−2i5−2i2i0000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000000000
χ618-88i−8i000000-2225−252i5−2i5−2i2i000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000000000
χ628-88i−8i000000-22−2525−2i52i5−2i2i000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000000000
χ638-88i−8i000000-22−2525−2i52i5−2i2i0000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000000000
χ648-8−8i8i0000008-80000−8i8i00000000000000000000000000000000000000000000000000
χ658-8−8i8i000000-2225−25−2i52i52i−2i0000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000000000
χ668-8−8i8i000000-2225−25−2i52i52i−2i000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000000000
χ678-8−8i8i000000-22−25252i5−2i52i−2i000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000000000
χ688-8−8i8i000000-22−25252i5−2i52i−2i0000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000000000

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