Finite Group Databasebeta

← Group #13019808

Character table — Group #13019808

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444444810101010161616161616161616161616161616162020202040404040404040404040404040404040408080
order12222244445101010101010104444444202020202020202020202020202044444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111-1-111-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111-1-1-1-11111111111111111-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111-1-1-1-11111111111111111-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111111-1-111111111-111111-1-1-1-1-1-1-111-1-11111-1-111-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-111111111-111111-1-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-111-1-111-1-1111-1
χ1111111111-1-111111111-11111-11-1-1111111-1-1-1-1-1-1-1-111-111-1-111-1-1-1-111-1-111-11
χ1211111111-1-111111111-11111-11-1-1111111-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-111-1-1-11
χ1311111111-1-111111111-1-1-1-1-11-1-1-1-1-1-1-111-1-1111111-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111111-1-111111111-1-1-1-1-11-1-1-1-1-1-1-111-1-1111111-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111111-1-111111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-11ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111111-1-111111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-11−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222-2-22222222222-2222200220000-2-2-2-2000022-2-2-2000000000000000000
χ18222222-2-22222222222-2-2-2-2-200220000-2-2-2-20000-2-2222000000000000000000
χ19222222-2-2-2-2222222222222200-2-20000-2-2220000-2-2-2-22000000000000000000
χ20222222-2-2-2-2222222222-2-2-2-200-2-20000-2-22200002222-2000000000000000000
χ212222-2-22-20022-2-22-2-22022-2-2000000002-2000000002-20002i−2i002i−2i0000000000
χ222222-2-22-20022-2-22-2-22022-2-2000000002-2000000002-2000−2i2i00−2i2i0000000000
χ232222-2-22-20022-2-22-2-220-2-222000000002-200000000-220002-200-220000000000
χ242222-2-22-20022-2-22-2-220-2-222000000002-200000000-22000-22002-20000000000
χ252222-2-2-220022-2-22-2-22022-2-200000000-2200000000-2202i−2i002i−2i000000000000
χ262222-2-2-220022-2-22-2-22022-2-200000000-2200000000-220−2i2i00−2i2i000000000000
χ272222-2-2-220022-2-22-2-220-2-22200000000-22000000002-202-200-22000000000000
χ282222-2-2-220022-2-22-2-220-2-22200000000-22000000002-20-22002-2000000000000
χ292-2-22-22002-22-2222-2-2-202i−2i2i−2i002-20000000000002i−2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00
χ302-2-22-22002-22-2222-2-2-202i−2i2i−2i002-20000000000002i−2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00
χ312-2-22-22002-22-2222-2-2-20−2i2i−2i2i002-2000000000000−2i2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00
χ322-2-22-22002-22-2222-2-2-20−2i2i−2i2i002-2000000000000−2i2i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00
χ332-2-22-2200-222-2222-2-2-202i−2i2i−2i00-22000000000000−2i2i000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00
χ342-2-22-2200-222-2222-2-2-202i−2i2i−2i00-22000000000000−2i2i00000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00
χ352-2-22-2200-222-2222-2-2-20−2i2i−2i2i00-220000000000002i−2i000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00
χ362-2-22-2200-222-2222-2-2-20−2i2i−2i2i00-220000000000002i−2i00000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00
χ374444444444-1-1-1-1-1-1-1-14000044-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ384444444444-1-1-1-1-1-1-1-140000-4-4-1-11111-1-1-1-1111100000000000000000000000
χ3944444444-4-4-1-1-1-1-1-1-1-1-400004-4111111-1-111-1-1-1-100000000000000000000000
χ4044444444-4-4-1-1-1-1-1-1-1-1-40000-4411-1-1-1-1-1-111111100000000000000000000000
χ41444444-4-444-1-1-1-1-1-1-1-1-4000000-1-155−5−5111155−5−500000000000000000000000
χ42444444-4-444-1-1-1-1-1-1-1-1-4000000-1-1−5−5551111−5−55500000000000000000000000
χ43444444-4-4-4-4-1-1-1-1-1-1-1-140000001155−5−511-1-1−5−55500000000000000000000000
χ44444444-4-4-4-4-1-1-1-1-1-1-1-1400000011−5−55511-1-155−5−500000000000000000000000
χ454-4-444-400004-4-4-4444-404i−4i−4i4i000000000000000000000000000000000000000
χ464-4-444-400004-4-4-4444-40−4i4i4i−4i000000000000000000000000000000000000000
χ478888-8-88-800-2-222-222-20000000000000-2200000000000000000000000000000
χ488888-8-8-8800-2-222-222-200000000000002-200000000000000000000000000000
χ4988-8-80000008800-800-800000000000000000000000000000000000000000000
χ5088-8-8000000-2-225−25225−2520000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000000
χ5188-8-8000000-2-225−25225−252000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000000
χ5288-8-8000000-2-2−25252−25252000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000000
χ5388-8-8000000-2-2−25252−252520000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000000
χ548-88-80000008-800-800800000000000000000000000000000000000000000000
χ558-88-8000000-2225−252−2525-2000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000
χ568-88-8000000-2225−252−2525-200000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000
χ578-88-8000000-22−2525225−25-200000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ588-88-8000000-22−2525225−25-2000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ598-8-888-80000-2222-2-2-220000000000000002i5−2i5000000000000000000000000000
χ608-8-888-80000-2222-2-2-22000000000000000−2i52i5000000000000000000000000000
χ618-8-88-88008-8-22-2-2-22220000000-2200000000000000000000000000000000000
χ628-8-88-8800-88-22-2-2-222200000002-200000000000000000000000000000000000

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