Finite Group Databasebeta

← Group #13020376

Character table — Group #13020376

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11114444444888888101010101010161616161616162020202020202020203232323240404040404040408080808080
order12224445101010248820204444444202040404040288888888102020202488888848888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1
χ311111111111111111-1-1-1-1-1-11111111-1iiii−i−i−i−i1111-1-1-1-1ii−i−i-1ii−i−i
χ411111111111111111-1-1-1-1-1-11111111-1−i−i−i−iiiii1111-1-1-1-1−i−iii-1−i−iii
χ51111111111111-1-111111111-111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1
χ61111111111111-1-111111111-111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11111
χ71111111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i1−i−iii
χ81111111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1−i−i−i−iiiii11-1-1-1-111−i−iii1ii−i−i
χ911111111111-1-11111111111-1111111111-1-111-1-1-1-1-1-1-1-1111-11-1-11-11-1
χ1011111111111-1-11111111111-11111111-1-111-1-111-1-1-1-1-1-111-11-11-1-11-11
χ1111111111111-1-11111-1-1-1-1-1-1-1111111-1ii−i−i−i−iii-1-1-1-111-1-1i−i−ii1i−i−ii
χ1211111111111-1-11111-1-1-1-1-1-1-1111111-1−i−iiiii−i−i-1-1-1-111-1-1−iii−i1−iii−i
χ1311111111111-1-1-1-111111111111-1-1-1-1111-1-111-1-1-1-111-1-1-1-11-11-11-11-11
χ1411111111111-1-1-1-111111111111-1-1-1-11-1-111-1-111-1-111-1-1-1-1-11-1111-11-1
χ1511111111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1ii−i−i−i−iii-1-1111111i−i−ii-1−iii−i
χ1611111111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1−i−iiiii−i−i-1-1111111−iii−i-1i−i−ii
χ1722222-2-222220000-2-22-22-2-2-202-200002002i2i00−2i−2i000000000−2i02i00000
χ1822222-2-222220000-2-22-22-2-2-202-20000200−2i−2i002i2i0000000002i0−2i00000
χ1922222-2-222220000-2-2-22-222202-20000-200220022000000000-20-200000
χ2022222-2-222220000-2-2-22-222202-20000-200-2-200-2-200000000020200000
χ212222-22-222220000-2-22-2222-20-220000-22200220000000000-20-2000000
χ222222-22-222220000-2-22-2222-20-220000-2-2-200-2-20000000000202000000
χ232222-22-222220000-2-2-22-2-2-220-22000022i2i00−2i−2i0000000000−2i02i000000
χ242222-22-222220000-2-2-22-2-2-220-2200002−2i−2i002i2i00000000002i0−2i000000
χ252222-2-2222222-20022222-2-220-2-20000-2000000002-2002-200000000000
χ262222-2-2222222-20022-2-2-222-20-2-200002000000002-200-2200000000000
χ272222-2-222222-220022222-2-220-2-20000-200000000-2200-2200000000000
χ282222-2-222222-220022-2-2-222-20-2-20000200000000-22002-200000000000
χ294444444-1-1-1-14444-1-10000004-1-1-1-1-1-1000000000-1-1-1-10000000000000
χ304444444-1-1-1-144-4-4-1-1000000-4-1-11111000000000-1-1110000000000000
χ314444444-1-1-1-1-4-444-1-1000000-4-1-1-1-1-1-100000000011110000000000000
χ324444444-1-1-1-1-4-4-4-4-1-10000004-1-1111100000000011-1-10000000000000
χ334444-4-44-1-1-1-14-400-1-100000001155−5−5000000000-115−50000000000000
χ344444-4-44-1-1-1-14-400-1-1000000011−5−555000000000-11−550000000000000
χ354444-4-44-1-1-1-1-4400-1-100000001155−5−50000000001-1−550000000000000
χ364444-4-44-1-1-1-1-4400-1-1000000011−5−5550000000001-15−50000000000000
χ3744-4-400044-4-400000040-40000000000022−220022−220000000000000000000
χ3844-4-400044-4-400000040-400000000000−222200−22220000000000000000000
χ3944-4-400044-4-4000000-404000000000002i2−2i200−2i22i20000000000000000000
χ4044-4-400044-4-4000000-40400000000000−2i22i2002i2−2i20000000000000000000
χ414-44-40004-44-4002i−2i000004-400002i−2i2i−2i0000000000000002i−2i000000000
χ424-44-40004-44-4002i−2i00000-4400002i−2i2i−2i000000000000000−2i2i000000000
χ434-44-40004-44-400−2i2i000004-40000−2i2i−2i2i000000000000000−2i2i000000000
χ444-44-40004-44-400−2i2i00000-440000−2i2i−2i2i0000000000000002i−2i000000000
χ454-4-440004-4-4400000004000-400000000002i2−2i2002i2−2i200000000000000000
χ464-4-440004-4-4400000004000-40000000000−2i22i200−2i22i200000000000000000
χ474-4-440004-4-440000000-40004000000000022−2200−222200000000000000000
χ484-4-440004-4-440000000-400040000000000−22220022−2200000000000000000
χ4988888-8-8-2-2-2-20000220000000-22000000000000000000000000000000
χ508888-88-8-2-2-2-200002200000002-2000000000000000000000000000000
χ518-88-8000-22-22004i−4i25−25000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000
χ528-88-8000-22-22004i−4i−2525000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000
χ538-88-8000-22-2200−4i4i25−250000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000
χ548-88-8000-22-2200−4i4i−25250000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000
χ551616-16-16000-4-444000000000000000000000000000000000000000000000
χ5616-16-1616000-444-4000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.