Finite Group Databasebeta

← Group #13020006

Character table — Group #13020006

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112244444488888888101010101010161616161616161616162020202020202020203232404040404040404040404040808080
order12222244510101044881010202022224442020202020404040404444444442020444444888888444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-1
χ311111111111111111111-1-1-1-1-1-11111111111-1ii−i−iii−i−i11-1-1ii−i−i-1-1ii−i−i-1i−i
χ411111111111111111111-1-1-1-1-1-11111111111-1−i−iii−i−iii11-1-1−i−iii-1-1−i−iii-1−ii
χ511111111111111-1-11111111111-11-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111-1-11111111111-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-111
χ711111111111111-1-11111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1ii−i−i11−i−iii1−ii
χ811111111111111-1-11111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−iii11ii−i−i1i−i
χ9111111111111-1-1111111111111-11-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-1111111-1-1-1
χ10111111111111-1-1111111111111-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11-1111-1-1-1-1-111
χ11111111111111-1-1111111-1-1-1-1-1-1-11-1-1-1-11111-1ii−i−i−i−iii-1-111i−i−ii-1-1ii−i−i1−ii
χ12111111111111-1-1111111-1-1-1-1-1-1-11-1-1-1-11111-1−i−iiiii−i−i-1-111−iii−i-1-1−i−iii1i−i
χ13111111111111-1-1-1-11111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1111
χ14111111111111-1-1-1-11111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-11-11-1-111111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1ii−i−i−i−iii-1-111i−i−ii11−i−iii-1i−i
χ16111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1−i−iiiii−i−i-1-111−iii−i11ii−i−i-1−ii
χ17222222-2-22222000022-2-22222-2-20-200000000-2222200000000-20-20000000000
χ18222222-2-22222000022-2-22222-2-20-200000000-2-2-2-2-2000000002020000000000
χ19222222-2-22222000022-2-2-2-2-2-2220-20000000022i2i−2i−2i00000000−2i02i0000000000
χ20222222-2-22222000022-2-2-2-2-2-2220-2000000002−2i−2i2i2i000000002i0−2i0000000000
χ212222-2-22-222220000-2-2-2-22-22-2-2-20200000000200002i2i−2i−2i00000−2i02i000000000
χ222222-2-22-222220000-2-2-2-22-22-2-2-2020000000020000−2i−2i2i2i000002i0−2i000000000
χ232222-2-22-222220000-2-2-2-2-22-22220200000000-20000222200000-20-2000000000
χ242222-2-22-222220000-2-2-2-2-22-22220200000000-20000-2-2-2-200000202000000000
χ252222-2-2-2222222-200-2-2222-22-2220-200000000-200000000-22-220000000000000
χ262222-2-2-2222222-200-2-222-22-22-2-20-200000000200000000-222-20000000000000
χ272222-2-2-222222-2200-2-2222-22-2220-200000000-2000000002-22-20000000000000
χ282222-2-2-222222-2200-2-222-22-22-2-20-2000000002000000002-2-220000000000000
χ2922-2-22-20022-2-2002−22-20022-2-20000000022−2−202-22-20000000000002−22−22−2000
χ3022-2-22-20022-2-2002−22-20022-2-20000000022−2−20-22-220000000000002−2−22−22000
χ3122-2-22-20022-2-2002−22-200-2-2220000000022−2−202i−2i−2i2i000000000000−22i2−i2−i2i2000
χ3222-2-22-20022-2-2002−22-200-2-2220000000022−2−20−2i2i2i−2i000000000000−22−i2i2i2−i2000
χ3322-2-22-20022-2-200−222-20022-2-200000000−2−22202-22-2000000000000−22−22−22000
χ3422-2-22-20022-2-200−222-20022-2-200000000−2−2220-22-22000000000000−222−22−2000
χ3522-2-22-20022-2-200−222-200-2-22200000000−2−22202i−2i−2i2i0000000000002−2−i2i2i2−i2000
χ3622-2-22-20022-2-200−222-200-2-22200000000−2−2220−2i2i2i−2i0000000000002−2i2−i2−i2i2000
χ3744444444-1-1-1-14444-1-1-1-10000004-1-1-1-1-1-1-1-1-1000000000-1-1000000000000000
χ3844444444-1-1-1-144-4-4-1-1-1-1000000-4-111111111000000000-1-1000000000000000
χ3944444444-1-1-1-1-4-444-1-1-1-1000000-4-11111-1-1-1-100000000011000000000000000
χ4044444444-1-1-1-1-4-4-4-4-1-1-1-10000004-1-1-1-1-1111100000000011000000000000000
χ414444-4-4-44-1-1-1-14-40011-1-10000000155−5−55−55−50000000001-1000000000000000
χ424444-4-4-44-1-1-1-14-40011-1-100000001−5−555−55−550000000001-1000000000000000
χ434444-4-4-44-1-1-1-1-440011-1-10000000155−5−5−55−55000000000-11000000000000000
χ444444-4-4-44-1-1-1-1-440011-1-100000001−5−5555−55−5000000000-11000000000000000
χ4544-4-4-440044-4-40000-44004-4-4400000000000000000000000000000000000000
χ4644-4-4-440044-4-40000-4400-444-400000000000000000000000000000000000000
χ474-4-4400004-44-40000000000004i−4i0000000000000002+2i−2−2i2−2i−2+2i00000000000000000
χ484-4-4400004-44-40000000000004i−4i000000000000000−2−2i2+2i−2+2i2−2i00000000000000000
χ494-4-4400004-44-4000000000000−4i4i0000000000000002−2i−2+2i2+2i−2−2i00000000000000000
χ504-4-4400004-44-4000000000000−4i4i000000000000000−2+2i2−2i−2−2i2+2i00000000000000000
χ51888888-8-8-2-2-2-20000-2-222000000020000000000000000000000000000000000
χ528888-8-88-8-2-2-2-2000022220000000-20000000000000000000000000000000000
χ5388-8-88-800-2-2220042−42-2200000000000000−2−22200000000000000000000000000
χ5488-8-88-800-2-22200−4242-220000000000000022−2−200000000000000000000000000
χ5588-8-8-8800-2-22200002-20000000000000010−10−101000000000000000000000000000
χ5688-8-8-8800-2-22200002-200000000000000−101010−1000000000000000000000000000
χ578-88-800008-8-8800000000000000000000000000000000000000000000000000
χ588-88-80000-222-200000025−25000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000
χ598-88-80000-222-200000025−2500000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000
χ608-88-80000-222-2000000−252500000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000
χ618-88-80000-222-2000000−2525000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000
χ6216-16-16160000-44-4400000000000000000000000000000000000000000000000000

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