Finite Group Databasebeta

← Group #72221528

Character table — Group #72221528

Order 2560.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97
size112222222444444558888888888810101010101010161616161616161616161616161616162020202020202020202020202020202020202020323232323232323240404040808080808080808080808080160160
order1224488884458810222244102020404040402448888248810101010202020202020404044888888888888888888101020204040404022442488161616161616161644
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-11-111111111111111-1-11-111-1-111-1-1111111111111111111111111-1-1-1-111-1-11-11-1-1-11-11111-1-1-1-1-1-1
χ4111111111111111111-11-111111111111111-1-11-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1-1-11-1-1-1-1-1111111
χ511111111111111111-11-1111111111111111-1-1-11-1-111-1-111111111111111111111111111-1-1-1-1-1-111-11-11-1-1-11-1-1-1-11111-1-1
χ611111111111111111-11-1111111111111111-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-1-111111-1-1-1-111
χ711111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1
χ9111111111111111-1-111111111111-1-1-1-1-1-1-11111111111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−i
χ10111111111111111-1-111111111111-1-1-1-1-1-1-11111111111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−iii−i−iii−ii
χ11111111111111111-1-11-11-11111111-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-1-1-11-1111-11ii−i−i−i−iii−ii
χ12111111111111111-1-11-11-11111111-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-1-1-11-1111-11−i−iiiii−i−ii−i
χ13111111111111111-1-1-11-111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1111-11-1111-1−i−iiiii−i−i−ii
χ14111111111111111-1-1-11-111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1111-11-1111-1ii−i−i−i−iiii−i
χ15111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11111-1-111−i−iii−i−iiii−i
χ16111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11111-1-111ii−i−iii−i−i−ii
χ172222222-2-2-2-222-2222020222222-2-222222-2-2000-200220022-2-22-2-2-22-20000000000000000000000-2-20202000-20000000000
χ182222222-2-2-2-222-22220-20-222222-2-222222-2-2000200-2-200-2-2-2-22-2-2-22-20000000000000000000000220-20-200020000000000
χ192222222-2-2-2-222-22-2-2020222222-2-2-2-2-2-2-222000-200220022-2-22-222-220000000000000000000000-2-20-20-200020000000000
χ202222222-2-2-2-222-22-2-20-20-222222-2-2-2-2-2-2-222000200-2-200-2-2-2-22-222-220000000000000000000000220202000-20000000000
χ2122222-2-222-2-22-222222020222-2-222222-2-22200-2022002200-2-2-22-2-2-2200000000000000000000-2-200202000-200000000000
χ2222222-2-222-2-22-22222-20-20222-2-222222-2-2220020-2-200-2-200-2-2-22-2-2-22000000000000000000002200-20-2000200000000000
χ2322222-2-222-2-22-222-2-22020222-2-222-2-2-222-2-200-2022002200-2-2-22222-200000000000000000000-2-200-20-2000200000000000
χ2422222-2-222-2-22-222-2-2-20-20222-2-222-2-2-222-2-20020-2-200-2-200-2-2-22222-2000000000000000000002200202000-200000000000
χ2522222-2-2-2-2222-2-22220000222-2-2-2-2222-2-2-2-22-2000000000022-2-222-2-2000000000000000022-2-2000000002-2000000000000
χ2622222-2-2-2-2222-2-22220000222-2-2-2-2222-2-2-2-2-22000000000022-2-222-2-20000000000000000-2-22200000000-22000000000000
χ2722222-2-2-2-2222-2-22-2-20000222-2-2-2-2-2-2-222222-2000000000022-2-2-2-222000000000000000022-2-200000000-22000000000000
χ2822222-2-2-2-2222-2-22-2-20000222-2-2-2-2-2-2-22222-22000000000022-2-2-2-2220000000000000000-2-222000000002-2000000000000
χ2922-22-200-2-20020222220-20-22-200-2-2-22-200-2-200002200-2-20000020002i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000020-200000i2−i2i2−i2000000
χ3022-22-200-2-20020222220-20-22-200-2-2-22-200-2-200002200-2-20000020002−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000020-200000−i2i2−i2i2000000
χ3122-22-200-2-200202222-2020-22-200-2-2-22-200-2-20000-2-200220000020002i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000-20200000−i2i2−i2i2000000
χ3222-22-200-2-200202222-2020-22-200-2-2-22-200-2-20000-2-200220000020002−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000-20200000i2−i2i2−i2000000
χ3322-22-200-2-2002022-2-220-20-22-200-2-22-22002200002200-2-2000002000-22222−2−2−2−2−2−2−2−2222200000000-202000002−2−22000000
χ3422-22-200-2-2002022-2-220-20-22-200-2-22-22002200002200-2-2000002000-2−2−2−2−222222222−2−2−2−200000000-20200000−222−2000000
χ3522-22-200-2-2002022-2-2-2020-22-200-2-22-2200220000-2-20022000002000-22222−2−2−2−2−2−2−2−222220000000020-200000−222−2000000
χ3622-22-200-2-2002022-2-2-2020-22-200-2-22-2200220000-2-20022000002000-2−2−2−2−222222222−2−2−2−20000000020-2000002−2−22000000
χ3722-2-22-2-20000220222020-2-2-22-2-200-2-22-2-2000000002200-2-200200020i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000020-200000000i2−i2i2−i200
χ3822-2-22-2-20000220222020-2-2-22-2-200-2-22-2-2000000002200-2-200200020−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000020-200000000−i2i2−i2i200
χ3922-2-22-2-200002202220-202-2-22-2-200-2-22-2-200000000-2-2002200200020i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000-20200000000−i2i2−i2i200
χ4022-2-22-2-200002202220-202-2-22-2-200-2-22-2-200000000-2-2002200200020−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000-20200000000i2−i2i2−i200
χ4122-2-22-2-200002202-2-2020-2-2-22-2-20022-222000000002200-2-2002000-2022−2−222−2−2−2−222−2−222000000000-202000000002−2−2200
χ4222-2-22-2-200002202-2-2020-2-2-22-2-20022-222000000002200-2-2002000-20−2−222−2−22222−2−222−2−2000000000-20200000000−222−200
χ4322-2-22-2-200002202-2-20-202-2-22-2-20022-22200000000-2-20022002000-2022−2−222−2−2−2−222−2−22200000000020-200000000−222−200
χ4422-2-22-2-200002202-2-20-202-2-22-2-20022-22200000000-2-20022002000-20−2−222−2−22222−2−222−2−200000000020-2000000002−2−2200
χ4544444444444-144-1004444-1-1-1-1-1-1-100000004444-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1000000000000000000
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χ4744444444444-144-100-44-44-1-1-1-1-1-1-10000000-4-4-4411-1-111-1-1-1-1-1-100000000000000000000111111-1-1000000000000000000
χ4844444444444-144-100-4-4-4-4-1-1-1-1-1-1-1000000044-4-411111111-1-1-1-100000000000000000000-1-1-1-11111000000000000000000
χ494444444-4-4-4-4-14-4-1000404-1-1-1-1-1110000000000-45−5-1-15−5-1-111-11000000000000000000005−55−55−511000000000000000000
χ504444444-4-4-4-4-14-4-1000404-1-1-1-1-1110000000000-4−55-1-1−55-1-111-1100000000000000000000−55−55−5511000000000000000000
χ514444444-4-4-4-4-14-4-1000-40-4-1-1-1-1-111000000000045−5115−51111-1100000000000000000000−55−555−5-1-1000000000000000000
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χ61444-4-400000040044400004-4-400004-4-400000000000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000
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χ8988-8-88880000-2-80-200000022-2-2-200000000000000025−2500−252500200000000000000000000000000000000000000000000000
χ9088-8-88880000-2-80-200000022-2-2-2000000000000000−25250025−2500200000000000000000000000000000000000000000000000
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χ9288-8-88-8-80000-280-2000-80822-2220000000000000002200-2-200-200000000000000000000000000000000000000000000000
χ93161616-16-16000000-400-4000000-4440000000000000000000000000000000000000000000000000000000000000000000000000
χ9416-160008i2−8i28i2−8i28-8-4004000000000−2i22i2−2i22i20000000000000000000-22000000000000000000000000000000000000000000000000
χ9516-160008i2−8i2−8i28i2-88-4004000000000−2i22i22i2−2i200000000000000000002-2000000000000000000000000000000000000000000000000
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χ9716-16000−8i28i2−8i28i28-8-40040000000002i2−2i22i2−2i20000000000000000000-22000000000000000000000000000000000000000000000000

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