Finite Group Databasebeta

← Group #13022248

Character table — Group #13022248

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444444444444444448888888888888888888888888888101010101010101010101010202020202020202020202020202020202020404040404040404040404040
order12222222222244444451010101010101010101010101010104444202020202020202020202020202020202020202020202020222222224444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−i−i−iiiii
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ14111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ15111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1711-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-11-1i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ1811-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-11-1i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−ii−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii-11−ii
χ1911-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-11-1i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−iiii−i−i-1-111−i−iii11-1-1-11−iii−i-11−ii1-1
χ2011-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-11-1i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−ii−i−iii11-1-1ii−i−i-1-111-11−ii−ii1-1i−i-11
χ2111-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-1-11−ii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ2211-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-1-11−ii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−ii−i-1-111−i−iii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ2311-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-1-11−ii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iii−iiii−i−i-1-111−i−iii11-1-11-1i−i−ii1-1i−i-11
χ2411-1-111-1-111-1-1ii−i−ii−i1111111-1-1-1-1-1-1-11-1-11−ii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iii−ii−i−iii11-1-1ii−i−i-1-1111-1i−ii−i-11−ii1-1
χ2511-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-11-1−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ2611-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-11-1−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−ii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i-11i−i
χ2711-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-11-1−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−ii−iii−i−i11-1-1−i−iii-1-111-11i−ii−i1-1−ii-11
χ2811-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-11-1−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−ii−i−i−iii-1-111ii−i−i11-1-1-11i−i−ii-11i−i1-1
χ2911-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-1-11i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i
χ3011-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-1-11i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iii−ii-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ3111-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-1-11i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−ii−iii−i−i11-1-1−i−iii-1-1111-1−ii−ii-11i−i1-1
χ3211-1-111-1-111-1-1−i−iii−ii1111111-1-1-1-1-1-1-11-1-11i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−ii−i−i−iii-1-111ii−i−i11-1-11-1−iii−i1-1−ii-11
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χ3522222222-2-2-2-2-2-2-2-222222-2-2-2-2222-2-2-2-222000000000000-2-222-2-222000000002-22-22-22-2-2-2-2-2220000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-222222-2-2-2-2222-2-2-2-222000000000000-2-222-2-22200000000-22-22-22-222222-2-20000000000000000000000000000
χ372222-2-2-2-22-22-200000022-222-2-222-222-2-2-2-2000000000000000000000000000022-22-2-22-200000000002-22-200002-22-2000000000000
χ382222-2-2-2-22-22-200000022-222-2-222-222-2-2-2-2000000000000000000000000000022-22-2-22-20000000000-22-220000-22-22000000000000
χ392222-2-2-2-22-22-200000022-222-2-222-222-2-2-2-20000000000000000000000000000-2-22-222-2200000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ402222-2-2-2-22-22-200000022-222-2-222-222-2-2-2-20000000000000000000000000000-2-22-222-220000000000−2i2i−2i2i00002i−2i2i−2i000000000000
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χ1018-88-8-88-880000000000-22-225−25−2525-22225−25−25252-20000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-88-880000000000-22-2−252525−25-222−252525−252-20000000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-888-80000000000-22-225−25−25252-2-2−252525−25220000000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-888-80000000000-22-2−252525−252-2-225−25−2525220000000000000000000000000000000000000000000000000000000000000000000000

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