Finite Group Databasebeta

← Group #13103768

Character table — Group #13103768

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size112444455101010101011244445510101010102248888101020202020202248888101020202020202248888101020202020202248888101020202020205510202020202525505050505055102020202025255050505050
order12251010104448888222101010104448888510105101010202020404040405101051010102020204040404010101010101010202020404040401010101010101020202040404040444202020204448888444202020204448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1
χ31111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i
χ41111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii
χ511-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-1
χ611-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-11
χ711-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii
χ811-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i
χ92-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i00000
χ102-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i00000
χ11444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000
χ1244-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-1110000000
χ134-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−50000000
χ144-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−550000000
χ15111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ171111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i-1-1-1-1-1-1-1111−i−iii-1-1-1-1-1-1-1111−i−iii
χ181111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii1111111-1-1-1−i−iii-1-1-1-1-1-1-1111ii−i−i-1-1-1-1-1-1-1111ii−i−i
χ1911-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-111-111-1-111-11-11-1-1-11-1-111-1-11-11-11-1-11-1-111-1-11-11-11
χ2011-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-1111-111-1-111-1-11-11-1-11-1-111-1-111-11-1-1-11-1-111-1-111-11-1
χ2111-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii-1-11-1-11111-1−iii−i-1-11-1-11111-1−iii−i
χ2211-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i-1-11-1-11111-1i−i−ii-1-11-1-11111-1i−i−ii
χ232-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i000002-202-2002i−2i00000-220-2200−2i2i00000-220-2200−2i2i00000
χ242-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i000002-202-200−2i2i00000-220-22002i−2i00000-220-22002i−2i00000
χ25444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000444-1-1-1-10000000-4-4-411110000000-4-4-411110000000
χ2644-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-111000000044-4-1-1110000000-4-4411-1-10000000-4-4411-1-10000000
χ274-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−500000004-40-115−50000000-4401-1−550000000-4401-1−550000000
χ284-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−5500000004-40-11−550000000-4401-15−50000000-4401-15−50000000
χ2911111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ301111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii
χ311111111-1-1-1ii−i−i-1-1-1-1-1-1-1111−i−iii1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i-1-1-1-1-1-1-1111−i−iii-1-1-1-1-1-1-1111−i−iiiiiiiiii−i−i−i-1-111−i−i−i−i−i−i−iiii11-1-1
χ321111111-1-1-1−i−iii-1-1-1-1-1-1-1111ii−i−i1111111-1-1-1−i−iii1111111-1-1-1−i−iii-1-1-1-1-1-1-1111ii−i−i-1-1-1-1-1-1-1111ii−i−iiiiiiii−i−i−i11-1-1−i−i−i−i−i−i−iiii-1-111
χ3311-111-1-111-11-11-1-1-11-1-111-1-11-11-1111-111-1-111-11-11-111-111-1-111-11-11-1-1-11-1-111-1-11-11-11-1-11-1-111-1-11-11-11ii−iii−i−iii−ii−ii−i−i−ii−i−iii−i−ii−ii−ii
χ3411-111-1-111-1-11-11-1-11-1-111-1-111-11-111-111-1-111-1-11-1111-111-1-111-1-11-11-1-11-1-111-1-111-11-1-1-11-1-111-1-111-11-1ii−iii−i−iii−i−ii−ii−i−ii−i−iii−i−iii−ii−i
χ3511-111-1-1-1-11i−i−ii-1-11-1-11111-1−iii−i11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii-1-11-1-11111-1−iii−i-1-11-1-11111-1−iii−iii−iii−i−i−i−ii-111-1−i−ii−i−iiiii−i1-1-11
χ3611-111-1-1-1-11−iii−i-1-11-1-11111-1i−i−ii11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i-1-11-1-11111-1i−i−ii-1-11-1-11111-1i−i−iiii−iii−i−i−i−ii1-1-11−i−ii−i−iiiii−i-111-1
χ372-202-2002i−2i00000-220-2200−2i2i000002-202-2002i−2i000002-202-2002i−2i00000-220-2200−2i2i00000-220-2200−2i2i000002i−2i02i−2i00-2200000−2i2i0−2i2i002-200000
χ382-202-200−2i2i00000-220-22002i−2i000002-202-200−2i2i000002-202-200−2i2i00000-220-22002i−2i00000-220-22002i−2i000002i−2i02i−2i002-200000−2i2i0−2i2i00-2200000
χ39444-1-1-1-10000000-4-4-411110000000444-1-1-1-10000000444-1-1-1-10000000-4-4-411110000000-4-4-4111100000004i4i4i−i−i−i−i0000000−4i−4i−4iiiii0000000
χ4044-4-1-1110000000-4-4411-1-1000000044-4-1-111000000044-4-1-1110000000-4-4411-1-10000000-4-4411-1-100000004i4i−4i−i−iii0000000−4i−4i4iii−i−i0000000
χ414-40-115−50000000-4401-1−5500000004-40-115−500000004-40-115−50000000-4401-1−550000000-4401-1−5500000004i−4i0−iii5−i50000000−4i4i0i−i−i5i50000000
χ424-40-11−550000000-4401-15−500000004-40-11−5500000004-40-11−550000000-4401-15−50000000-4401-15−500000004i−4i0−ii−i5i50000000−4i4i0i−ii5−i50000000
χ4311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiii
χ441111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiii−i−i−i−i
χ451111111-1-1-1ii−i−i-1-1-1-1-1-1-1111−i−iii1111111-1-1-1ii−i−i1111111-1-1-1ii−i−i-1-1-1-1-1-1-1111−i−iii-1-1-1-1-1-1-1111−i−iii−i−i−i−i−i−i−iiii11-1-1iiiiiii−i−i−i-1-111
χ461111111-1-1-1−i−iii-1-1-1-1-1-1-1111ii−i−i1111111-1-1-1−i−iii1111111-1-1-1−i−iii-1-1-1-1-1-1-1111ii−i−i-1-1-1-1-1-1-1111ii−i−i−i−i−i−i−i−i−iiii-1-111iiiiiii−i−i−i11-1-1
χ4711-111-1-111-11-11-1-1-11-1-111-1-11-11-1111-111-1-111-11-11-111-111-1-111-11-11-1-1-11-1-111-1-11-11-11-1-11-1-111-1-11-11-11−i−ii−i−iii−i−ii−ii−iiii−iii−i−iii−ii−ii−i
χ4811-111-1-111-1-11-11-1-11-1-111-1-111-11-111-111-1-111-1-11-1111-111-1-111-1-11-11-1-11-1-111-1-111-11-1-1-11-1-111-1-111-11-1−i−ii−i−iii−i−iii−ii−iii−iii−i−iii−i−ii−ii
χ4911-111-1-1-1-11i−i−ii-1-11-1-11111-1−iii−i11-111-1-1-1-11i−i−ii11-111-1-1-1-11i−i−ii-1-11-1-11111-1−iii−i-1-11-1-11111-1−iii−i−i−ii−i−iiiii−i1-1-11ii−iii−i−i−i−ii-111-1
χ5011-111-1-1-1-11−iii−i-1-11-1-11111-1i−i−ii11-111-1-1-1-11−iii−i11-111-1-1-1-11−iii−i-1-11-1-11111-1i−i−ii-1-11-1-11111-1i−i−ii−i−ii−i−iiiii−i-111-1ii−iii−i−i−i−ii1-1-11
χ512-202-2002i−2i00000-220-2200−2i2i000002-202-2002i−2i000002-202-2002i−2i00000-220-2200−2i2i00000-220-2200−2i2i00000−2i2i0−2i2i002-2000002i−2i02i−2i00-2200000
χ522-202-200−2i2i00000-220-22002i−2i000002-202-200−2i2i000002-202-200−2i2i00000-220-22002i−2i00000-220-22002i−2i00000−2i2i0−2i2i00-22000002i−2i02i−2i002-200000
χ53444-1-1-1-10000000-4-4-411110000000444-1-1-1-10000000444-1-1-1-10000000-4-4-411110000000-4-4-411110000000−4i−4i−4iiiii00000004i4i4i−i−i−i−i0000000
χ5444-4-1-1110000000-4-4411-1-1000000044-4-1-111000000044-4-1-1110000000-4-4411-1-10000000-4-4411-1-10000000−4i−4i4iii−i−i00000004i4i−4i−i−iii0000000
χ554-40-115−50000000-4401-1−5500000004-40-115−500000004-40-115−50000000-4401-1−550000000-4401-1−550000000−4i4i0i−i−i5i500000004i−4i0−iii5−i50000000
χ564-40-11−550000000-4401-15−500000004-40-11−5500000004-40-11−550000000-4401-15−50000000-4401-15−50000000−4i4i0i−ii5−i500000004i−4i0−ii−i5i50000000
χ572222222222222222222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000000000000000000000000
χ582222222222-2-2-2-22222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+520000000000000000000000000000
χ592222222-2-2-22i2i−2i−2i2222222-2-2-22i2i−2i−2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ70000000000000000000000000000
χ602222222-2-2-2−2i−2i2i2i2222222-2-2-2−2i−2i2i2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ70000000000000000000000000000
χ6122-222-2-222-22-22-222-222-2-222-22-22-2−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+52−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−52−1+521−52−1+521−52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+52−1−521+52−1−521+520000000000000000000000000000
χ6222-222-2-222-2-22-2222-222-2-222-2-22-22−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−52−1+52−1+521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+52−1−52−1−521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−520000000000000000000000000000
χ6322-222-2-2-2-222i−2i−2i2i22-222-2-2-2-222i−2i−2i2i−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ70000000000000000000000000000
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χ10622-222-2-2-2-22−2i2i2i−2i-2-22-2-22222-22i−2i−2i2i−1−52−1−521+52−1−52−1−521+521+521+521+52−1−52ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−1+52−1+521−52−1+52−1+521−521−521−521−52−1+52ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ191+521+52−1−521+521+52−1−52−1−52−1−52−1−521+52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ71−521−52−1+521−521−52−1+52−1+52−1+52−1+521−52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ190000000000000000000000000000
χ1074-404-4004i−4i00000-440-4400−4i4i00000−1−51+50−1−51+500−2ζ3−2ζ72ζ3+2ζ700000−1+51−50−1+51−500−2ζ11−2ζ192ζ11+2ζ19000001+5−1−501+5−1−5002ζ3+2ζ7−2ζ3−2ζ7000001−5−1+501−5−1+5002ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000000
χ1084-404-400−4i4i00000-440-44004i−4i00000−1−51+50−1−51+5002ζ3+2ζ7−2ζ3−2ζ700000−1+51−50−1+51−5002ζ11+2ζ19−2ζ11−2ζ19000001+5−1−501+5−1−500−2ζ3−2ζ72ζ3+2ζ7000001−5−1+501−5−1+500−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000000
χ109888-2-2-2-20000000-8-8-822220000000−2−25−2−25−2−251+521+521+521+520000000−2+25−2+25−2+251−521−521−521−5200000002+252+252+25−1−52−1−52−1−52−1−5200000002−252−252−25−1+52−1+52−1+52−1+5200000000000000000000000000000000000
χ11088-8-2-2220000000-8-8822-2-20000000−2−25−2−252+251+521+52−1−52−1−520000000−2+25−2+252−251−521−52−1+52−1+5200000002+252+25−2−25−1−52−1−521+521+5200000002−252−25−2+25−1+52−1+521−521−5200000000000000000000000000000000000
χ1118-80-2225−250000000-8802-2−25250000000−2−252+2501+52−1−52−5−525+520000000−2+252−2501−52−1+525−52−5+5200000002+25−2−250−1−521+525+52−5−5200000002−25−2+250−1+521−52−5+525−5200000000000000000000000000000000000
χ1128-80-22−25250000000-8802-225−250000000−2−252+2501+52−1−525+52−5−520000000−2+252−2501−52−1+52−5+525−5200000002+25−2−250−1−521+52−5−525+5200000002−25−2+250−1+521−525−52−5+5200000000000000000000000000000000000

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