Finite Group Databasebeta

← Group #72260345

Character table — Group #72260345

Order 4800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11334444555588888812121212151515151616161616161616202020202424242425253232323232323232404040406060606075758080808080808080150150150150150150150150150150150150150150150150200200
order1222551010444435561010101010104444151515153030303020202020101010102215151515303030301212121220202020226060606060606060444444444444444466
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111-1-1111111111111-1-11111111111-1-11111-1-11111111111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ41111111111-1-1111111111111-1-11111111111-1-11111-1-11111111111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ511111111-1-1111111111111-1-11111111111-1-1111111-1-111111111-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i-1-1
χ611111111-1-1111111111111-1-11111111111-1-1111111-1-111111111-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii-1-1
χ711111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ811111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ91-11-111-1-1i−ii−i111-1-1-111-1-1i−ii−i1111-1-1-1-1i−ii−i11-1-11-11111-1-1-1-1i−ii−ii−ii−i1-1ii−i−iii−i−i1-1i−ii−i1-11-1i−ii−i1-11-1
χ101-11-111-1-1i−ii−i111-1-1-111-1-1i−ii−i1111-1-1-1-1i−ii−i11-1-11-11111-1-1-1-1i−ii−ii−ii−i1-1ii−i−iii−i−i-11−ii−ii-11-11−ii−ii-111-1
χ111-11-111-1-1i−i−ii111-1-1-111-1-1i−i−ii1111-1-1-1-1i−i−ii11-1-1-111111-1-1-1-1i−i−iii−i−ii-11ii−i−i−i−iiii−i-111-1−iii−i-111-1−ii-11
χ121-11-111-1-1i−i−ii111-1-1-111-1-1i−i−ii1111-1-1-1-1i−i−ii11-1-1-111111-1-1-1-1i−i−iii−i−ii-11ii−i−i−i−iii−ii1-1-11i−i−ii1-1-11i−i-11
χ131-11-111-1-1−iii−i111-1-1-111-1-1−iii−i1111-1-1-1-1−iii−i11-1-1-111111-1-1-1-1−iii−i−iii−i-11−i−iiiii−i−ii−i1-1-11−iii−i1-1-11−ii-11
χ141-11-111-1-1−iii−i111-1-1-111-1-1−iii−i1111-1-1-1-1−iii−i11-1-1-111111-1-1-1-1−iii−i−iii−i-11−i−iiiii−i−i−ii-111-1i−i−ii-111-1i−i-11
χ151-11-111-1-1−ii−ii111-1-1-111-1-1−ii−ii1111-1-1-1-1−ii−ii11-1-11-11111-1-1-1-1−ii−ii−ii−ii1-1−i−iii−i−iii1-1−ii−ii1-11-1−ii−ii1-11-1
χ161-11-111-1-1−ii−ii111-1-1-111-1-1−ii−ii1111-1-1-1-1−ii−ii11-1-11-11111-1-1-1-1−ii−ii−ii−ii1-1−i−iii−i−iii-11i−ii−i-11-11i−ii−i-111-1
χ17222222222222-122-12222222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-10000000000000000-1-1
χ182222222222-2-2-122-122222222-2-2-1-1-1-1-1-1-1-122-2-22222-2-2-1-1-1-1-1-1-1-1-1-11122-2-2-2-2-1-1-1-11111000000000000000011
χ1922222222-2-222-122-1222222-2-222-1-1-1-1-1-1-1-1-2-2222222-2-2-1-1-1-1-1-1-1-111-1-1-2-222-2-21111-1-1-1-1000000000000000011
χ2022222222-2-2-2-2-122-1222222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-11111-2-2-2-222111111110000000000000000-1-1
χ212-22-222-2-22i−2i2i−2i-1221-2-222-2-22i−2i2i−2i-1-1-1-111112i−2i2i−2i22-2-22-2-1-1-1-11111−ii−ii2i−2i2i−2i2-2−i−iii−i−iii0000000000000000-11
χ222-22-222-2-22i−2i−2i2i-1221-2-222-2-22i−2i−2i2i-1-1-1-111112i−2i−2i2i22-2-2-22-1-1-1-11111−iii−i2i−2i−2i2i-22−i−iiiii−i−i00000000000000001-1
χ232-22-222-2-2−2i2i2i−2i-1221-2-222-2-2−2i2i2i−2i-1-1-1-11111−2i2i2i−2i22-2-2-22-1-1-1-11111i−i−ii−2i2i2i−2i-22ii−i−i−i−iii00000000000000001-1
χ242-22-222-2-2−2i2i−2i2i-1221-2-222-2-2−2i2i−2i2i-1-1-1-11111−2i2i−2i2i22-2-22-2-1-1-1-11111i−ii−i−2i2i−2i2i2-2ii−i−iii−i−i0000000000000000-11
χ2533-1-133333333033033-1-1-1-1-1-1-1-1000000003333-1-1-1-133000000000000-1-1-1-1-1-10000000011111111-1-1-1-1-1-1-1-100
χ2633-1-133333333033033-1-1-1-1-1-1-1-1000000003333-1-1-1-133000000000000-1-1-1-1-1-100000000-1-1-1-1-1-1-1-11111111100
χ2733-1-1333333-3-3033033-1-1-1-1-1-1110000000033-3-3-1-1-1-1-3-3000000000000-1-1111100000000iiii−i−i−i−i−i−i−i−iiiii00
χ2833-1-1333333-3-3033033-1-1-1-1-1-1110000000033-3-3-1-1-1-1-3-3000000000000-1-1111100000000−i−i−i−iiiiiiiii−i−i−i−i00
χ2933-1-13333-3-333033033-1-1-1-111-1-100000000-3-333-1-1-1-1-3-300000000000011-1-11100000000ii−i−iii−i−i−i−iii−i−iii00
χ3033-1-13333-3-333033033-1-1-1-111-1-100000000-3-333-1-1-1-1-3-300000000000011-1-11100000000−i−iii−i−iiiii−i−iii−i−i00
χ3133-1-13333-3-3-3-3033033-1-1-1-1111100000000-3-3-3-3-1-1-1-1330000000000001111-1-10000000011-1-1-1-111-1-11111-1-100
χ3233-1-13333-3-3-3-3033033-1-1-1-1111100000000-3-3-3-3-1-1-1-1330000000000001111-1-100000000-1-11111-1-111-1-1-1-11100
χ333-3-1133-3-33i−3i3i−3i0330-3-3-1-111−ii−ii000000003i−3i3i−3i-1-1113-3000000000000−ii−ii-11000000001-1i−ii−i1-1-11−ii−ii-1100
χ343-3-1133-3-33i−3i3i−3i0330-3-3-1-111−ii−ii000000003i−3i3i−3i-1-1113-3000000000000−ii−ii-1100000000-11−ii−ii-111-1i−ii−i1-100
χ353-3-1133-3-33i−3i−3i3i0330-3-3-1-111−iii−i000000003i−3i−3i3i-1-111-33000000000000−iii−i1-100000000i−i-111-1−ii−ii1-1-11i−i00
χ363-3-1133-3-33i−3i−3i3i0330-3-3-1-111−iii−i000000003i−3i−3i3i-1-111-33000000000000−iii−i1-100000000−ii1-1-11i−ii−i-111-1−ii00
χ373-3-1133-3-3−3i3i3i−3i0330-3-3-1-111i−i−ii00000000−3i3i3i−3i-1-111-33000000000000i−i−ii1-100000000i−i1-1-11−ii−ii-111-1i−i00
χ383-3-1133-3-3−3i3i3i−3i0330-3-3-1-111i−i−ii00000000−3i3i3i−3i-1-111-33000000000000i−i−ii1-100000000−ii-111-1i−ii−i1-1-11−ii00
χ393-3-1133-3-3−3i3i−3i3i0330-3-3-1-111i−ii−i00000000−3i3i−3i3i-1-1113-3000000000000i−ii−i-11000000001-1−ii−ii1-1-11i−ii−i-1100
χ403-3-1133-3-3−3i3i−3i3i0330-3-3-1-111i−ii−i00000000−3i3i−3i3i-1-1113-3000000000000i−ii−i-1100000000-11i−ii−i-111-1−ii−ii1-100
χ4144444-14-100444-1-14-1-14-14-1004444-1-144-1-100-1-1-1-1-1-100-1-1-1-1-1-1-1-1004400-1-1000000-1-1-1-1000000000000000000
χ4244444-14-10044-2-1-1-2-1-14-14-10044-2-21−i1521+i152-2-21−i1521+i15200-1-1-1-1-1-1001−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15200-2-200-1-10000001−i1521+i1521−i1521+i152000000000000000000
χ4344444-14-10044-2-1-1-2-1-14-14-10044-2-21+i1521−i152-2-21+i1521−i15200-1-1-1-1-1-1001+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15200-2-200-1-10000001+i1521−i1521+i1521−i152000000000000000000
χ4444444-14-100-4-44-1-14-1-14-14-100-4-444-1-144-1-10011-1-1-1-100-1-1-1-1-1-1-1-100-4-400110000001111000000000000000000
χ4544444-14-100-4-4-2-1-1-2-1-14-14-100-4-4-2-21−i1521+i152-2-21−i1521+i1520011-1-1-1-1001−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15200220011000000−1+i152−1−i152−1+i152−1−i152000000000000000000
χ4644444-14-100-4-4-2-1-1-2-1-14-14-100-4-4-2-21+i1521−i152-2-21+i1521−i1520011-1-1-1-1001+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15200220011000000−1−i152−1+i152−1−i152−1+i152000000000000000000
χ474444-14-1444004-1-14-1-1-14-144400-1-144-1-144-1-100-1-1-1-100-1-1-1-1-1-1-1-14400-1-10000-1-1-1-10000000000000000000000
χ484444-14-144400-2-1-1-2-1-1-14-1444001−i1521+i152-2-21−i1521+i152-2-2-1-100-1-1-1-1001−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-2-200-1-100001−i1521+i1521−i1521+i1520000000000000000000000
χ494444-14-144400-2-1-1-2-1-1-14-1444001+i1521−i152-2-21+i1521−i152-2-2-1-100-1-1-1-1001+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-2-200-1-100001+i1521−i1521+i1521−i1520000000000000000000000
χ504444-14-14-4-4004-1-14-1-1-14-14-4-400-1-144-1-1441100-1-1-1-100-1-1-1-1-1-1-1-1-4-40011000011110000000000000000000000
χ514444-14-14-4-400-2-1-1-2-1-1-14-14-4-4001−i1521+i152-2-21−i1521+i152-2-21100-1-1-1-1001−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1522200110000−1+i152−1−i152−1+i152−1−i1520000000000000000000000
χ524444-14-14-4-400-2-1-1-2-1-1-14-14-4-4001+i1521−i152-2-21+i1521−i152-2-21100-1-1-1-1001+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1522200110000−1−i152−1+i152−1−i152−1+i1520000000000000000000000
χ534-44-44-1-41004i−4i4-1-1-4114-1-41004i−4i44-1-1-4-41100−ii-1-11100-1-1-1-11111004i−4i00−ii000000−i−iii000000000000000000
χ544-44-44-1-41004i−4i-2-1-12114-1-41004i−4i-2-21−i1521+i15222−1+i152−1−i15200−ii-1-111001−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i15200−2i2i00−ii000000ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47000000000000000000
χ554-44-44-1-41004i−4i-2-1-12114-1-41004i−4i-2-21+i1521−i15222−1−i152−1+i15200−ii-1-111001+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i15200−2i2i00−ii000000ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59000000000000000000
χ564-44-44-1-4100−4i4i4-1-1-4114-1-4100−4i4i44-1-1-4-41100i−i-1-11100-1-1-1-1111100−4i4i00i−i000000ii−i−i000000000000000000
χ574-44-44-1-4100−4i4i-2-1-12114-1-4100−4i4i-2-21−i1521+i15222−1+i152−1−i15200i−i-1-111001−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152002i−2i00i−i000000−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47000000000000000000
χ584-44-44-1-4100−4i4i-2-1-12114-1-4100−4i4i-2-21+i1521−i15222−1−i152−1+i15200i−i-1-111001+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152002i−2i00i−i000000−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59000000000000000000
χ594-44-4-141-44i−4i004-1-1-411-141-44i−4i00-1-14411-4-4−ii00-1-11100-1-1-1-111114i−4i00−ii0000−i−iii0000000000000000000000
χ604-44-4-141-44i−4i00-2-1-1211-141-44i−4i001−i1521+i152-2-2−1+i152−1−i15222−ii00-1-111001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−2i2i00−ii0000ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ470000000000000000000000
χ614-44-4-141-44i−4i00-2-1-1211-141-44i−4i001+i1521−i152-2-2−1−i152−1+i15222−ii00-1-111001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−2i2i00−ii0000ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ590000000000000000000000
χ624-44-4-141-4−4i4i004-1-1-411-141-4−4i4i00-1-14411-4-4i−i00-1-11100-1-1-1-11111−4i4i00i−i0000ii−i−i0000000000000000000000
χ634-44-4-141-4−4i4i00-2-1-1211-141-4−4i4i001−i1521+i152-2-2−1+i152−1−i15222i−i00-1-111001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1522i−2i00i−i0000−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ470000000000000000000000
χ644-44-4-141-4−4i4i00-2-1-1211-141-4−4i4i001+i1521−i152-2-2−1−i152−1+i15222i−i00-1-111001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1522i−2i00i−i0000−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ590000000000000000000000
χ658888-2-2-2-2000083-283-2-2-2-2-20000-2-2-2-2-2-2-2-200003-23-2003-2-233-2-23000000000000000000000000000000000000
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χ688888-2-2-2-20000-43-2-43-2-2-2-2-200001+i151−i151+i151−i151+i151−i151+i151−i1500003-23-200−3−i15211−3+i152−3−i15211−3+i152000000000000000000000000000000000000
χ698888-2-2-2-20000-4-23-4-23-2-2-2-200001−i151+i151+i151−i151−i151+i151+i151−i150000-23-23001−3−i152−3+i15211−3−i152−3+i1521000000000000000000000000000000000000
χ708888-2-2-2-20000-4-23-4-23-2-2-2-200001+i151−i151−i151+i151+i151−i151−i151+i150000-23-23001−3+i152−3−i15211−3+i152−3−i1521000000000000000000000000000000000000
χ718-88-8-2-222000083-2-8-32-2-2220000-2-2-2-2222200003-2-32003-2-23-322-3000000000000000000000000000000000000
χ728-88-8-2-22200008-23-82-3-2-2220000-2-2-2-222220000-232-300-233-22-3-32000000000000000000000000000000000000
χ738-88-8-2-2220000-43-24-32-2-22200001−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i1500003-2-3200−3+i15211−3−i1523−i152-1-13+i152000000000000000000000000000000000000
χ748-88-8-2-2220000-43-24-32-2-22200001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i1500003-2-3200−3−i15211−3+i1523+i152-1-13−i152000000000000000000000000000000000000
χ758-88-8-2-2220000-4-2342-3-2-22200001−i151+i151+i151−i15−1+i15−1−i15−1−i15−1+i150000-232-3001−3−i152−3+i1521-13+i1523−i152-1000000000000000000000000000000000000
χ768-88-8-2-2220000-4-2342-3-2-22200001+i151−i151−i151+i15−1−i15−1+i15−1+i15−1−i150000-232-3001−3+i152−3−i1521-13−i1523+i152-1000000000000000000000000000000000000
χ771212-4-412-312-30012120-3-30-3-3-41-4100-4-40000000000-3-311110000000000000000110000000000000000000000000000
χ781212-4-412-312-300-12-120-3-30-3-3-41-41004400000000003311110000000000000000-1-10000000000000000000000000000
χ791212-4-4-312-3121212000-3-30-3-31-41-4-4-40000000000-3-30011110000000000000011000000000000000000000000000000
χ801212-4-4-312-312-12-12000-3-30-3-31-41-44400000000003300111100000000000000-1-1000000000000000000000000000000
χ8112-12-4412-3-1230012i−12i0-3-3033-414-100−4i4i0000000000−3i3i11-1-10000000000000000i−i0000000000000000000000000000
χ8212-12-4412-3-12300−12i12i0-3-3033-414-1004i−4i00000000003i−3i11-1-10000000000000000−ii0000000000000000000000000000
χ8312-12-44-3123-1212i−12i000-3-30331-4-14−4i4i0000000000−3i3i0011-1-100000000000000i−i000000000000000000000000000000
χ8412-12-44-3123-12−12i12i000-3-30331-4-144i−4i00000000003i−3i0011-1-100000000000000−ii000000000000000000000000000000
χ852424-8-8-6-6-6-6000009-609-622220000000000000000-32-320000000000000000000000000000000000000000000000
χ862424-8-8-6-6-6-600000-690-69222200000000000000002-32-30000000000000000000000000000000000000000000000
χ8724-24-88-6-666000009-60-9622-2-20000000000000000-323-20000000000000000000000000000000000000000000000
χ8824-24-88-6-66600000-6906-922-2-200000000000000002-3-230000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.