Finite Group Databasebeta

← Group #13103730

Character table — Group #13103730

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11222224444455888888888101010101010101616161616162020202020202020202020202020202020204040404040404040405050100100100100100
order12455101025102020445510101010101020224202020201010101020202444881010101020202020202020201010202020404040402444488
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1
χ311111111111111111111111-11-11111111111-111111-1-11111111111-1-111-11111-1-1-1-1-1-1-1
χ411111111111111111111111-11-11111111111-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111-1-11111111111-11-1-1-1-11111111-1i−ii−i11-1-1iiii−i−i−i−i11-1-11ii−i−i-1-1-1i−ii−i
χ6111111111111-1-11111111111-11-1-1-1-11111111-1−ii−ii11-1-1−i−i−i−iiiii11-1-11−i−iii-1-1-1−ii−ii
χ7111111111111-1-1111111111-1-1-1-1-1-1-1111111-1-1i−ii−i-1-1-1-1iiii−i−i−i−i-1-1-1-1-1ii−i−i111−ii−ii
χ8111111111111-1-1111111111-1-1-1-1-1-1-1111111-1-1−ii−ii-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−i−iii111i−ii−i
χ91111111-111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1111111111111-1-1-1-11-1-1-1-111-111-1-1
χ101111111-111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111
χ111111111-111111111-1-1-1-1111-11-11111-1-1-1-1111-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111
χ121111111-111111111-1-1-1-1111-11-11111-1-1-1-1111-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-11111-1-1111-1-1
χ131111111-11111-1-111-1-1-1-11111-11-1-1-1-1-1-1-1-111-11i−i−ii11-1-1iiii−i−i−i−i-1-1111−i−iii-1-11i−i−ii
χ141111111-11111-1-111-1-1-1-11111-11-1-1-1-1-1-1-1-111-11−iii−i11-1-1−i−i−i−iiiii-1-1111ii−i−i-1-11−iii−i
χ151111111-11111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111i−i−ii-1-1-1-1iiii−i−i−i−i1111-1−i−iii11-1−iii−i
χ161111111-11111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111−iii−i-1-1-1-1−i−i−i−iiiii1111-1ii−i−i11-1i−i−ii
χ17222−1+52−1−52−1+52−1−52222−1+52−1−5222−1+52−1−52−1+52−1−5222−1+52−1−522020−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−5202222200−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200−1+52−1−520−1+52−1−52−1+52−1−520000000
χ18222−1+52−1−52−1+52−1−52222−1+52−1−5222−1+52−1−52−1+52−1−5222−1+52−1−522020−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−5202-2-2-2-200−1+52−1−521−521−521+521+521−521−521+521+5200−1+52−1−5201−521+521−521+520000000
χ19222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2−1+52−1−52−1+52−1−5222−1+52−1−5220-201−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−520-22i−2i2i−2i001−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7001−521+520−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000
χ20222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2−1+52−1−52−1+52−1−5222−1+52−1−5220-201−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−520-2−2i2i−2i2i001−521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7001−521+520ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000
χ21222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−521−521+52-2-2−1+52−1−522020−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−520-222-2-200−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+5201−521+521−521+520000000
χ22222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−521−521+52-2-2−1+52−1−522020−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−520-2-2-22200−1+52−1−521−521−521+521+521−521−521+521+52001−521+520−1+52−1−52−1+52−1−520000000
χ23222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−521−521+52-2-2−1+52−1−5220-201−521−521+521+521−521−521+521+52−1+52−1−52022i−2i−2i2i001−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ700−1+52−1−520ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000
χ24222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−521−521+52-2-2−1+52−1−5220-201−521−521+521+521−521−521+521+52−1+52−1−5202−2i2i2i−2i001−521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ700−1+52−1−520−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000
χ25222−1−52−1+52−1−52−1+52222−1−52−1+5222−1−52−1+52−1−52−1+5222−1−52−1+522020−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+5202222200−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200−1−52−1+520−1−52−1+52−1−52−1+520000000
χ26222−1−52−1+52−1−52−1+52222−1−52−1+5222−1−52−1+52−1−52−1+5222−1−52−1+522020−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+5202-2-2-2-200−1−52−1+521+521+521−521−521+521+521−521−5200−1−52−1+5201+521−521+521−520000000
χ27222−1−52−1+52−1−52−1+52222−1−52−1+52-2-2−1−52−1+52−1−52−1+5222−1−52−1+5220-201+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+520-22i−2i2i−2i001+521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19001+521−520−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000
χ28222−1−52−1+52−1−52−1+52222−1−52−1+52-2-2−1−52−1+52−1−52−1+5222−1−52−1+5220-201+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+520-2−2i2i−2i2i001+521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19001+521−520ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000
χ29222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+521+521−52-2-2−1−52−1+522020−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+520-222-2-200−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−5201+521−521+521−520000000
χ30222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+521+521−52-2-2−1−52−1+522020−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+520-2-2-22200−1−52−1+521+521+521−521−521+521+521−521−52001+521−520−1−52−1+52−1−52−1+520000000
χ31222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-2−1−52−1+521+521−52-2-2−1−52−1+5220-201+521+521−521−521+521+521−521−52−1−52−1+52022i−2i−2i2i001+521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ1900−1−52−1+520ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000
χ32222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-2−1−52−1+521+521−52-2-2−1−52−1+5220-201+521+521−521−521+521+521−521−52−1−52−1+5202−2i2i2i−2i001+521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ1900−1−52−1+520−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000
χ3322-22222022-2-22222000022-22-2-222220000-2-200000022-2-2000000000000-20000-2200000
χ3422-22222022-2-22222000022-2-2-2222220000-2-2000000-2-2-2-2000000000000200002-200000
χ3522-22222022-2-2-2-222000022-222-2-2-2-2-20000-2-20000002222000000000000-200002-200000
χ3622-22222022-2-2-2-222000022-2-222-2-2-2-20000-2-2000000-2-22200000000000020000-2200000
χ3744444444-1-14400-1-144-1-1-1-1-14040000-1-1-1-1-1-1400000-1-10000000000-1-100-100000000000
χ3844444444-1-14400-1-144-1-1-1-1-1-40-40000-1-1-1-1-1-1-4000001100000000001100100000000000
χ394444444-4-1-14400-1-1-4-411-1-1-140400001111-1-1-400000-1-100000000001100-100000000000
χ404444444-4-1-14400-1-1-4-411-1-1-1-40-400001111-1-1400000110000000000-1-100100000000000
χ4144-444440-1-1-4-400-1-1005−5-1-1140-400005−55−511000000-1-100000000005−500100000000000
χ4244-444440-1-1-4-400-1-1005−5-1-11-40400005−55−511000000110000000000−5500-100000000000
χ4344-444440-1-1-4-400-1-100−55-1-1140-40000−55−5511000000-1-10000000000−5500100000000000
χ4444-444440-1-1-4-400-1-100−55-1-11-4040000−55−55110000001100000000005−500-100000000000
χ4544-4−1+5−1−5−1+5−1−50441−51+544−1+5−1−50000−1+5−1−5-40-40−1+5−1+5−1−5−1−500001−51+5000000001−51+5000000000000000000000000
χ4644-4−1+5−1−5−1+5−1−50441−51+5-4-4−1+5−1−50000−1+5−1−5-40401−51−51+51+500001−51+500000000−1+5−1−5000000000000000000000000
χ4744-4−1−5−1+5−1−5−1+50441+51−544−1−5−1+50000−1−5−1+5-40-40−1−5−1−5−1+5−1+500001+51−5000000001+51−5000000000000000000000000
χ4844-4−1−5−1+5−1−5−1+50441+51−5-4-4−1−5−1+50000−1−5−1+5-40401+51+51−51−500001+51−500000000−1−5−1+5000000000000000000000000
χ494-4044-4-404-4004i−4i440000-4-400004i−4i4i−4i0000000000000000000000000000000000000000
χ504-4044-4-404-400−4i4i440000-4-40000−4i4i−4i4i0000000000000000000000000000000000000000
χ514-40−1+5−1−51−51+504-4004i−4i−1+5−1−500001−51+50000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000−ζ6−ζ11+ζ14+ζ19ζ6+ζ11−ζ14−ζ19−ζ2+ζ3−ζ7+ζ18ζ2−ζ3+ζ7−ζ18ζ6−ζ11−ζ14+ζ19−ζ6+ζ11+ζ14−ζ19−ζ2−ζ3+ζ7+ζ18ζ2+ζ3−ζ7−ζ180000000000000000
χ524-40−1+5−1−51−51+504-4004i−4i−1+5−1−500001−51+50000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000ζ6+ζ11−ζ14−ζ19−ζ6−ζ11+ζ14+ζ19ζ2−ζ3+ζ7−ζ18−ζ2+ζ3−ζ7+ζ18−ζ6+ζ11+ζ14−ζ19ζ6−ζ11−ζ14+ζ19ζ2+ζ3−ζ7−ζ18−ζ2−ζ3+ζ7+ζ180000000000000000
χ534-40−1+5−1−51−51+504-400−4i4i−1+5−1−500001−51+500002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000ζ6−ζ11−ζ14+ζ19−ζ6+ζ11+ζ14−ζ19ζ2+ζ3−ζ7−ζ18−ζ2−ζ3+ζ7+ζ18−ζ6−ζ11+ζ14+ζ19ζ6+ζ11−ζ14−ζ19ζ2−ζ3+ζ7−ζ18−ζ2+ζ3−ζ7+ζ180000000000000000
χ544-40−1+5−1−51−51+504-400−4i4i−1+5−1−500001−51+500002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000−ζ6+ζ11+ζ14−ζ19ζ6−ζ11−ζ14+ζ19−ζ2−ζ3+ζ7+ζ18ζ2+ζ3−ζ7−ζ18ζ6+ζ11−ζ14−ζ19−ζ6−ζ11+ζ14+ζ19−ζ2+ζ3−ζ7+ζ18ζ2−ζ3+ζ7−ζ180000000000000000
χ554-40−1−5−1+51+51−504-4004i−4i−1−5−1+500001+51−50000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000−ζ2+ζ3−ζ7+ζ18ζ2−ζ3+ζ7−ζ18ζ6+ζ11−ζ14−ζ19−ζ6−ζ11+ζ14+ζ19ζ2+ζ3−ζ7−ζ18−ζ2−ζ3+ζ7+ζ18ζ6−ζ11−ζ14+ζ19−ζ6+ζ11+ζ14−ζ190000000000000000
χ564-40−1−5−1+51+51−504-4004i−4i−1−5−1+500001+51−50000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000ζ2−ζ3+ζ7−ζ18−ζ2+ζ3−ζ7+ζ18−ζ6−ζ11+ζ14+ζ19ζ6+ζ11−ζ14−ζ19−ζ2−ζ3+ζ7+ζ18ζ2+ζ3−ζ7−ζ18−ζ6+ζ11+ζ14−ζ19ζ6−ζ11−ζ14+ζ190000000000000000
χ574-40−1−5−1+51+51−504-400−4i4i−1−5−1+500001+51−500002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000−ζ2−ζ3+ζ7+ζ18ζ2+ζ3−ζ7−ζ18ζ6−ζ11−ζ14+ζ19−ζ6+ζ11+ζ14−ζ19ζ2−ζ3+ζ7−ζ18−ζ2+ζ3−ζ7+ζ18ζ6+ζ11−ζ14−ζ19−ζ6−ζ11+ζ14+ζ190000000000000000
χ584-40−1−5−1+51+51−504-400−4i4i−1−5−1+500001+51−500002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000ζ2+ζ3−ζ7−ζ18−ζ2−ζ3+ζ7+ζ18−ζ6+ζ11+ζ14−ζ19ζ6−ζ11−ζ14+ζ19−ζ2+ζ3−ζ7+ζ18ζ2−ζ3+ζ7−ζ18−ζ6−ζ11+ζ14+ζ19ζ6+ζ11−ζ14−ζ190000000000000000
χ59888−2+25−2−25−2+25−2−258-2-2−2+25−2−25001−521+52−2+25−2−25-2-21−521+52-200000001−521−521+521+521−521+520000000000000000000000000000000000
χ60888−2+25−2−25−2+25−2−25-8-2-2−2+25−2−25001−521+522−252+25221−521+52-20000000−1+52−1+52−1−52−1−521−521+520000000000000000000000000000000000
χ61888−2−25−2+25−2−25−2+258-2-2−2−25−2+25001+521−52−2−25−2+25-2-21+521−52-200000001+521+521−521−521+521−520000000000000000000000000000000000
χ62888−2−25−2+25−2−25−2+25-8-2-2−2−25−2+25001+521−522+252−25221+521−52-20000000−1−52−1−52−1+52−1+521+521−520000000000000000000000000000000000
χ6388-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+520025−251−521+52200000005−52−5+52−5−525+52−1+52−1−520000000000000000000000000000000000
χ6488-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+5200−25251−521+5220000000−5+525−525+52−5−52−1+52−1−520000000000000000000000000000000000
χ6588-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−520025−251+521−5220000000−5−525+525−52−5+52−1−52−1+520000000000000000000000000000000000
χ6688-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−5200−25251+521−52200000005+52−5−52−5+525−52−1−52−1+520000000000000000000000000000000000
χ678-8088-8-80-220000-2-20000220000000000000000000025−2500000000000000000000000000
χ688-8088-8-80-220000-2-200002200000000000000000000−252500000000000000000000000000
χ6916-160−4+45−4−454−454+450-4400001−51+50000−1+5−1−5000000000000000000000000000000000000000000000000
χ7016-160−4−45−4+454+454−450-4400001+51−50000−1−5−1+5000000000000000000000000000000000000000000000000

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