Finite Group Databasebeta

← Group #13103736

Character table — Group #13103736

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size112222244444558888888101010101016161616161616202020202020202020202020202020202040404040404040405050505080100100100100
order12455101025102020445510101010202202020201010101010202024448881010202020202020202020204040404040408888104888
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1
χ3111111111111111111111111111111111-1111-111111111111111-1-11111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-11-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-111
χ5111111111111-1-11111111-1-1-1-1-111111111-1i−i1i−i-1-1iiii−i−i−i−i-1-111ii−i−iii−i−i1-1-1i−i
χ6111111111111-1-11111111-1-1-1-1-111111111-1−ii1−ii-1-1−i−i−i−iiiii-1-111−i−iii−i−iii1-1-1−ii
χ7111111111111-1-11111111-1-1-1-1-11111111-1-1i−i-1i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−i−i−iii-111−ii
χ8111111111111-1-11111111-1-1-1-1-11111111-1-1−ii-1−ii-1-1−i−i−i−iiiii-1-1-1-1−i−iiiii−i−i-111i−i
χ91111111-111111111-1-111111111-1-1-1-1-1111-111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-111
χ101111111-111111111-1-111111111-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1
χ111111111-111111111-1-111111111-1-1-1-1-111-1-1111-1-11111111111-1-111-1-1-1-11111-1-11-1-1
χ121111111-111111111-1-111111111-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111
χ131111111-11111-1-111-1-1111-1-1-1-1-1-1-1-1-1-11111i−i-1−ii-1-1iiii−i−i−i−i11-1-1−i−iii−i−iii1-11i−i
χ141111111-11111-1-111-1-1111-1-1-1-1-1-1-1-1-1-11111−ii-1i−i-1-1−i−i−i−iiiii11-1-1ii−i−iii−i−i1-11−ii
χ151111111-11111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111-11i−i1−ii-1-1iiii−i−i−i−i1111−i−iiiii−i−i-11-1−ii
χ161111111-11111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111-11−ii1i−i-1-1−i−i−i−iiiii1111ii−i−i−i−iii-11-1i−i
χ17222−1+52−1−52−1+52−1−52222−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1−520222022−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−5200−1+52−1−52−1+52−1−52000000000
χ18222−1+52−1−52−1+52−1−52222−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1−5202-2-20-2-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52001−521+521−521+52000000000
χ19222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521−521+521+522−1+52−1+52−1−52−1−52−1+52−1−520-22i−2i02i−2i1−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ141−521+5200−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14000000000
χ20222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521−521+521+522−1+52−1+52−1−52−1−52−1+52−1−520-2−2i2i0−2i2i1−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ141−521+5200ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14000000000
χ21222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−521−521+52−1+52−1−5222−1+52−1+52−1−52−1−52-21−521−521+521+52−1+52−1−520-2220-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+52001−521+521−521+52000000000
χ22222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−521−521+52−1+52−1−5222−1+52−1+52−1−52−1−52-21−521−521+521+52−1+52−1−520-2-2-2022−1+52−1−521−521−521+521+521−521−521+521+521−521+5200−1+52−1−52−1+52−1−52000000000
χ23222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−521−521+52−1+52−1−522-21−521−521+521+52-21−521−521+521+52−1+52−1−52022i−2i0−2i2i1−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1−5200ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14000000000
χ24222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−521−521+52−1+52−1−522-21−521−521+521+52-21−521−521+521+52−1+52−1−5202−2i2i02i−2i1−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−1+52−1−5200−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14000000000
χ25222−1−52−1+52−1−52−1+52222−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+522−1−52−1−52−1+52−1+52−1−52−1+520222022−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+5200−1−52−1+52−1−52−1+52000000000
χ26222−1−52−1+52−1−52−1+52222−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+522−1−52−1−52−1+52−1+52−1−52−1+5202-2-20-2-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52001+521−521+521−52000000000
χ27222−1−52−1+52−1−52−1+52222−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521+521−521−522−1−52−1−52−1+52−1+52−1−52−1+520-22i−2i02i−2i1+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ381+521−5200−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38000000000
χ28222−1−52−1+52−1−52−1+52222−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521+521−521−522−1−52−1−52−1+52−1+52−1−52−1+520-2−2i2i0−2i2i1+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ381+521−5200ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38000000000
χ29222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+521+521−52−1−52−1+5222−1−52−1−52−1+52−1+52-21+521+521−521−52−1−52−1+520-2220-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−52001+521−521+521−52000000000
χ30222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+521+521−52−1−52−1+5222−1−52−1−52−1+52−1+52-21+521+521−521−52−1−52−1+520-2-2-2022−1−52−1+521+521+521−521−521+521+521−521−521+521−5200−1−52−1+52−1−52−1+52000000000
χ31222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-2−1−52−1+521+521−52−1−52−1+522-21+521+521−521−52-21+521+521−521−52−1−52−1+52022i−2i0−2i2i1+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−1−52−1+5200ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38000000000
χ32222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-2−1−52−1+521+521−52−1−52−1+522-21+521+521−521−52-21+521+521−521−52−1−52−1+5202−2i2i02i−2i1+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−1−52−1+5200−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38000000000
χ3322-22222022-2-222220022-2-2222200000-2-20000000-2-200000000000000002-22-200000
χ3422-22222022-2-222220022-2-2222200000-2-20000000-2-20000000000000000-22-2200000
χ3522-22222022-2-2-2-2220022-22-2-2-2-200000-2-200000002200000000000000002i−2i−2i2i00000
χ3622-22222022-2-2-2-2220022-22-2-2-2-200000-2-20000000220000000000000000−2i2i2i−2i00000
χ3744444444-1-14400-1-144-1-1-100000-1-1-1-1-1-1-14000400000000000000-1-100000000-10000
χ3844444444-1-14400-1-144-1-1-100000-1-1-1-1-1-1-1-4000-400000000000000110000000010000
χ394444444-4-1-14400-1-1-4-4-1-1-10000011111-1-14000-4000000000000001100000000-10000
χ404444444-4-1-14400-1-1-4-4-1-1-10000011111-1-1-4000400000000000000-1-10000000010000
χ4144-4−1+5−1−5−1+5−1−50441−51+544−1+5−1−500−1+5−1−5-4-4−1+5−1+5−1−5−1−5000001−51+500000001−51+50000000000000000000000000
χ4244-4−1+5−1−5−1+5−1−50441−51+5-4-4−1+5−1−500−1+5−1−5-441−51−51+51+5000001−51+50000000−1+5−1−50000000000000000000000000
χ4344-4−1−5−1+5−1−5−1+50441+51−544−1−5−1+500−1−5−1+5-4-4−1−5−1−5−1+5−1+5000001+51−500000001+51−50000000000000000000000000
χ4444-4−1−5−1+5−1−5−1+50441+51−5-4-4−1−5−1+500−1−5−1+5-441+51+51−51−5000001+51−50000000−1−5−1+50000000000000000000000000
χ454-4044-4-404-4004i−4i4400-4-4004i−4i4i−4i00000000000000000000000000000000000000000
χ464-4044-4-404-400−4i4i4400-4-400−4i4i−4i4i00000000000000000000000000000000000000000
χ474-40−1+5−1−51−51+504-4004i−4i−1+5−1−5001−51+500−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000−ζ12−ζ22+ζ28+ζ38ζ12+ζ22−ζ28−ζ38−ζ4+ζ6−ζ14+ζ36ζ4−ζ6+ζ14−ζ36ζ12−ζ22−ζ28+ζ38−ζ12+ζ22+ζ28−ζ38−ζ4−ζ6+ζ14+ζ36ζ4+ζ6−ζ14−ζ3600000000000000000
χ484-40−1+5−1−51−51+504-4004i−4i−1+5−1−5001−51+500−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000ζ12+ζ22−ζ28−ζ38−ζ12−ζ22+ζ28+ζ38ζ4−ζ6+ζ14−ζ36−ζ4+ζ6−ζ14+ζ36−ζ12+ζ22+ζ28−ζ38ζ12−ζ22−ζ28+ζ38ζ4+ζ6−ζ14−ζ36−ζ4−ζ6+ζ14+ζ3600000000000000000
χ494-40−1+5−1−51−51+504-400−4i4i−1+5−1−5001−51+5002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000ζ12−ζ22−ζ28+ζ38−ζ12+ζ22+ζ28−ζ38ζ4+ζ6−ζ14−ζ36−ζ4−ζ6+ζ14+ζ36−ζ12−ζ22+ζ28+ζ38ζ12+ζ22−ζ28−ζ38ζ4−ζ6+ζ14−ζ36−ζ4+ζ6−ζ14+ζ3600000000000000000
χ504-40−1+5−1−51−51+504-400−4i4i−1+5−1−5001−51+5002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000−ζ12+ζ22+ζ28−ζ38ζ12−ζ22−ζ28+ζ38−ζ4−ζ6+ζ14+ζ36ζ4+ζ6−ζ14−ζ36ζ12+ζ22−ζ28−ζ38−ζ12−ζ22+ζ28+ζ38−ζ4+ζ6−ζ14+ζ36ζ4−ζ6+ζ14−ζ3600000000000000000
χ514-40−1−5−1+51+51−504-4004i−4i−1−5−1+5001+51−500−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000−ζ4+ζ6−ζ14+ζ36ζ4−ζ6+ζ14−ζ36ζ12+ζ22−ζ28−ζ38−ζ12−ζ22+ζ28+ζ38ζ4+ζ6−ζ14−ζ36−ζ4−ζ6+ζ14+ζ36ζ12−ζ22−ζ28+ζ38−ζ12+ζ22+ζ28−ζ3800000000000000000
χ524-40−1−5−1+51+51−504-4004i−4i−1−5−1+5001+51−500−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000ζ4−ζ6+ζ14−ζ36−ζ4+ζ6−ζ14+ζ36−ζ12−ζ22+ζ28+ζ38ζ12+ζ22−ζ28−ζ38−ζ4−ζ6+ζ14+ζ36ζ4+ζ6−ζ14−ζ36−ζ12+ζ22+ζ28−ζ38ζ12−ζ22−ζ28+ζ3800000000000000000
χ534-40−1−5−1+51+51−504-400−4i4i−1−5−1+5001+51−5002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000−ζ4−ζ6+ζ14+ζ36ζ4+ζ6−ζ14−ζ36ζ12−ζ22−ζ28+ζ38−ζ12+ζ22+ζ28−ζ38ζ4−ζ6+ζ14−ζ36−ζ4+ζ6−ζ14+ζ36ζ12+ζ22−ζ28−ζ38−ζ12−ζ22+ζ28+ζ3800000000000000000
χ544-40−1−5−1+51+51−504-400−4i4i−1−5−1+5001+51−5002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000ζ4+ζ6−ζ14−ζ36−ζ4−ζ6+ζ14+ζ36−ζ12+ζ22+ζ28−ζ38ζ12−ζ22−ζ28+ζ38−ζ4+ζ6−ζ14+ζ36ζ4−ζ6+ζ14−ζ36−ζ12−ζ22+ζ28+ζ38ζ12+ζ22−ζ28−ζ3800000000000000000
χ55888−2+25−2−25−2+25−2−258-2-2−2+25−2−25001−521+52−2+25−2−251−521+52-200000-21−521−521+521+521−521+520000000000000000000000000000000000
χ56888−2+25−2−25−2+25−2−25-8-2-2−2+25−2−25001−521+522−252+251−521+52-2000002−1+52−1+52−1−52−1−521−521+520000000000000000000000000000000000
χ57888−2−25−2+25−2−25−2+258-2-2−2−25−2+25001+521−52−2−25−2+251+521−52-200000-21+521+521−521−521+521−520000000000000000000000000000000000
χ58888−2−25−2+25−2−25−2+25-8-2-2−2−25−2+25001+521−522+252−251+521−52-2000002−1−52−1−52−1+52−1+521+521−520000000000000000000000000000000000
χ5988-888880-2-2-8-800-2-200-2-220000000000220000000000000000000000000000000000
χ6088-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+52001−521+522000000−2ζ4−ζ12+ζ28+2ζ362ζ4+ζ12−ζ28−2ζ36−ζ4+2ζ12−2ζ28+ζ36ζ4−2ζ12+2ζ28−ζ36−1+52−1−520000000000000000000000000000000000
χ6188-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+52001−521+5220000002ζ4+ζ12−ζ28−2ζ36−2ζ4−ζ12+ζ28+2ζ36ζ4−2ζ12+2ζ28−ζ36−ζ4+2ζ12−2ζ28+ζ36−1+52−1−520000000000000000000000000000000000
χ6288-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−52001+521−522000000−ζ4+2ζ12−2ζ28+ζ36ζ4−2ζ12+2ζ28−ζ362ζ4+ζ12−ζ28−2ζ36−2ζ4−ζ12+ζ28+2ζ36−1−52−1+520000000000000000000000000000000000
χ6388-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−52001+521−522000000ζ4−2ζ12+2ζ28−ζ36−ζ4+2ζ12−2ζ28+ζ36−2ζ4−ζ12+ζ28+2ζ362ζ4+ζ12−ζ28−2ζ36−1−52−1+520000000000000000000000000000000000
χ648-8088-8-80-220000-2-200220000000000000000000000000000000010−100000000000000
χ658-8088-8-80-220000-2-2002200000000000000000000000000000000−10100000000000000
χ6616-160−4+45−4−454−454+450-4400001−51+500−1+5−1−500000000000000000000000000000000000000000000000
χ6716-160−4−45−4+454+454−450-4400001+51−500−1−5−1+500000000000000000000000000000000000000000000000

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