Finite Group Databasebeta

← Group #13103722

Character table — Group #13103722

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size11222224444455888888810101010101010101010101616161616161620202020202020202020202020202525252540404040404040405050505080100100100
order12455101025102020225510101010204888888101010101010101010202022442020404040404040404044441010202020204040448810244
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ31111111111111111111111-1-11111111111111111-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111
χ5111111111111-1-11111111-111ii−i−i-1-1-1-11111111-11i−i-1-1iiii−i−i−i−iii−i−i-1-1ii−i−i11i−i-1-11-1i−i
χ6111111111111-1-11111111-111−i−iii-1-1-1-11111111-11−ii-1-1−i−i−i−iiiii−i−iii-1-1−i−iii11−ii-1-11-1−ii
χ7111111111111-1-11111111-1-1-1ii−i−i-1-1-1-11111111-1-1i−i-1-1iiii−i−i−i−i−i−iii-1-1ii−i−i-1-1−ii11-11−ii
χ8111111111111-1-11111111-1-1-1−i−iii-1-1-1-11111111-1-1−ii-1-1−i−i−i−iiiiiii−i−i-1-1−i−iii-1-1i−i11-11i−i
χ91111111-111111111-1-111111111111111-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1
χ101111111-111111111-1-1111111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ111111111-111111111-1-11111-1-111111111-1-1-1-1-111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ121111111-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-111-111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111-11111-1-111-1-1111-111ii−i−i-1-1-1-1-1-1-1-1-1111-1−ii-1-1iiii−i−i−i−iii−i−i11−i−iii11i−i-1-1-11−ii
χ141111111-11111-1-111-1-1111-111−i−iii-1-1-1-1-1-1-1-1-1111-1i−i-1-1−i−i−i−iiiii−i−iii11ii−i−i11−ii-1-1-11i−i
χ151111111-11111-1-111-1-1111-1-1-1ii−i−i-1-1-1-1-1-1-1-1-11111−ii-1-1iiii−i−i−i−i−i−iii11−i−iii-1-1−ii111-1i−i
χ161111111-11111-1-111-1-1111-1-1-1−i−iii-1-1-1-1-1-1-1-1-11111i−i-1-1−i−i−i−iiiiiii−i−i11ii−i−i-1-1i−i111-1−ii
χ17222−1+52−1−52−1+52−1−52222−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5222002222−1+52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−522022−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ18222−1+52−1−52−1+52−1−52222−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−522200-2-2-2-2−1+52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−5220-2-2−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−521−521+521−521+520000000000
χ19222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-2002i2i−2i−2i1−521+521−521+522−1+52−1+52−1−52−1−52−1+52−1−52-202i−2i1−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ1400001−521+52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ20222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-200−2i−2i2i2i1−521+521−521+522−1+52−1+52−1−52−1−52−1+52−1−52-20−2i2i1−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ1400001−521+52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ21222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−521−521+52−1+52−1−5222002222−1+52−1−52−1+52−1−52-21−521−521+521+52−1+52−1−52-20-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200001−521+521−521+521−521+520000000000
χ22222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−521−521+52−1+52−1−522200-2-2-2-2−1+52−1−52−1+52−1−52-21−521−521+521+52−1+52−1−52-2022−1+52−1−521−521−521+521+521−521−521+521+5200001−521+52−1+52−1−52−1+52−1−520000000000
χ23222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−521−521+52−1+52−1−522-2002i2i−2i−2i1−521+521−521+52-21−521−521+521+52−1+52−1−5220−2i2i1−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000−1+52−1−52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ24222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−521−521+52−1+52−1−522-200−2i−2i2i2i1−521+521−521+52-21−521−521+521+52−1+52−1−52202i−2i1−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000−1+52−1−52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ25222−1−52−1+52−1−52−1+52222−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5222002222−1−52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+522022−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ26222−1−52−1+52−1−52−1+52222−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+522200-2-2-2-2−1−52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+5220-2-2−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+521+521−521+521−520000000000
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+522-2002i2i−2i−2i1+521−521+521−522−1−52−1−52−1+52−1+52−1−52−1+52-202i−2i1+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ3800001+521−52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
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+522-200−2i−2i2i2i1+521−521+521−522−1−52−1−52−1+52−1+52−1−52−1+52-20−2i2i1+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ3800001+521−52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ29222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+521+521−52−1−52−1+5222002222−1−52−1+52−1−52−1+52-21+521+521−521−52−1−52−1+52-20-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200001+521−521+521−521+521−520000000000
χ30222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+521+521−52−1−52−1+522200-2-2-2-2−1−52−1+52−1−52−1+52-21+521+521−521−52−1−52−1+52-2022−1−52−1+521+521+521−521−521+521+521−521−5200001+521−52−1−52−1+52−1−52−1+520000000000
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+522-2002i2i−2i−2i1+521−521+521−52-21+521+521−521−52−1−52−1+5220−2i2i1+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000−1−52−1+52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
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+522-200−2i−2i2i2i1+521−521+521−52-21+521+521−521−52−1−52−1+52202i−2i1+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000−1−52−1+52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ3322-22222022-2-222220022-2-2000000222200000-2-20000-2-200000000222200000000-2-2000000
χ3422-22222022-2-222220022-2-2000000222200000-2-20000-2-200000000-2-2-2-20000000022000000
χ3522-22222022-2-2-2-2220022-22000000-2-2-2-200000-2-2000022000000002i2i−2i−2i00000000−2i2i000000
χ3622-22222022-2-2-2-2220022-22000000-2-2-2-200000-2-200002200000000−2i−2i2i2i000000002i−2i000000
χ372-2022-2-202-2002-22200-2-2002−2i2−i2i2−i222-2-20000000000000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000002−2002−20000
χ382-2022-2-202-2002-22200-2-2002−2−i2i2−i2i222-2-20000000000000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000002−2002−20000
χ392-2022-2-202-2002-22200-2-200−22i2−i2i2−i222-2-20000000000000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i000000−2200−220000
χ402-2022-2-202-2002-22200-2-200−22−i2i2−i2i222-2-20000000000000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i000000−2200−220000
χ412-2022-2-202-200-222200-2-2002−22−2−22-2-22200000000000002−22−2−22−222-2-220000002−200−220000
χ422-2022-2-202-200-222200-2-2002−2−222−2-2-2220000000000000−22−222−22−2-222-20000002−200−220000
χ432-2022-2-202-200-222200-2-200−222−2−22-2-22200000000000002−22−2−22−22-222-2000000−22002−20000
χ442-2022-2-202-200-222200-2-200−22−222−2-2-2220000000000000−22−222−22−22-2-22000000−22002−20000
χ4544444444-1-14400-1-144-1-1-104400000000-1-1-1-1-1-1-1040000000000000000000000-1-10000-1000
χ4644444444-1-14400-1-144-1-1-10-4-400000000-1-1-1-1-1-1-10-400000000000000000000001100001000
χ474444444-4-1-14400-1-1-4-4-1-1-10440000000011111-1-10-40000000000000000000000-1-100001000
χ484444444-4-1-14400-1-1-4-4-1-1-10-4-40000000011111-1-1040000000000000000000000110000-1000
χ4944-4−1+5−1−5−1+5−1−50441−51+544−1+5−1−500−1+5−1−5-4-4000000−1+5−1−5−1+5−1−5000001−51+500001−51+50000000000000000000000000000
χ5044-4−1+5−1−5−1+5−1−50441−51+5-4-4−1+5−1−500−1+5−1−5-440000001−51+51−51+5000001−51+50000−1+5−1−50000000000000000000000000000
χ5144-4−1−5−1+5−1−5−1+50441+51−544−1−5−1+500−1−5−1+5-4-4000000−1−5−1+5−1−5−1+5000001+51−500001+51−50000000000000000000000000000
χ5244-4−1−5−1+5−1−5−1+50441+51−5-4-4−1−5−1+500−1−5−1+5-440000001+51−51+51−5000001+51−50000−1−5−1+50000000000000000000000000000
χ534-40−1+5−1−51−51+504-4004-4−1+5−1−5001−51+500002i2−2i22i2−2i2−1+5−1−51−51+50000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ3900000000000000000000
χ544-40−1+5−1−51−51+504-4004-4−1+5−1−5001−51+50000−2i22i2−2i22i2−1+5−1−51−51+50000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ3900000000000000000000
χ554-40−1+5−1−51−51+504-400-44−1+5−1−5001−51+5000022−22−22221−51+5−1+5−1−50000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900000000000000000000
χ564-40−1+5−1−51−51+504-400-44−1+5−1−5001−51+50000−222222−221−51+5−1+5−1−50000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900000000000000000000
χ574-40−1−5−1+51+51−504-4004-4−1−5−1+5001+51−500002i2−2i22i2−2i2−1−5−1+51+51−50000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ3700000000000000000000
χ584-40−1−5−1+51+51−504-4004-4−1−5−1+5001+51−50000−2i22i2−2i22i2−1−5−1+51+51−50000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ3700000000000000000000
χ594-40−1−5−1+51+51−504-400-44−1−5−1+5001+51−5000022−22−22221+51−5−1−5−1+50000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700000000000000000000
χ604-40−1−5−1+51+51−504-400-44−1−5−1+5001+51−50000−222222−221+51−5−1−5−1+50000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700000000000000000000
χ61888−2+25−2−25−2+25−2−258-2-2−2+25−2−25001−521+52−2+25−2−251−521+52-200000000000-21−521−521+521+521−521+520000000000000000000000000000000000
χ62888−2+25−2−25−2+25−2−25-8-2-2−2+25−2−25001−521+522−252+251−521+52-2000000000002−1+52−1+52−1−52−1−521−521+520000000000000000000000000000000000
χ63888−2−25−2+25−2−25−2+258-2-2−2−25−2+25001+521−52−2−25−2+251+521−52-200000000000-21+521+521−521−521+521−520000000000000000000000000000000000
χ64888−2−25−2+25−2−25−2+25-8-2-2−2−25−2+25001+521−522+252−251+521−52-2000000000002−1−52−1−52−1+52−1+521+521−520000000000000000000000000000000000
χ6588-888880-2-2-8-800-2-200-2-220000000000000000220000000000000000000000000000000000
χ6688-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+52001−521+522000000000000−2ζ4−ζ12+ζ28+2ζ362ζ4+ζ12−ζ28−2ζ36−ζ4+2ζ12−2ζ28+ζ36ζ4−2ζ12+2ζ28−ζ36−1+52−1−520000000000000000000000000000000000
χ6788-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+52001−521+5220000000000002ζ4+ζ12−ζ28−2ζ36−2ζ4−ζ12+ζ28+2ζ36ζ4−2ζ12+2ζ28−ζ36−ζ4+2ζ12−2ζ28+ζ36−1+52−1−520000000000000000000000000000000000
χ6888-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−52001+521−522000000000000−ζ4+2ζ12−2ζ28+ζ36ζ4−2ζ12+2ζ28−ζ362ζ4+ζ12−ζ28−2ζ36−2ζ4−ζ12+ζ28+2ζ36−1−52−1+520000000000000000000000000000000000
χ6988-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−52001+521−522000000000000ζ4−2ζ12+2ζ28−ζ36−ζ4+2ζ12−2ζ28+ζ36−2ζ4−ζ12+ζ28+2ζ362ζ4+ζ12−ζ28−2ζ36−1−52−1+520000000000000000000000000000000000
χ708-8088-8-80-220000-2-200220042−42000000000000000000000000000000000000000−2200000000
χ718-8088-8-80-220000-2-2002200−42420000000000000000000000000000000000000002−200000000
χ7216-160−4+45−4−454−454+450-4400001−51+500−1+5−1−500000000000000000000000000000000000000000000000000000
χ7316-160−4−45−4+454+454−450-4400001+51−500−1−5−1+500000000000000000000000000000000000000000000000000000

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