Finite Group Databasebeta

← Group #13103751

Character table — Group #13103751

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size112222244444558888888101010101016161616161616202020202020202020202020202020202040404040404040405050505080100100100100
order12455101045102020225510102020204101010102020202020202044448882020404040404040404020202020202040404444204448
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11
χ31111111111111111111111111111111111-111-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1
χ5111111111111-1-11111111-1-1-1-1-11111111-11i−i1i−i-1-1iiii−i−i−i−i-1-1ii−i−i11i−ii−i1-1i−i-1
χ6111111111111-1-11111111-1-1-1-1-11111111-11−ii1−ii-1-1−i−i−i−iiiii-1-1−i−iii11−ii−ii1-1−ii-1
χ7111111111111-1-11111111-1-1-1-1-11111111-1-1i−i-1i−i-1-1iiii−i−i−i−i-1-1ii−i−i-1-1−ii−ii-11−ii1
χ8111111111111-1-11111111-1-1-1-1-11111111-1-1−ii-1−ii-1-1−i−i−i−iiiii-1-1−i−iii-1-1i−ii−i-11i−i1
χ91111111-11111111111-1-1111111-111-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1
χ101111111-11111111111-1-1111111-111-1-1-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1
χ111111111-11111111111-1-1111111-111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111
χ121111111-11111111111-1-1111111-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-11
χ131111111-11111-1-11111-1-11-1-1-1-1-1-111-1-1-1-111i−i-1−ii-1-1−i−i−i−iiiii11ii−i−i-1-1i−ii−i1-1−ii1
χ141111111-11111-1-11111-1-11-1-1-1-1-1-111-1-1-1-111−ii-1i−i-1-1iiii−i−i−i−i11−i−iii-1-1−ii−ii1-1i−i1
χ151111111-11111-1-11111-1-11-1-1-1-1-1-111-1-1-1-11-1i−i1−ii-1-1−i−i−i−iiiii11ii−i−i11−ii−ii-11i−i-1
χ161111111-11111-1-11111-1-11-1-1-1-1-1-111-1-1-1-11-1−ii1i−i-1-1iiii−i−i−i−i11−i−iii11i−ii−i-11−ii-1
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+52−1−52−1−522022022−1+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+52−1−5200000000000
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+52−1−52−1−5220-2-20-2-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521+521−521+5200000000000
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+52−1−52−1−52-202i−2i02i−2i1−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ141−521+52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ1400000000000
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+52−1−52−1−52-20−2i2i0−2i2i1−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ141−521+52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ1400000000000
χ21222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−52−1+52−1−521−521+5222−1+52−1−52−1+52−1−52-2−1+52−1−521−521−521+521+52-20220-2-2−1+52−1−521−521−521+521+521−521−521+521+521−521+52−1+52−1−52−1+52−1−5200000000000
χ22222−1+52−1−52−1+52−1−52-222−1+52−1−5222−1+52−1−52−1+52−1−521−521+5222−1+52−1−52−1+52−1−52-2−1+52−1−521−521−521+521+52-20-2-2022−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+5200000000000
χ23222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−52−1+52−1−521−521+522-21−521+521−521+52-2−1+52−1−521−521−521+521+52202i−2i0−2i2i1−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−1+52−1−52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ1400000000000
χ24222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-2−1+52−1−52−1+52−1−521−521+522-21−521+521−521+52-2−1+52−1−521−521−521+521+5220−2i2i02i−2i1−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1−52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ1400000000000
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+522022022−1−52−1+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+5200000000000
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+5220-2-20-2-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521−521+521−5200000000000
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+52-202i−2i02i−2i1+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ381+521−52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ3800000000000
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+52-20−2i2i0−2i2i1+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ381+521−52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ3800000000000
χ29222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+52−1−52−1+521+521−5222−1−52−1+52−1−52−1+52-2−1−52−1+521+521+521−521−52-20220-2-2−1−52−1+521+521+521−521−521+521+521−521−521+521−52−1−52−1+52−1−52−1+5200000000000
χ30222−1−52−1+52−1−52−1+52-222−1−52−1+5222−1−52−1+52−1−52−1+521+521−5222−1−52−1+52−1−52−1+52-2−1−52−1+521+521+521−521−52-20-2-2022−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−5200000000000
χ31222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521−522-21+521−521+521−52-2−1−52−1+521+521+521−521−52202i−2i0−2i2i1+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−1−52−1+52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ3800000000000
χ32222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521−522-21+521−521+521−52-2−1−52−1+521+521+521−521−5220−2i2i02i−2i1+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−1−52−1+52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ3800000000000
χ3322-22222022-2-222222200-2-222220-2-200000000000-2-2000000000000000022-2-200000
χ3422-22222022-2-222222200-2-222220-2-200000000000-2-20000000000000000-2-22200000
χ3522-22222022-2-2-2-2222200-22-2-2-2-20-2-2000000000002200000000000000002i−2i−2i2i00000
χ3622-22222022-2-2-2-2222200-22-2-2-2-20-2-200000000000220000000000000000−2i2i2i−2i00000
χ3744444444-1-14400-1-1-1-144-100000-1-1-1-1-1-1-104004000000000000000000-1-10000-10000
χ3844444444-1-14400-1-1-1-144-100000-1-1-1-1-1-1-10-400-400000000000000000011000010000
χ394444444-4-1-14400-1-1-1-1-4-4-1000001-1-111110400-4000000000000000000110000-10000
χ404444444-4-1-14400-1-1-1-1-4-4-1000001-1-111110-4004000000000000000000-1-1000010000
χ4144-4−1+5−1−5−1+5−1−50441−51+544−1+5−1−5−1+5−1−500-4-4−1+5−1−5−1+5−1−501−51+5000000000001−51+50000000000000000000000000
χ4244-4−1+5−1−5−1+5−1−50441−51+5-4-4−1+5−1−5−1+5−1−500-441−51+51−51+501−51+500000000000−1+5−1−50000000000000000000000000
χ4344-4−1−5−1+5−1−5−1+50441+51−544−1−5−1+5−1−5−1+500-4-4−1−5−1+5−1−5−1+501+51−5000000000001+51−50000000000000000000000000
χ4444-4−1−5−1+5−1−5−1+50441+51−5-4-4−1−5−1+5−1−5−1+500-441+51−51+51−501+51−500000000000−1−5−1+50000000000000000000000000
χ454-4044-4-404-4004-444-4-40000-4-44400000000000000000000000000000000000000000
χ464-4044-4-404-400-4444-4-4000044-4-400000000000000000000000000000000000000000
χ474-40−1+5−1−51−51+504-4004-4−1+5−1−51−51+500001−51+5−1+5−1−50000000000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ3900000000000000000
χ484-40−1+5−1−51−51+504-4004-4−1+5−1−51−51+500001−51+5−1+5−1−50000000000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ3900000000000000000
χ494-40−1+5−1−51−51+504-400-44−1+5−1−51−51+50000−1+5−1−51−51+50000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ3900000000000000000
χ504-40−1+5−1−51−51+504-400-44−1+5−1−51−51+50000−1+5−1−51−51+50000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ3900000000000000000
χ514-40−1−5−1+51+51−504-4004-4−1−5−1+51+51−500001+51−5−1−5−1+50000000000000000−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+ζ3700000000000000000
χ524-40−1−5−1+51+51−504-4004-4−1−5−1+51+51−500001+51−5−1−5−1+50000000000000000ζ21−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−ζ3700000000000000000
χ534-40−1−5−1+51+51−504-400-44−1−5−1+51+51−50000−1−5−1+51+51−50000000000000000−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−ζ3700000000000000000
χ544-40−1−5−1+51+51−504-400-44−1−5−1+51+51−50000−1−5−1+51+51−50000000000000000ζ21−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+ζ3700000000000000000
χ55888−2+25−2−25−2+25−2−258-2-2−2+25−2−25001−521+521−521+52−2+25−2−25-200000-21−521+521−521−521+521+520000000000000000000000000000000000
χ56888−2+25−2−25−2+25−2−25-8-2-2−2+25−2−25001−521+521−521+522−252+25-20000021−521+52−1+52−1+52−1−52−1−520000000000000000000000000000000000
χ57888−2−25−2+25−2−25−2+258-2-2−2−25−2+25001+521−521+521−52−2−25−2+25-200000-21+521−521+521+521−521−520000000000000000000000000000000000
χ58888−2−25−2+25−2−25−2+25-8-2-2−2−25−2+25001+521−521+521−522+252−25-20000021+521−52−1−52−1−52−1+52−1+520000000000000000000000000000000000
χ5988-888880-2-2-8-800-2-2-2-20020000002200000000000000000000000000000000000000
χ6088-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+521−521+52002000000−1+52−1−52−2ζ4−ζ12+ζ28+2ζ362ζ4+ζ12−ζ28−2ζ36−ζ4+2ζ12−2ζ28+ζ36ζ4−2ζ12+2ζ28−ζ360000000000000000000000000000000000
χ6188-8−2+25−2−25−2+25−2−250-2-22−252+25001−521+521−521+52002000000−1+52−1−522ζ4+ζ12−ζ28−2ζ36−2ζ4−ζ12+ζ28+2ζ36ζ4−2ζ12+2ζ28−ζ36−ζ4+2ζ12−2ζ28+ζ360000000000000000000000000000000000
χ6288-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−521+521−52002000000−1−52−1+52−ζ4+2ζ12−2ζ28+ζ36ζ4−2ζ12+2ζ28−ζ362ζ4+ζ12−ζ28−2ζ36−2ζ4−ζ12+ζ28+2ζ360000000000000000000000000000000000
χ6388-8−2−25−2+25−2−25−2+250-2-22+252−25001+521−521+521−52002000000−1−52−1+52ζ4−2ζ12+2ζ28−ζ36−ζ4+2ζ12−2ζ28+ζ36−2ζ4−ζ12+ζ28+2ζ362ζ4+ζ12−ζ28−2ζ360000000000000000000000000000000000
χ648-8088-8-80-220000-2-2220000000000000000000000000000000000000010−10000000000
χ658-8088-8-80-220000-2-22200000000000000000000000000000000000000−1010000000000
χ6616-160−4+45−4−454−454+450-4400001−51+5−1+5−1−50000000000000000000000000000000000000000000000000
χ6716-160−4−45−4+454+454−450-4400001+51−5−1−5−1+50000000000000000000000000000000000000000000000000

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