Finite Group Databasebeta

← Group #14511611

Character table — Group #14511611

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size1122223366661212121212122020242424242424242424242424242432324848484864646464120120120120120160160
order125510102210101010442020202044248820204040404040404040361010202015153030244881212
χ1111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111
χ3111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1
χ4111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-11111-1-1
χ52222222222222222222200002200000000-1-10000-1-1-1-120000-1-1
χ6222222222222222222-2-200002200000000-1-10000-1-1-1-1-2000011
χ722−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52002222−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000
χ822−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−5200-2-2-2-2−1+52−1−521−521−521−521−521+521+521+521+52221−521+521−521+52−1+52−1−52−1+52−1−520000000
χ922−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52002222−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000
χ1022−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+5200-2-2-2-2−1−52−1+521+521+521+521+521−521−521−521−52221+521−521+521−52−1−52−1+52−1−52−1+520000000
χ112-222-2-22-22-22-20000002i−2i00i2−i200i2i2−i2−i2i2i2−i2−i2-110000-1-1110002−2i−i
χ122-222-2-22-22-22-20000002i−2i00−i2i200−i2−i2i2i2−i2−i2i2i2-110000-1-111000−22i−i
χ132-222-2-22-22-22-2000000−2i2i00i2−i200i2i2−i2−i2i2i2−i2−i2-110000-1-111000−22−ii
χ142-222-2-22-22-22-2000000−2i2i00−i2i200−i2−i2i2i2−i2−i2i2i2-110000-1-1110002−2−ii
χ15333333333333-1-1-1-1-1-13311-1-1-1-1-1-1-1-1-1-1-1-10011110000-111-1-100
χ16333333333333-1-1-1-1-1-133-1-111-1-11111111100-1-1-1-10000-1-1-11100
χ17333333333333-1-1-1-1-1-1-3-311-1-1-1-1-1-1-1-1-1-1-1-100111100001-1-11100
χ18333333333333-1-1-1-1-1-1-3-3-1-111-1-11111111100-1-1-1-10000111-1-100
χ1944−1+5−1−5−1+5−1−544−1+5−1+5−1−5−1−544−1+5−1+5−1−5−1−5000000−1+5−1−500000000-2-200001−521+521−521+520000000
χ2044−1−5−1+5−1−5−1+544−1−5−1−5−1+5−1+544−1−5−1−5−1+5−1+5000000−1−5−1+500000000-2-200001+521−521+521−520000000
χ214-444-4-44-44-44-40000004i−4i000000000000001-1000011-1-100000−ii
χ224-444-4-44-44-44-4000000−4i4i000000000000001-1000011-1-100000i−i
χ234-4−1+5−1−51−51+54-4−1+51−5−1−51+500000000002i2−2i200ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39-2200001−521+52−1+52−1−520000000
χ244-4−1+5−1−51−51+54-4−1+51−5−1−51+50000000000−2i22i200−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39-2200001−521+52−1+52−1−520000000
χ254-4−1−5−1+51+51−54-4−1−51+5−1+51−500000000002i2−2i200ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37-2200001+521−52−1−52−1+520000000
χ264-4−1−5−1+51+51−54-4−1−51+5−1+51−50000000000−2i22i200−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37-2200001+521−52−1−52−1+520000000
χ27666666-2-2-2-2-2-22-22222000000-2-200000000000000000002-20000
χ28666666-2-2-2-2-2-22-22222000000-2-20000000000000000000-220000
χ29666666-2-2-2-2-2-2-22-2-2-2-2002-20022000000000022-2-200000000000
χ30666666-2-2-2-2-2-2-22-2-2-2-200-2200220000000000-2-22200000000000
χ3166−3+352−3−352−3+352−3−35266−3+352−3+352−3−352−3−352-2-21−521−521+521+520022-2-21−521+521−521−521−521−521+521+521+521+5200−1+52−1−52−1+52−1−5200000000000
χ3266−3+352−3−352−3+352−3−35266−3+352−3+352−3−352−3−352-2-21−521−521+521+5200-2-2221−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52001−521+521−521+5200000000000
χ3366−3+352−3−352−3+352−3−352-2-21−521−521+521+52-22ζ12−2ζ22+ζ28+2ζ38ζ12+2ζ22+ζ28−2ζ38ζ4+2ζ6−2ζ14+ζ36ζ4−2ζ6+2ζ14+ζ36002-200−1+52−1−52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ1400−1+52−1−521−521+5200000000000
χ3466−3+352−3−352−3+352−3−352-2-21−521−521+521+52-22ζ12−2ζ22+ζ28+2ζ38ζ12+2ζ22+ζ28−2ζ38ζ4+2ζ6−2ζ14+ζ36ζ4−2ζ6+2ζ14+ζ3600-2200−1+52−1−52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14001−521+52−1+52−1−5200000000000
χ3566−3+352−3−352−3+352−3−352-2-21−521−521+521+52-22ζ12+2ζ22+ζ28−2ζ38ζ12−2ζ22+ζ28+2ζ38ζ4−2ζ6+2ζ14+ζ36ζ4+2ζ6−2ζ14+ζ36002-200−1+52−1−52ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ1400−1+52−1−521−521+5200000000000
χ3666−3+352−3−352−3+352−3−352-2-21−521−521+521+52-22ζ12+2ζ22+ζ28−2ζ38ζ12−2ζ22+ζ28+2ζ38ζ4−2ζ6+2ζ14+ζ36ζ4+2ζ6−2ζ14+ζ3600-2200−1+52−1−52−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14001−521+52−1+52−1−5200000000000
χ3766−3−352−3+352−3−352−3+35266−3−352−3−352−3+352−3+352-2-21+521+521−521−520022-2-21+521−521+521+521+521+521−521−521−521−5200−1−52−1+52−1−52−1+5200000000000
χ3866−3−352−3+352−3−352−3+35266−3−352−3−352−3+352−3+352-2-21+521+521−521−5200-2-2221+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52001+521−521+521−5200000000000
χ3966−3−352−3+352−3−352−3+352-2-21+521+521−521−52-22ζ4+2ζ6−2ζ14+ζ36ζ4−2ζ6+2ζ14+ζ36ζ12+2ζ22+ζ28−2ζ38ζ12−2ζ22+ζ28+2ζ38002-200−1−52−1+52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ3800−1−52−1+521+521−5200000000000
χ4066−3−352−3+352−3−352−3+352-2-21+521+521−521−52-22ζ4+2ζ6−2ζ14+ζ36ζ4−2ζ6+2ζ14+ζ36ζ12+2ζ22+ζ28−2ζ38ζ12−2ζ22+ζ28+2ζ3800-2200−1−52−1+52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ38001+521−52−1−52−1+5200000000000
χ4166−3−352−3+352−3−352−3+352-2-21+521+521−521−52-22ζ4−2ζ6+2ζ14+ζ36ζ4+2ζ6−2ζ14+ζ36ζ12−2ζ22+ζ28+2ζ38ζ12+2ζ22+ζ28−2ζ38002-200−1−52−1+52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ38−ζ22+ζ38ζ22−ζ3800−1−52−1+521+521−5200000000000
χ4266−3−352−3+352−3−352−3+352-2-21+521+521−521−52-22ζ4−2ζ6+2ζ14+ζ36ζ4+2ζ6−2ζ14+ζ36ζ12−2ζ22+ζ28+2ζ38ζ12+2ζ22+ζ28−2ζ3800-2200−1−52−1+52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ38ζ22−ζ38−ζ22+ζ38001+521−52−1−52−1+5200000000000
χ438-8−2+25−2−252−252+258-8−2+252−25−2−252+2500000000000000000000002-20000−1+52−1−521−521+520000000
χ448-8−2−25−2+252+252−258-8−2−252+25−2+252−2500000000000000000000002-20000−1−52−1+521+521−520000000
χ451212−3+35−3−35−3+35−3−35-4-41−51−51+51+54-4−1+5−1+5−1−5−1−50000001−51+50000000000000000000000000
χ461212−3−35−3+35−3−35−3+35-4-41+51+51−51−54-4−1−5−1−5−1+5−1+50000001+51−50000000000000000000000000
χ4712-121212-12-12-44-44-44000000000000000000000000000000000000000
χ4812-12−3+35−3−353−353+35-441−5−1+51+5−1−500000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ3900000000000000000
χ4912-12−3+35−3−353−353+35-441−5−1+51+5−1−500000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ3900000000000000000
χ5012-12−3−35−3+353+353−35-441+5−1−51−5−1+500000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ3700000000000000000
χ5112-12−3−35−3+353+353−35-441+5−1−51−5−1+500000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ3700000000000000000

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