Finite Group Databasebeta

← Group #14513614

Character table — Group #14513614

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size112222244466888810101212121212121216161616162024242424242424242430303232323232323248484848484860606060608080120120160
order12455101022020243610108844410102020121515303044882020202020208863030303060602020404040402248824242812
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-11111111111-1-1-111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-11-111-1-11
χ31111111111111111-1-1111111111111-1111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111-1-11-1-1111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-111-11-1-111-1
χ51111111-1111111-1-111-111111111111-1-11-1-1-1111111-1-1-1-1-111-1-111-1-1-1111111-1-1-1
χ61111111-1111111-1-111-1-1-1111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-11111-1
χ71111111-1111111-1-1-1-1-1111111111111-11-1-1-11111-1-1-1-1-1-1-111-1-111-1-11-1-1-1-1-1-1111
χ81111111-1111111-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-111-1-1-1-1-11111-1-111111-11-1-1-1-11
χ9222222222222-1-122222002222-1-1-1-1-1200022000000-1-1-1-1-1-1-100000020020-1-100-1
χ10222222222222-1-122-2-22002222-1-1-1-1-1-200022000000-1-1-1-1-1-1-1000000-200-2011001
χ112222222-22222-1-1-2-222-2002222-1-1-1-1-1-2000-2-200000011111-1-1000000-20020-1-1001
χ122222222-22222-1-1-2-2-2-2-2002222-1-1-1-1-12000-2-200000011111-1-1000000200-201100-1
χ13222−1−52−1+52−1−52−1+522−1−52−1+522222−1−52−1+5200222−1−52−1+52−1−52−1+522−1−52−1+52−1−52−1+520222−1−52−1+52−1−52−1−52−1+52−1+52002−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ14222−1−52−1+52−1−52−1+522−1−52−1+522222−1−52−1+52002-2-2−1−52−1+52−1−52−1+522−1−52−1+52−1−52−1+520-2-2-2−1−52−1+521+521+521−521−52002−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−521+521−520000000000
χ15222−1−52−1+52−1−52−1+52-2−1−52−1+5222221+521−5200-222−1−52−1+52−1−52−1+522−1−52−1+52−1−52−1+520-22-21+521−52−1−52−1−52−1+52−1+5200-21+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−520000000000
χ16222−1−52−1+52−1−52−1+52-2−1−52−1+5222221+521−5200-2-2-2−1−52−1+52−1−52−1+522−1−52−1+52−1−52−1+5202-221+521−521+521+521−521−5200-21+521+521−521−52−1−52−1+52−1−52−1+521+521−52−1−52−1+520000000000
χ17222−1+52−1−52−1+52−1−522−1+52−1−522222−1+52−1−5200222−1+52−1−52−1+52−1−522−1+52−1−52−1+52−1−520222−1+52−1−52−1+52−1+52−1−52−1−52002−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ18222−1+52−1−52−1+52−1−522−1+52−1−522222−1+52−1−52002-2-2−1+52−1−52−1+52−1−522−1+52−1−52−1+52−1−520-2-2-2−1+52−1−521−521−521+521+52002−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+521−521+520000000000
χ19222−1+52−1−52−1+52−1−52-2−1+52−1−5222221−521+5200-222−1+52−1−52−1+52−1−522−1+52−1−52−1+52−1−520-22-21−521+52−1+52−1+52−1−52−1−5200-21−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+520000000000
χ20222−1+52−1−52−1+52−1−52-2−1+52−1−5222221−521+5200-2-2-2−1+52−1−52−1+52−1−522−1+52−1−52−1+52−1−5202-221−521+521−521−521+521+5200-21−521−521+521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−520000000000
χ2122-222220-2-2-22220000000-2-222-2222200000000002200000-2-200000002-20-200000
χ2222-222220-2-2-22220000000-2-222-222220000000000-2-200000-2-20000000-220200000
χ233333333333-1-1003333-111-1-1-1-1000003-1-11-1-11111110000000-1-1-1-111-1-1-1-1100-110
χ243333333333-1-1003333-1-1-1-1-1-1-100000311-1-1-1-1-1-1-1-1-100000001111-1-1-111-1-1001-10
χ253333333333-1-10033-3-3-111-1-1-1-100000-3-1-11-1-11111-1-10000000-1-1-1-1111111-1001-10
χ263333333333-1-10033-3-3-1-1-1-1-1-1-100000-311-1-1-1-1-1-1-11100000001111-1-11-1-11100-110
χ273333333-333-1-100-3-333111-1-1-1-100000-31-1-111111111000000011-1-1-1-11-1-1-11001-10
χ283333333-333-1-100-3-3331-1-1-1-1-1-100000-3-11111-1-1-1-1-1-10000000-1-11111111-1-100-110
χ293333333-333-1-100-3-3-3-3111-1-1-1-10000031-1-1111111-1-1000000011-1-1-1-1-1111-100-110
χ303333333-333-1-100-3-3-3-31-1-1-1-1-1-1000003-11111-1-1-1-1110000000-1-11111-1-1-111001-10
χ31444−1−5−1+5−1−5−1+54−1−5−1+544-2-2−1−5−1+500400−1−5−1+5−1−5−1+5-21+521−521+521−520000−1−5−1+5000000-21+521+521−521−521+521−520000000000000000
χ32444−1−5−1+5−1−5−1+5-4−1−5−1+544-2-21+51−500-400−1−5−1+5−1−5−1+5-21+521−521+521−5200001+51−50000002−1−52−1−52−1+52−1+521+521−520000000000000000
χ33444−1+5−1−5−1+5−1−54−1+5−1−544-2-2−1+5−1−500400−1+5−1−5−1+5−1−5-21−521+521−521+520000−1+5−1−5000000-21−521−521+521+521−521+520000000000000000
χ34444−1+5−1−5−1+5−1−5-4−1+5−1−544-2-21−51+500-400−1+5−1−5−1+5−1−5-21−521+521−521+5200001−51+50000002−1+52−1+52−1−52−1−521−521+520000000000000000
χ3544-444440-4-4-44-2-20000000-4-4442-2-2-2-200000000000000000220000000000000000
χ3644-4−1−5−1+5−1−5−1+501+51−5-444400000001+51−5−1−5−1+5-4−1−5−1+5−1−5−1+5000000000000000001+51−50000000000000000
χ3744-4−1−5−1+5−1−5−1+501+51−5-44-2-200000001+51−5−1−5−1+521+521−521+521−520000000000000ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−1−52−1+520000000000000000
χ3844-4−1−5−1+5−1−5−1+501+51−5-44-2-200000001+51−5−1−5−1+521+521−521+521−520000000000000−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116−1−52−1+520000000000000000
χ3944-4−1+5−1−5−1+5−1−501−51+5-444400000001−51+5−1+5−1−5-4−1+5−1−5−1+5−1−5000000000000000001−51+50000000000000000
χ4044-4−1+5−1−5−1+5−1−501−51+5-44-2-200000001−51+5−1+5−1−521−521+521−521+520000000000000−ζ4+ζ44+ζ76−ζ116ζ4−ζ44−ζ76+ζ116−ζ28+ζ52+ζ68−ζ92ζ28−ζ52−ζ68+ζ92−1+52−1−520000000000000000
χ4144-4−1+5−1−5−1+5−1−501−51+5-44-2-200000001−51+5−1+5−1−521−521+521−521+520000000000000ζ4−ζ44−ζ76+ζ116−ζ4+ζ44+ζ76−ζ116ζ28−ζ52−ζ68+ζ92−ζ28+ζ52+ζ68−ζ92−1+52−1−520000000000000000
χ424-4044-4-400000-2200−2i22i202-200000-2-2220000002-22-2−2i22i2000000000000000000−i2i2000
χ434-4044-4-400000-2200−2i22i20-2200000-2-222000000-22-222i2−2i2000000000000000000−i2i2000
χ444-4044-4-400000-22002i2−2i202-200000-2-2220000002-22-22i2−2i2000000000000000000i2−i2000
χ454-4044-4-400000-22002i2−2i20-2200000-2-222000000-22-22−2i22i2000000000000000000i2−i2000
χ46666−3−352−3+352−3−352−3+3526−3−352−3+352-2-200−3−352−3+35200-2221+521−521+521−52000000-2-221+521−52−1−52−1−52−1+52−1+520000000001+521−521+521−52−1−52−1+520000000000
χ47666−3−352−3+352−3−352−3+3526−3−352−3+352-2-200−3−352−3+35200-2-2-21+521−521+521−5200000022-21+521−521+521+521−521−52000000000−1−52−1+52−1−52−1+521+521−520000000000
χ48666−3−352−3+352−3−352−3+352-6−3−352−3+352-2-2003+3523−352002221+521−521+521−520000002-2-2−1−52−1+52−1−52−1−52−1+52−1+52000000000−1−52−1+521+521−521+521−520000000000
χ49666−3−352−3+352−3−352−3+352-6−3−352−3+352-2-2003+3523−352002-2-21+521−521+521−52000000-222−1−52−1+521+521+521−521−520000000001+521−52−1−52−1+52−1−52−1+520000000000
χ50666−3+352−3−352−3+352−3−3526−3+352−3−352-2-200−3+352−3−35200-2221−521+521−521+52000000-2-221−521+52−1+52−1+52−1−52−1−520000000001−521+521−521+52−1+52−1−520000000000
χ51666−3+352−3−352−3+352−3−3526−3+352−3−352-2-200−3+352−3−35200-2-2-21−521+521−521+5200000022-21−521+521−521−521+521+52000000000−1+52−1−52−1+52−1−521−521+520000000000
χ52666−3+352−3−352−3+352−3−352-6−3+352−3−352-2-2003−3523+352002221−521+521−521+520000002-2-2−1+52−1−52−1+52−1+52−1−52−1−52000000000−1+52−1−521−521+521−521+520000000000
χ53666−3+352−3−352−3+352−3−352-6−3+352−3−352-2-2003−3523+352002-2-21−521+521−521+52000000-222−1+52−1−521−521−521+521+520000000001−521+52−1+52−1−52−1+52−1−520000000000
χ5466-666660-6-62-200000000022-2-20000000000000002200000000000000-220-200000
χ5566-666660-6-62-200000000022-2-2000000000000000-2-2000000000000002-20200000
χ568-8088-8-8000002-200−4i24i20000000022-2-2000000000000000000000000000000i2−i2000
χ578-8088-8-8000002-2004i2−4i20000000022-2-2000000000000000000000000000000−i2i2000
χ588-80−2−25−2+252+252−2500000-44000004-4000001+51−5−1−5−1+5000000−1−51+5−1+51−50000000000000000000000000
χ598-80−2−25−2+252+252−2500000-4400000-44000001+51−5−1−5−1+50000001+5−1−51−5−1+50000000000000000000000000
χ608-80−2+25−2−252−252+2500000-44000004-4000001−51+5−1+5−1−5000000−1+51−5−1−51+50000000000000000000000000
χ618-80−2+25−2−252−252+2500000-4400000-44000001−51+5−1+5−1−50000001−5−1+51+5−1−50000000000000000000000000
χ621212-12−3−35−3+35−3−35−3+3503+353−354-4000000000−1−5−1+51+51−50000000000000000000000000000000000000000
χ631212-12−3+35−3−35−3+35−3−3503−353+354-4000000000−1+5−1−51−51+50000000000000000000000000000000000000000
χ6416-160−4−45−4+454+454−45000004-4000000000000−1−5−1+51+51−500000000000000000000000000000000000
χ6516-160−4+45−4−454−454+45000004-4000000000000−1+5−1−51−51+500000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.