Finite Group Databasebeta

← Group #14278035

Character table — Group #14278035

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222222444444444444448888888888888888888881616161616161616161616161616162020202040404040808080120120120120120120120120
order12234466651010101212151530303030303082020242440404040606060601201201201201201201201202661010101030303030303030302488612242441212888816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iii
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i
χ922222222222222222222222-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000022-2-222-2-200000000000
χ1022222222222222222222222-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000-2-222-2-22200000000000
χ112222-2-22222222-2-2222222220-2-2000000-2-2-2-2000000000000000000000002-2002-2000000000−i2i2−i2i2
χ122222-2-22222222-2-2222222220-2-2000000-2-2-2-2000000000000000000000002-2002-2000000000i2−i2i2−i2
χ132222-2-22222222-2-2222222220-2-2000000-2-2-2-200000000000000000000000-2200-220000000002−2−22
χ142222-2-22222222-2-2222222220-2-2000000-2-2-2-200000000000000000000000-2200-22000000000−222−2
χ15222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12-1-100000000
χ16222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-21100000000
χ17222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-2-2-2111111112222-1-1-1-1-21100000000
χ18222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-2-2-211111111-2-2-2-211112-1-100000000
χ19222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-22211-2-2-2-2-1-1-1-1111111110−i3i30000−i3−i3−i3−i3i3i3i3i322-2-2-1-1110−i3i300000000
χ20222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-22211-2-2-2-2-1-1-1-1111111110−i3i30000−i3−i3−i3−i3i3i3i3i3-2-22211-1-10i3−i300000000
χ21222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-22211-2-2-2-2-1-1-1-1111111110i3−i30000i3i3i3i3−i3−i3−i3−i322-2-2-1-1110i3−i300000000
χ22222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-22211-2-2-2-2-1-1-1-1111111110i3−i30000i3i3i3i3−i3−i3−i3−i3-2-22211-1-10−i3i300000000
χ2322-222-22-2-22-2-222-222-2-2-2-22202-200000022-2-200000000000000000000000002i−2i002i−2i0001+i−1−i1−i−1+i0000
χ2422-222-22-2-22-2-222-222-2-2-2-22202-200000022-2-200000000000000000000000002i−2i002i−2i000−1−i1+i−1+i1−i0000
χ2522-222-22-2-22-2-222-222-2-2-2-22202-200000022-2-20000000000000000000000000−2i2i00−2i2i0001−i−1+i1+i−1−i0000
χ2622-222-22-2-22-2-222-222-2-2-2-22202-200000022-2-20000000000000000000000000−2i2i00−2i2i000−1+i1−i−1−i1+i0000
χ27444444444-1-1-1-144-1-1-1-1-1-1-1-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000
χ28444444444-1-1-1-144-1-1-1-1-1-1-1-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-41111111111110000000000000000000
χ29444444444-1-1-1-144-1-1-1-1-1-1-1-1-4-1-1-4-41111-1-1-1-111111111000−5−555−5−555−5−5550000000000000000000
χ30444444444-1-1-1-144-1-1-1-1-1-1-1-1-4-1-1-4-41111-1-1-1-11111111100055−5−555−5−555−5−50000000000000000000
χ31444-244-2-2-2-1-1-1-1-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1524-1-1-2-2-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1524-2-2-1-1-1-11−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1520000000000000000000
χ32444-244-2-2-2-1-1-1-1-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1524-1-1-2-2-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i152-4221111−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i1520000000000000000000
χ33444-244-2-2-2-1-1-1-1-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152-4-1-12211111−i1521+i1521−i1521+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1520−2i32i355−5−5ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ1160000000000000000000
χ34444-244-2-2-2-1-1-1-1-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i152-4-1-12211111−i1521+i1521−i1521+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i15202i3−2i3−5−555−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ1160000000000000000000
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χ36444-244-2-2-2-1-1-1-1-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1524-1-1-2-2-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i152-4221111−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i1520000000000000000000
χ37444-244-2-2-2-1-1-1-1-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152-4-1-12211111+i1521−i1521+i1521−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1520−2i32i3−5−555ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ920000000000000000000
χ38444-244-2-2-2-1-1-1-1-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i152-4-1-12211111+i1521−i1521+i1521−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i15202i3−2i355−5−5−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ920000000000000000000
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χ40444-2-4-4-2-2-2444422-2-2-2-2-2-2-2-20-4-4000000222200000000000000000000000-44002-20000000000000
χ4144-44-444-4-44-4-44-4444-4-4-4-4440-44000000-4-444000000000000000000000000000000000000000000
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χ4344-44-444-4-4-111-1-44-1-11111-1-101-100−5−55511-1-1−5−555−5−555000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ1160000000000000000000
χ4444-44-444-4-4-111-1-44-1-11111-1-101-10055−5−511-1-155−5−555−5−5000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1160000000000000000000
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χ4744-4-24-4-2224-4-44-22-2-22222-2-204-4000000-2-2220000000000000000000000000−4i4i002i−2i00000000000
χ4844-4-2-44-2224-4-442-2-2-22222-2-20-44−2i32i3000022-2-2−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000
χ4944-4-2-44-2224-4-442-2-2-22222-2-20-442i3−2i3000022-2-22i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000
χ5044-4-2-44-222-111-12-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15201-1−2i32i355−5−5−1+i152−1−i1521−i1521+i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116ζ4−ζ68−ζ76+ζ92−ζ4+ζ68+ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ28+ζ44+ζ52−ζ116ζ28−ζ44−ζ52+ζ1160000000000000000000
χ5144-4-2-44-222-111-12-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15201-1−2i32i355−5−5−1+i152−1−i1521−i1521+i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ1160000000000000000000
χ5244-4-2-44-222-111-12-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15201-12i3−2i3−5−555−1+i152−1−i1521−i1521+i152−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ1160000000000000000000
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χ5444-4-2-44-222-111-12-21+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i15201-1−2i32i3−5−555−1−i152−1+i1521+i1521−i152ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92−ζ28−ζ44+ζ52+ζ116ζ28+ζ44−ζ52−ζ116ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ116−ζ4−ζ68+ζ76+ζ92ζ4+ζ68−ζ76−ζ920000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.