Finite Group Databasebeta

← Group #14512491

Character table — Group #14512491

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11233444556888881012121215151616161616161620242424303232323232324040606060606060606060808080120120120120
order1242245104443620202024101044121212151530302202020260606060606012122444444446668888
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ311111111-1-1111111-1111-1-11111111-1111-1111111-1-1-1ii−i−iii−i−i-1-1-1i−ii−i
χ411111111-1-1111111-1111-1-11111111-1111-1111111-1-1-1−i−iii−i−iii-1-1-1−ii−ii
χ511111-111111111-1-11-111111-1-11111-11-1-1111-1-1-1-111-1111111111-1-1-1-1-1-1
χ611111-111111111-1-11-111111-1-11111-11-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-11111
χ711111-111-1-11111-1-1-1-111-1-11-1-1111111-1-1-111-1-1-1-1-1-11ii−i−iii−i−i-111−ii−ii
χ811111-111-1-11111-1-1-1-111-1-11-1-1111111-1-1-111-1-1-1-1-1-11−i−iii−i−iii-111i−ii−i
χ922222222222-1-1222222222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1200000000-1-1-10000
χ1022222222-2-22-1-1222-2222-2-2-1-1-1-1-1-1-1-2222-2-1-1-1-1-1-111-2000000001110000
χ1122222-222222-1-12-2-22-22222-111-1-1-1-1-22-2-22-1-11111-1-1-200000000-1110000
χ1222222-222-2-22-1-12-2-2-2-222-2-2-111-1-1-1-122-2-2-2-1-11111112000000001-1-10000
χ1322-22202222-222-200-202222-20022220-200-2-2-2000022000000000-2000000
χ1422-22202222-2-1-1-200-2022221−i3i3-1-1-1-10-200-211−i3−i3i3i3-1-10000000001−i3i30000
χ1522-22202222-2-1-1-200-2022221i3−i3-1-1-1-10-200-211i3i3−i3−i3-1-10000000001i3−i30000
χ1622-222022-2-2-222-2002022-2-2-20022220-2002-2-20000-2-20000000002000000
χ1722-222022-2-2-2-1-1-2002022-2-21−i3i3-1-1-1-10-200211−i3−i3i3i311000000000-1i3−i30000
χ1822-222022-2-2-2-1-1-2002022-2-21i3−i3-1-1-1-10-200211i3i3−i3−i311000000000-1−i3i30000
χ192-202-202-22i−2i02-2000002-22i−2i00022-2-2000000000002i−2i01+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000
χ202-202-202-22i−2i02-2000002-22i−2i00022-2-2000000000002i−2i0−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000
χ212-202-202-2−2i2i02-2000002-2−2i2i00022-2-200000000000−2i2i01−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000
χ222-202-202-2−2i2i02-2000002-2−2i2i00022-2-200000000000−2i2i0−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000
χ23333-1-133333-1003333-1-1-1-1-100000003-1-1-1-100000000-11111-1-1-1-100011-1-1
χ24333-1-133333-1003333-1-1-1-1-100000003-1-1-1-100000000-1-1-1-1-11111000-1-111
χ25333-1-1333-3-3-100333-3-1-1-1110000000-3-1-1-11000000001ii−i−i−i−iii000i−i−ii
χ26333-1-1333-3-3-100333-3-1-1-1110000000-3-1-1-11000000001−i−iiiii−i−i000−iii−i
χ27333-1-1-33333-1003-3-331-1-1-1-10000000-3-111-10000000011111-1-1-1-1000-1-111
χ28333-1-1-33333-1003-3-331-1-1-1-10000000-3-111-1000000001-1-1-1-1111100011-1-1
χ29333-1-1-333-3-3-1003-3-3-31-1-11100000003-111100000000-1ii−i−i−i−iii000−iii−i
χ30333-1-1-333-3-3-1003-3-3-31-1-11100000003-111100000000-1−i−iiiii−i−i000i−i−ii
χ31444444-1-100444-1-1-104-1-100444-1-1-1-10-1-1-10-1-1-1-1-1-1000000000000000000
χ32444444-1-1004-2-2-1-1-104-1-100-2-2-21−i1521+i1521−i1521+i1520-1-1-101−i1521+i1521−i1521+i1521−i1521+i152000000000000000000
χ33444444-1-1004-2-2-1-1-104-1-100-2-2-21+i1521−i1521+i1521−i1520-1-1-101+i1521−i1521+i1521−i1521+i1521−i152000000000000000000
χ3444444-4-1-100444-1110-4-1-1004-4-4-1-1-1-10-1110-1-11111000000000000000000
χ3544444-4-1-1004-2-2-1110-4-1-100-2221−i1521+i1521−i1521+i1520-11101−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000
χ3644444-4-1-1004-2-2-1110-4-1-100-2221+i1521−i1521+i1521−i1520-11101+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000
χ3744-4440-1-100-4441−5500-1-100-400-1-1-1-101−55011−555−5000000000000000000
χ3844-4440-1-100-44415−500-1-100-400-1-1-1-1015−50115−5−55000000000000000000
χ3944-4440-1-100-4-2-21−5500-1-1002−2i32i31+i1521−i1521+i1521−i15201−550−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58000000000000000000
χ4044-4440-1-100-4-2-21−5500-1-10022i3−2i31−i1521+i1521−i1521+i15201−550−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46000000000000000000
χ4144-4440-1-100-4-2-215−500-1-1002−2i32i31−i1521+i1521−i1521+i152015−50−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46000000000000000000
χ4244-4440-1-100-4-2-215−500-1-10022i3−2i31+i1521−i1521+i1521−i152015−50−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58000000000000000000
χ434-404-404-44i−4i0-22000004-44i−4i000-2-22200000000000−2i2i0000000000000000
χ444-404-404-4−4i4i0-22000004-4−4i4i000-2-222000000000002i−2i0000000000000000
χ4566-6-2-206666200-600-60-2-2-2-2000000002002000000000000000000000000
χ4666-6-2-2066-6-6200-60060-2-22200000000200-2000000000000000000000000
χ476-60-2206-66i−6i00000000-22−2i2i0000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000
χ486-60-2206-66i−6i00000000-22−2i2i000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000
χ496-60-2206-6−6i6i00000000-222i−2i0000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000
χ506-60-2206-6−6i6i00000000-222i−2i000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000
χ518-808-80-220008-800000-2200000-2-22200000000000000000000000000000
χ528-808-80-22000-4400000-22000001−i151+i15−1+i15−1−i1500000000000000000000000000000
χ538-808-80-22000-4400000-22000001+i151−i15−1−i15−1+i1500000000000000000000000000000
χ54121212-4-412-3-300-400-3-3-30-41100000000001110000000000000000000000000
χ55121212-4-4-12-3-300-400-333041100000000001-1-10000000000000000000000000
χ561212-12-4-40-3-3004003−353500110000000000-15−50000000000000000000000000
χ571212-12-4-40-3-300400335−3500110000000000-1−550000000000000000000000000
χ5824-240-880-6600000000002-200000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.