Finite Group Databasebeta

← Group #11762163

Character table — Group #11762163

Order 1080.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1222444444445888888888888910101018202020202036363645454545459090909090
order133333333515152151515151515151515151515266666666610303024444612121212
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11-1-1-1-1
χ31111111111111111111111111-1111-111111-1-1-1-111-1-1-111-1-1
χ41111111111111111111111111-1111-111111-1-1-1-1-1-111-1-1-111
χ5111111111111-11111111111111-1-1-11-1-1-1-1-1111-1i−ii−i-1i−ii−i
χ6111111111111-11111111111111-1-1-11-1-1-1-1-1111-1−ii−ii-1−ii−ii
χ7111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11i−i−ii1i−i−ii
χ8111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11−iii−i1−iii−i
χ9222-12-1-1-1-12-1-122222-1-1-1-1-1-1-1-12-122-12-1-1-1-12-1-120000-10000
χ10222-12-1-1-1-12-1-122222-1-1-1-1-1-1-1-1-2-12212-1-1-1-1-211-2000010000
χ11222-12-1-1-1-12-1-1-22222-1-1-1-1-1-1-1-121-2-2-1-211112-1-1-2000010000
χ12222-12-1-1-1-12-1-1-22222-1-1-1-1-1-1-1-1-21-2-21-21111-21120000-10000
χ1322-12-12-1-1-122222-1-1-122-1-1-1-1-1-1022-10-12-1-1-100000022000-1-1
χ1422-12-12-1-1-122222-1-1-122-1-1-1-1-1-1022-10-12-1-1-1000000-2-200011
χ1522-12-12-1-1-1222-22-1-1-122-1-1-1-1-1-10-2-2101-21110000002i−2i000−ii
χ1622-12-12-1-1-1222-22-1-1-122-1-1-1-1-1-10-2-2101-2111000000−2i2i000i−i
χ172-122-1-12-1-12222-12-1-1-1-122-1-1-1-102-120-1-12-1-1000022000-1-100
χ182-122-1-12-1-12222-12-1-1-1-122-1-1-1-102-120-1-12-1-10000-2-20001100
χ192-122-1-12-1-1222-2-12-1-1-1-122-1-1-1-10-21-2011-21100002i−2i000−ii00
χ202-122-1-12-1-1222-2-12-1-1-1-122-1-1-1-10-21-2011-2110000−2i2i000i−i00
χ21444444444-1-1-10-1-1-1-1-1-1-1-1-1-1-1-14000400000-1-1-10000000000
χ22444444444-1-1-10-1-1-1-1-1-1-1-1-1-1-1-1-4000-4000001110000000000
χ23444-24-2-2-2-2-11−i1521+i1520-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1524000-200000-11−i1521+i1520000000000
χ24444-24-2-2-2-2-11−i1521+i1520-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-40002000001−1+i152−1−i1520000000000
χ25444-24-2-2-2-2-11+i1521−i1520-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1524000-200000-11+i1521−i1520000000000
χ26444-24-2-2-2-2-11+i1521−i1520-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-40002000001−1−i152−1+i1520000000000
χ2744-2-2-2-21114-2-244-2-2-2-2-21111110-24-20-2-21110000000000000
χ2844-2-2-2-21114-2-2-44-2-2-2-2-211111102-42022-1-1-10000000000000
χ294-24-2-21-2114-2-24-24-2-211-2-211110-2-240-21-2110000000000000
χ304-24-2-21-2114-2-2-4-24-2-211-2-21111022-402-12-1-10000000000000
χ314-2-241-2-2114444-2-211-2-2-2-2111104-2-201-2-2110000000000000
χ324-2-241-2-211444-4-2-211-2-2-2-211110-4220-122-1-10000000000000
χ334-2-2-2111−1−3i32−1+3i324-2-24-2-2111111−1−3i32−1+3i32−1−3i32−1+3i320-2-2-20111−1−3i32−1+3i320000000000000
χ344-2-2-2111−1−3i32−1+3i324-2-2-4-2-2111111−1−3i32−1+3i32−1−3i32−1+3i3202220-1-1-11+3i321−3i320000000000000
χ354-2-2-2111−1+3i32−1−3i324-2-24-2-2111111−1+3i32−1−3i32−1+3i32−1−3i320-2-2-20111−1+3i32−1−3i320000000000000
χ364-2-2-2111−1+3i32−1−3i324-2-2-4-2-2111111−1+3i32−1−3i32−1+3i32−1−3i3202220-1-1-11−3i321+3i320000000000000
χ3788-48-48-4-4-4-2-2-20-2111-2-211111100000000000000000000000
χ3888-4-4-4-4222-21−i151+i150-21111−i151+i15−1+i152−1−i152−1+i152−1+i152−1−i152−1−i15200000000000000000000000
χ3988-4-4-4-4222-21+i151−i150-21111+i151−i15−1−i152−1+i152−1−i152−1−i152−1+i152−1+i15200000000000000000000000
χ408-488-4-48-4-4-2-2-201-21111-2-2111100000000000000000000000
χ418-48-4-42-422-21−i151+i1501-211−1+i152−1−i1521−i151+i15−1+i152−1+i152−1−i152−1−i15200000000000000000000000
χ428-48-4-42-422-21+i151−i1501-211−1−i152−1+i1521+i151−i15−1−i152−1−i152−1+i152−1+i15200000000000000000000000
χ438-4-482-4-422-2-2-2011−1−352−1+3521111−1−352−1+352−1+352−1−35200000000000000000000000
χ448-4-482-4-422-2-2-2011−1+352−1−3521111−1+352−1−352−1−352−1+35200000000000000000000000
χ458-4-4-4222−1−3i3−1+3i3-21−i151+i15011−1+352−1−352−1+i152−1−i152−1+i152−1−i152ζ14−2ζ22+ζ26−2ζ58−2ζ14+ζ22−2ζ26+ζ58ζ2−2ζ34+ζ38−2ζ46−2ζ2+ζ34−2ζ38+ζ4600000000000000000000000
χ468-4-4-4222−1−3i3−1+3i3-21+i151−i15011−1−352−1+352−1−i152−1+i152−1−i152−1+i152ζ2−2ζ34+ζ38−2ζ46−2ζ2+ζ34−2ζ38+ζ46ζ14−2ζ22+ζ26−2ζ58−2ζ14+ζ22−2ζ26+ζ5800000000000000000000000
χ478-4-4-4222−1+3i3−1−3i3-21−i151+i15011−1−352−1+352−1+i152−1−i152−1+i152−1−i152−2ζ14+ζ22−2ζ26+ζ58ζ14−2ζ22+ζ26−2ζ58−2ζ2+ζ34−2ζ38+ζ46ζ2−2ζ34+ζ38−2ζ4600000000000000000000000
χ488-4-4-4222−1+3i3−1−3i3-21+i151−i15011−1+352−1−352−1−i152−1+i152−1−i152−1+i152−2ζ2+ζ34−2ζ38+ζ46ζ2−2ζ34+ζ38−2ζ46−2ζ14+ζ22−2ζ26+ζ58ζ14−2ζ22+ζ26−2ζ5800000000000000000000000

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