Finite Group Databasebeta

← Group #14268438

Character table — Group #14268438

Order 1800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size12244488888888888888888888888888254545505075757575100150150150150180180
order133355551515151515151515151515151515151515151515151515152226644446121212121010
χ1111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-11-1-1-1-111
χ3111111111111111111111111111111111-1-11111-1-1111-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-1111-1-111-1-1
χ511111111111111111111111111111111-11-1-1-1i−ii−i-1i−ii−i1-1
χ611111111111111111111111111111111-11-1-1-1−ii−ii-1−ii−ii1-1
χ711111111111111111111111111111111-1-11-1-1i−i−ii-1i−i−ii-11
χ811111111111111111111111111111111-1-11-1-1−iii−i-1−iii−i-11
χ922-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-10022-100-1-100
χ1022-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-100-2-2-1001100
χ1122-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-200-21002i−2i100−ii00
χ1222-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-200-2100−2i2i100i−i00
χ132-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-122200-1-1-10000
χ142-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-12-2-200-1110000
χ152-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2001-22i−2i001−ii0000
χ162-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2001-2−2i2i001i−i0000
χ1744444-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1004000000000000-1
χ1844444-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-40000000000001
χ194444-14-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-104000000000000-10
χ204444-14-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-400000000000010
χ214-2-214444-2-2-2-21111-2-2-2-2-2-2-2-211111111400-2-200001000000
χ224-2-214444-2-2-2-21111-2-2-2-2-2-2-2-211111111-400220000-1000000
χ238888-2-23-2-2-2-2-2-2-2-2-233-2-233-2-23333-2-2-2-20000000000000000
χ248888-2-2-23-2-2-2-2-2-2-2-2-2-233-2-233-2-2-2-233330000000000000000
χ2588-4-48-2-2-28-2-41-4-411-2-2-2-21111111111110000000000000000
χ2688-4-4-28-2-2-281-411-4-4-2-2-2-21111111111110000000000000000
χ2788-4-4-2-23-2-2-211111133-2-2−3−5i32−3+5i3211−3−5i32−3−5i32−3+5i32−3+5i3211110000000000000000
χ2888-4-4-2-23-2-2-211111133-2-2−3+5i32−3−5i3211−3+5i32−3+5i32−3−5i32−3−5i3211110000000000000000
χ2988-4-4-2-2-23-2-2111111-2-23311−3−5i32−3+5i321111−3−5i32−3−5i32−3+5i32−3+5i320000000000000000
χ3088-4-4-2-2-23-2-2111111-2-23311−3+5i32−3−5i321111−3+5i32−3+5i32−3−5i32−3−5i320000000000000000
χ318-48-48-2-2-2-418-2-4-4111111-2-2-2-2111111110000000000000000
χ328-48-4-28-2-21-4-2811-4-41111-2-2-2-2111111110000000000000000
χ338-48-4-2-23-211-2-21111−3−i152−3+i1521−i151+i1533-2-2−3−i152−3+i152−3−i152−3+i1521−i151+i151−i151+i150000000000000000
χ348-48-4-2-23-211-2-21111−3+i152−3−i1521+i151−i1533-2-2−3+i152−3−i152−3+i152−3−i1521+i151−i151+i151−i150000000000000000
χ358-48-4-2-2-2311-2-211111−i151+i15−3+i152−3−i152-2-2331−i151+i151−i151+i15−3+i152−3−i152−3+i152−3−i1520000000000000000
χ368-48-4-2-2-2311-2-211111+i151−i15−3−i152−3+i152-2-2331+i151−i151+i151−i15−3−i152−3+i152−3−i152−3+i1520000000000000000
χ378-4-428-2-2-2-41-4122−1−352−1+35211111111−1−352−1+352−1+352−1−352−1−352−1+352−1+352−1−3520000000000000000
χ388-4-428-2-2-2-41-4122−1+352−1−35211111111−1+352−1−352−1−352−1+352−1+352−1−352−1−352−1+3520000000000000000
χ398-4-42-28-2-21-41-4−1−352−1+3522211111111−1−352−1+352−1+352−1−352−1+352−1−352−1−352−1+3520000000000000000
χ408-4-42-28-2-21-41-4−1+352−1−3522211111111−1+352−1−352−1−352−1+352−1−352−1+352−1+352−1−3520000000000000000
χ418-4-42-2-23-21111−1−352−1+352−1−352−1+352−3−i152−3+i1521−i151+i15−3−5i32−3+5i3211ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−1+i152−1−i152−1+i152−1−i1520000000000000000
χ428-4-42-2-23-21111−1−352−1+352−1−352−1+352−3+i152−3−i1521+i151−i15−3+5i32−3−5i3211−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−1−i152−1+i152−1−i152−1+i1520000000000000000
χ438-4-42-2-23-21111−1+352−1−352−1+352−1−352−3−i152−3+i1521−i151+i15−3+5i32−3−5i3211−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58−1+i152−1−i152−1+i152−1−i1520000000000000000
χ448-4-42-2-23-21111−1+352−1−352−1+352−1−352−3+i152−3−i1521+i151−i15−3−5i32−3+5i3211ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−1−i152−1+i152−1−i152−1+i1520000000000000000
χ458-4-42-2-2-231111−1−352−1+352−1+352−1−3521−i151+i15−3+i152−3−i15211−3−5i32−3+5i32−1+i152−1−i152−1+i152−1−i152ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ460000000000000000
χ468-4-42-2-2-231111−1−352−1+352−1+352−1−3521+i151−i15−3−i152−3+i15211−3+5i32−3−5i32−1−i152−1+i152−1−i152−1+i152−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ580000000000000000
χ478-4-42-2-2-231111−1+352−1−352−1−352−1+3521−i151+i15−3+i152−3−i15211−3+5i32−3−5i32−1+i152−1−i152−1+i152−1−i152−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ580000000000000000
χ488-4-42-2-2-231111−1+352−1−352−1−352−1+3521+i151−i15−3−i152−3+i15211−3−5i32−3+5i32−1−i152−1+i152−1−i152−1+i152ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ580000000000000000

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