Finite Group Databasebeta

← Group #11772199

Character table — Group #11772199

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size11222448888888888888888991818181818181836363636363636367272727272727272
order124881616361212242424244848484848484848442888888441616161616161616161616161616
χ1111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111111111-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii
χ511111111111111111111111-1-1-1-1-1ii−i−ii−i-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ611111111111111111111111-1-1-1-1-1ii−i−ii−i-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ711111111111111111111111-1-1-1-1-1−i−iii−ii-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ811111111111111111111111-1-1-1-1-1−i−iii−ii-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ911111-1-111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11-11-11-11-1
χ1011111-1-111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-11-11-11-11
χ1111111-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ1211111-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ1311111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−i11−i−iiiζ2−ζ2−ζ2ζ2ζ6−ζ6−ζ6ζ6
χ1411111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−i11−i−iii−ζ2ζ2ζ2−ζ2−ζ6ζ6ζ6−ζ6
χ1511111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii11ii−i−iζ6−ζ6−ζ6ζ6ζ2−ζ2−ζ2ζ2
χ1611111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii11ii−i−i−ζ6ζ6ζ6−ζ6−ζ2ζ2ζ2−ζ2
χ17222-2-2002222-2-2-2-200000000222-2-22222-2-200000000000000
χ18222-2-2002222-2-2-2-200000000222-2-2-2-2-2-22200000000000000
χ19222-2-2002222-2-2-2-200000000-2-2-2222i2i−2i−2i−2i2i00000000000000
χ20222-2-2002222-2-2-2-200000000-2-2-222−2i−2i2i2i2i−2i00000000000000
χ2122-200i2−i222-2-20000i2i2i2i2−i2−i2−i2−i222-2002-22-200i2−i2i2−i2i2−i200000000
χ2222-200i2−i222-2-20000i2i2i2i2−i2−i2−i2−i222-200-22-2200i2−i2−i2i2−i2i200000000
χ2322-200i2−i222-2-20000i2i2i2i2−i2−i2−i2−i2-2-22002i−2i−2i2i00−i2i2−222−200000000
χ2422-200i2−i222-2-20000i2i2i2i2−i2−i2−i2−i2-2-2200−2i2i2i−2i00−i2i22−2−2200000000
χ2522-200−i2i222-2-20000−i2−i2−i2−i2i2i2i2i222-2002-22-200−i2i2−i2i2−i2i200000000
χ2622-200−i2i222-2-20000−i2−i2−i2−i2i2i2i2i222-200-22-2200−i2i2i2−i2i2−i200000000
χ2722-200−i2i222-2-20000−i2−i2−i2−i2i2i2i2i2-2-22002i−2i−2i2i00i2−i22−2−2200000000
χ2822-200−i2i222-2-20000−i2−i2−i2−i2i2i2i2i2-2-2200−2i2i2i−2i00i2−i2−222−200000000
χ294-402i2−2i2004-4002i22i2−2i2−2i2000000004i−4i022−2200000000000000000000
χ304-402i2−2i2004-4002i22i2−2i2−2i200000000−4i4i0−222200000000000000000000
χ314-40−2i22i2004-400−2i2−2i22i22i2000000004i−4i0−222200000000000000000000
χ324-40−2i22i2004-400−2i2−2i22i22i200000000−4i4i022−2200000000000000000000
χ338888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ3488888-8-8-1-1-1-1-1-1-1-1111111110000000000000000000000000
χ35888-8-800-1-1-1-111113i3i−3i−3i3i3i−3i−3i0000000000000000000000000
χ36888-8-800-1-1-1-11111−3i−3i3i3i−3i−3i3i3i0000000000000000000000000
χ3788-8004i2−4i2-1-1113i−3i3i−3iζ2−2ζ6ζ2−2ζ6−2ζ2+ζ6−2ζ2+ζ6−ζ2+2ζ6−ζ2+2ζ62ζ2−ζ62ζ2−ζ60000000000000000000000000
χ3888-8004i2−4i2-1-111−3i3i−3i3i−2ζ2+ζ6−2ζ2+ζ6ζ2−2ζ6ζ2−2ζ62ζ2−ζ62ζ2−ζ6−ζ2+2ζ6−ζ2+2ζ60000000000000000000000000
χ3988-800−4i24i2-1-1113i−3i3i−3i−ζ2+2ζ6−ζ2+2ζ62ζ2−ζ62ζ2−ζ6ζ2−2ζ6ζ2−2ζ6−2ζ2+ζ6−2ζ2+ζ60000000000000000000000000
χ4088-800−4i24i2-1-111−3i3i−3i3i2ζ2−ζ62ζ2−ζ6−ζ2+2ζ6−ζ2+2ζ6−2ζ2+ζ6−2ζ2+ζ6ζ2−2ζ6ζ2−2ζ60000000000000000000000000
χ418-804i2−4i200-113i−3iζ2−2ζ6−2ζ2+ζ6−ζ2+2ζ62ζ2−ζ63ζ−3ζ3ζ3−3ζ33ζ5−3ζ53ζ7−3ζ70000000000000000000000000
χ428-804i2−4i200-113i−3iζ2−2ζ6−2ζ2+ζ6−ζ2+2ζ62ζ2−ζ6−3ζ3ζ−3ζ33ζ3−3ζ53ζ5−3ζ73ζ70000000000000000000000000
χ438-804i2−4i200-11−3i3i−2ζ2+ζ6ζ2−2ζ62ζ2−ζ6−ζ2+2ζ63ζ3−3ζ3−3ζ3ζ−3ζ73ζ73ζ5−3ζ50000000000000000000000000
χ448-804i2−4i200-11−3i3i−2ζ2+ζ6ζ2−2ζ62ζ2−ζ6−ζ2+2ζ6−3ζ33ζ33ζ−3ζ3ζ7−3ζ7−3ζ53ζ50000000000000000000000000
χ458-80−4i24i200-113i−3i−ζ2+2ζ62ζ2−ζ6ζ2−2ζ6−2ζ2+ζ63ζ5−3ζ5−3ζ73ζ7−3ζ3ζ3ζ3−3ζ30000000000000000000000000
χ468-80−4i24i200-113i−3i−ζ2+2ζ62ζ2−ζ6ζ2−2ζ6−2ζ2+ζ6−3ζ53ζ53ζ7−3ζ73ζ−3ζ−3ζ33ζ30000000000000000000000000
χ478-80−4i24i200-11−3i3i2ζ2−ζ6−ζ2+2ζ6−2ζ2+ζ6ζ2−2ζ63ζ7−3ζ73ζ5−3ζ53ζ3−3ζ33ζ−3ζ0000000000000000000000000
χ488-80−4i24i200-11−3i3i2ζ2−ζ6−ζ2+2ζ6−2ζ2+ζ6ζ2−2ζ6−3ζ73ζ7−3ζ53ζ5−3ζ33ζ3−3ζ3ζ0000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.