Finite Group DatabasebetaFinite Group Databasebeta| order | 7980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊AGL(1,𝔽7))⋊D19 |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D19)⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C19 | C22×C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,7,19|e^a=e^6,f^a=f^18,d^b=d^4,e^b=e^6,e^c=e^2181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7980, 85);