Finite Group DatabasebetaFinite Group Databasebeta| order | 7854 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C17⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | C17⋊(C11⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D187 |
| unambiguous semidirect product | D1309⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C11×C17 | C2×C3 |
| LCS | G ▷ C7×C11×C17 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11,17|c^a=c^6,d^a=d^10,e^a=e^16,c^b=c^2472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7854, 24);