Finite Group DatabasebetaFinite Group Databasebeta| order | 17094 |
| isoclinism | isoclinic class of C11⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C11⋊AGL(1,𝔽7) |
| unambiguous semidirect product | C11⋊(C37×AGL(1,𝔽7)) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D11×C37) |
| unambiguous semidirect product | D77⋊(C3×C37) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C11⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7×C11 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C37 | C2×C3 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C37 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2849 |
1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17094, 42);