Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C92 · Schur multiplier (H2) = C32×C9 |
| direct product | C92×ΓL(1,𝔽8) |
| Fitting | C7×C92 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C92 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C3×C92 |
| Frattini | C32 | C32×ΓL(1,𝔽8) |
| Fitting | C7×C92 | C3 |
| socle, cosocle | C32×C7 | C33 |
| prime radical | C32×ΓL(1,𝔽8) | C32 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C92 | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)×C9⋊D9, C92×AGL(1,𝔽7), #72229869, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×C9⋊D9, C92×AGL(1,𝔽7), #72229869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 154);