Finite Group DatabasebetaFinite Group Databasebeta| order | 25746 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C613 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽7)×C613 |
| unambiguous semidirect product | D7⋊(C3×C613) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C613) |
| Fitting, socle, Hall | C7×C613 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C2×C3×C613 |
| Hall | ΓL(1,𝔽8)×C613 ⋊ C2 |
| Hall | D7×C613 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C613 |
| Hall | D7 ⋊ C3×C613 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C613 | AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7 | C2×C3×C613 |
| Frattini | C1 | G |
| Fitting, socle | C7×C613 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C613 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4291 |
4291 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25746, 18);