Finite Group DatabasebetaFinite Group Databasebeta| order | 26660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C31⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C31⋊(AGL(1,𝔽5)×C43) |
| Fitting, socle, Hall | C5×C31×C43 ⋊ C4 |
| derived, Hall | C5×C31 ⋊ C4×C43 |
| Hall | C31×C43 ⋊ AGL(1,𝔽5) |
| Hall | C5×C43 ⋊ Dic31 |
| Sylow | C31 ⋊ AGL(1,𝔽5)×C43 |
| Sylow | C5 ⋊ C43×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C31⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C31 | C4×C43 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C43 | C4 |
| prime radical | D5×C31×C43 | C2 |
| cosocle | D5×C31 | C2×C43 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6665 |
2795 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26660, 22);