Finite Group DatabasebetaFinite Group Databasebeta| order | 27140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×C23⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C23⋊(AGL(1,𝔽5)×C59) |
| Fitting, socle, Hall | C5×C23×C59 ⋊ C4 |
| derived, Hall | C5×C23 ⋊ C4×C59 |
| Hall | C23×C59 ⋊ AGL(1,𝔽5) |
| Hall | C5×C59 ⋊ Dic23 |
| Sylow | C23 ⋊ AGL(1,𝔽5)×C59 |
| Sylow | C5 ⋊ C59×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | C23⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C23 | C4×C59 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C59 | C4 |
| prime radical | D5×C23×C59 | C2 |
| cosocle | D5×C23 | C2×C59 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C59 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6785 |
2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27140, 13);