Finite Group DatabasebetaFinite Group Databasebeta| order | 26076 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C3⋊#4223 |
| unambiguous semidirect product | C3⋊(C53×#4223) |
| Fitting, socle, Hall | C3×C41×C53 ⋊ C4 |
| derived, Hall | C3×C41 ⋊ C4×C53 |
| Hall | C41×C53 ⋊ Dic3 |
| Hall | C3×C53 ⋊ #4223 |
| Sylow | C41 ⋊ Dic3×C53 |
| Sylow | C3 ⋊ C53×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C3⋊#4223 |
| commutator, hypocenter | C3×C41 | C4×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C53 | C4 |
| prime radical | C3×C53×D41 | C2 |
| cosocle | C3×D41 | C2×C53 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6519 |
1908 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26076, 19);