Finite Group DatabasebetaFinite Group Databasebeta| order | 25122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D159 |
| unambiguous semidirect product | C3⋊(C79×D53) |
| unambiguous semidirect product | C53⋊(D3×C79) |
| Fitting, socle, Hall | C3×C53×C79 ⋊ C2 |
| derived, Hall | C3×C53 ⋊ C2×C79 |
| Hall | C53×C79 ⋊ D3 |
| Hall | C3×C79 ⋊ D53 |
| Sylow | C53 ⋊ D3×C79 |
| Sylow | C3 ⋊ C79×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D159 |
| commutator, cosocle, hypocenter | C3×C53 | C2×C79 |
| Frattini | C1 | G |
| Fitting, socle | C3×C53×C79 | C2 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C79 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12561 |
6399 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25122, 8);