Finite Group DatabasebetaFinite Group Databasebeta| order | 25818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C331 · Schur multiplier (H2) = C1 |
| direct product | D13⋊C3×C331 |
| unambiguous semidirect product | D13⋊(C3×C331) |
| unambiguous semidirect product | (C13⋊C3)⋊(C2×C331) |
| Fitting, socle, Hall | C13×C331 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C2×C3×C331 |
| Hall | C13⋊C3×C331 ⋊ C2 |
| Hall | D13×C331 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×C331 |
| Hall | D13 ⋊ C3×C331 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C331 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C331 |
| Frattini | C1 | G |
| Fitting, socle | C13×C331 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C331 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4303 |
2648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25818, 18);