Finite Group DatabasebetaFinite Group Databasebeta| order | 25668 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×Dic69 |
| unambiguous semidirect product | C3⋊(Dic23×C31⋊C3) |
| unambiguous semidirect product | C23⋊(Dic3×C31⋊C3) |
| unambiguous semidirect product | (C31×Dic69)⋊C3 |
| derived | C3×C23×C31 ⋊ C3×C4 |
| Hall | C3×C23×C31⋊C3 ⋊ C4 |
| Hall | C23×C31 ⋊ C3×Dic3 |
| Hall | C3×C31⋊C3 ⋊ Dic23 |
| Sylow | C31 ⋊ C3×Dic69 |
| Sylow | C23 ⋊ Dic3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C31⋊C3×D69 |
| commutator, hypocenter | C3×C23×C31 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C23×C31 | C2×C3 |
| prime radical | C2×C3×C23×C31⋊C3 | C2 |
| LCS | G ▷ C3×C23×C31 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8556 |
936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25668, 42);