Finite Group DatabasebetaFinite Group Databasebeta| order | 25047 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C121 · Schur multiplier (H2) = C3 |
| direct product | C32×C23⋊C121 |
| unambiguous semidirect product | C23⋊(C32×C121) |
| unambiguous semidirect product | (C3×C23)⋊(C3×C121) |
| unambiguous semidirect product | (C32×C23)⋊C121 |
| derived, Sylow | C23 ⋊ C32×C121 |
| Hall | C32×C23 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C11 | C23⋊C11 |
| commutator, hypocenter | C23 | C32×C121 |
| Frattini | C11 | C32×C23⋊C11 |
| Fitting, socle, prime radical | C32×C11×C23 | C11 |
| cosocle | C11×C23 | C32×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C32×C11 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25047 |
1287 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25047, 4);