Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic43⋊C49 |
| unambiguous semidirect product | (C3×Dic43)⋊C49 |
| derived, Sylow | C43 ⋊ C3×C4×C49 |
| Hall | C3×C43⋊C49 ⋊ C4 |
| Hall | C43⋊C49 ⋊ C3×C4 |
| Hall | C3×Dic43 ⋊ C49 |
| Hall | Dic43 ⋊ C3×C49 |
| Hall | C3×C43 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D43⋊C7 |
| commutator, hypocenter | C43 | C3×C4×C49 |
| Frattini | C2×C7 | C3×D43⋊C7 |
| Fitting, socle, prime radical | C2×C3×C7×C43 | C2×C7 |
| cosocle | C2×C7×C43 | C2×C3×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C3×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25284 |
714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 4);