Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C49 · Schur multiplier (H2) = C2 |
| direct product | C22×C3×C43⋊C49 |
| unambiguous semidirect product | (C22×C3×C43)⋊C49 |
| derived, Sylow | C43 ⋊ C22×C3×C49 |
| Hall | C22×C3×C43 ⋊ C49 |
| Hall | C22×C43 ⋊ C3×C49 |
| Hall | C3×C43 ⋊ C22×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C7 | C43⋊C7 |
| commutator, hypocenter | C43 | C22×C3×C49 |
| Frattini | C7 | C22×C3×C43⋊C7 |
| Fitting, socle, prime radical | C22×C3×C7×C43 | C7 |
| cosocle | C7×C43 | C22×C3×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C22×C3×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25284 |
1092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 44);