Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C2 |
| direct product | C43×C22⋊(C49⋊C3) |
| unambiguous semidirect product | C22⋊(C43×C49⋊C3) |
| unambiguous semidirect product | C49⋊(A4×C43) |
| Fitting, Hall | C22×C43×C49 ⋊ C3 |
| derived, Hall | C22×C49 ⋊ C3×C43 |
| Hall | C43×C49 ⋊ A4 |
| Hall | C22×C43 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ A4×C43 |
| Sylow | C22 ⋊ C43×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C22⋊(C49⋊C3) |
| commutator, cosocle, hypocenter | C22×C49 | C3×C43 |
| Frattini | C7 | C43×C22⋊ΓL(1,𝔽8) |
| Fitting | C22×C43×C49 | C3 |
| socle | C22×C7×C43 | ΓL(1,𝔽8) |
| LCS | G ▷ C22×C49 | |
| UCS | C1 ◁ C43 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8428 |
2924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 70);