Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#20263466 |
| Fitting, derived, Hall | C22×C43×C49 ⋊ C3 |
| Hall | C43×C49 ⋊ A4 |
| Hall | C22×C49 ⋊ C43⋊C3 |
| Hall | C22×C43 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C22⋊(C43⋊C3) |
| Sylow | C43 ⋊ C22⋊(C49⋊C3) |
| Sylow | C22 ⋊ #20263466 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C43×C49 | C3 |
| Frattini | C7 | C22⋊#11744748 |
| socle | C22×C7×C43 | ΓL(1,𝔽8) |
| LCS | G ▷ C22×C43×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8428 |
Polycyclic presentation:
3,2^2,7,43,7|d^7=f^2,b^a=c,c^a=bc,d^a=d^2f,e^a=e^6,f^a=f^22812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 72);