Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16813400⋊C7 |
| derived | C7×C43 ⋊ C3×C4×C7 |
| Hall | C7×Dic43⋊C7 ⋊ C3 |
| Hall | #11744748⋊C7 ⋊ C4 |
| Hall | C7×C43⋊C7 ⋊ C3×C4 |
| Hall | Dic43 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C43 ⋊ C4×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #14268587⋊C7 |
| commutator, hypocenter | C7×C43 | C3×C4×C7 |
| Fitting, socle, cosocle | C2×C7×C43 | C2×C3×C7 |
| prime radical | C2×#11744748⋊C7 | C2 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1204 |
Polycyclic presentation:
2,3,7^2,43,2|a^2=f,e^a=e^42,d^b=d^2,e^b=e^6,e^c=e^41154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 89);