Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊#10596868 |
| derived, Hall | C43×#3862 ⋊ C4 |
| Hall | C72×C43 ⋊ Dic3 |
| Hall | #3862 ⋊ Dic43 |
| Sylow | C72 ⋊ Dic129 |
| Sylow | C43 ⋊ #10596868 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C43⋊#64418 |
| commutator, hypocenter | C43×#3862 | C4 |
| Fitting, socle | C2×C72×C43 | D3 |
| prime radical, cosocle | C2×C43×#3862 | C2 |
| LCS | G ▷ C43×#3862 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1204 |
Polycyclic presentation:
2,3,43,7^2,2|a^2=f,b^a=b^2,c^a=c^42,d^a=d^2e^3,e^a=d^6e^5,d^b=d^4e^4,e^b=e^2838 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 159);