Finite Group DatabasebetaFinite Group Databasebeta| order | 4300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊#1035 |
| Fitting, derived, Hall | C25×C43 ⋊ C4 |
| Sylow | C43 ⋊ #1035 |
| Sylow | C25 ⋊ Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C43 | C4 |
| Frattini | C5 | C43⋊AGL(1,𝔽5) |
| socle | C5×C43 | AGL(1,𝔽5) |
| prime radical, cosocle | C43×D25 | C2 |
| LCS | G ▷ C25×C43 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 68 |
| transitive degree | μt(G) = 1075 |
Polycyclic presentation:
2^2,5,43,5|a^2=b,c^5=e^2,c^a=c^3e,d^a=d^42,e^a=e^3,c^b=c^4e^3,e^b=e^4304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4300, 7);