Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#87709 |
| derived, Hall | C3×C25 ⋊ C16 |
| Sylow | C25 ⋊ C3⋊C16 |
| Sylow | C3 ⋊ #87709 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊#1035 |
| commutator, hypocenter | C3×C25 | C16 |
| Frattini | C4×C5 | ΓL(1,𝔽16) |
| Fitting | C3×C4×C25 | C4 |
| socle, prime radical | C2×C3×C5 | #170 |
| cosocle | C3×#6014 | C2 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1200 |
Polycyclic presentation:
2^4,3,5^2|a^2=b,b^2=c,c^2=d,f^5=g,e^a=e^2,f^a=f^2g,g^a=g^2,f^b=f^4g^4,g^b=g^496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 6);