Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#87763 |
| derived, Hall | C3×C52 ⋊ C16 |
| Sylow | C52 ⋊ C3⋊C16 |
| Sylow | C3 ⋊ #87763 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C3⋊#1042 |
| commutator, hypocenter | C3×C52 | C16 |
| Fitting | C3×C4×C52 | C4 |
| socle, prime radical | C2×C3×C52 | C8 |
| cosocle | C3×C5×#168 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C4 | |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5^2|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^2,g^a=g^4,f^b=f^4132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 265);