Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊#87756 |
| derived, Hall | C3×C52 ⋊ C16 |
| Sylow | C52 ⋊ C3⋊C16 |
| Sylow | C3 ⋊ #87756 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | C3⋊(C5⋊D5) |
| commutator, hypocenter | C3×C52 | C16 |
| Fitting, cosocle | C3×C52×C8 | C2 |
| socle, prime radical | C2×C3×C52 | C8 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C8 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1200 |
Polycyclic presentation:
2^4,3,5^2|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^4,g^a=g^4312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 190);