Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊#6016 |
| unambiguous semidirect product | (C2×C3)⋊#6016 |
| derived, Hall | C3×C25 ⋊ C2×C8 |
| Sylow | C25 ⋊ C2×C3⋊C8 |
| Sylow | C3 ⋊ C2×#6016 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#1035 |
| commutator, hypocenter | C3×C25 | C2×C8 |
| Frattini | C2×C5 | C2×ΓL(1,𝔽16) |
| Fitting | C22×C3×C25 | C4 |
| socle, prime radical | C22×C3×C5 | AGL(1,𝔽5) |
| cosocle | C3×Dic25 | C22 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C22 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1200 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 116);