Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×C3⋊#1035 |
| Fitting | C3×C4×C25 ⋊ C4 |
| derived, Hall | C3×C25 ⋊ C42 |
| Sylow | C25 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊#1035 |
| commutator, hypocenter | C3×C25 | C42 |
| Frattini | C2×C5 | C2×ΓL(1,𝔽16) |
| Fitting | C3×C4×C25 | C4 |
| socle | C2×C3×C5 | C2×AGL(1,𝔽5) |
| prime radical, cosocle | C2×C3×D25 | C22 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C4 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 114);