Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D3×D25 |
| Fitting | C3×C4×C25 ⋊ C22 |
| derived, Hall | C3×C25 ⋊ C22×C4 |
| Sylow | C25 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×D25 |
| commutator, hypocenter | C3×C25 | C22×C4 |
| Frattini | C2×C5 | C2×D3×D5 |
| Fitting | C3×C4×C25 | C22 |
| socle | C2×C3×C5 | C22×D5 |
| prime radical | C2×D3×D25 | C2 |
| cosocle | C2×C3×C25 | C23 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C4 | |
162 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 300 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 129);