Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×D52 |
| unambiguous semidirect product | (C5×D5)⋊(C23×C3) |
| Fitting, socle | C22×C3×C52 ⋊ C22 |
| derived, Sylow | C52 ⋊ C24×C3 |
| Hall | C3×C52 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D52 |
| commutator, cosocle, hypocenter | C52 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C3 | |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1025);