Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×A4×D25 |
| unambiguous semidirect product | C25⋊(C22×A4) |
| unambiguous semidirect product | (C2×C25)⋊(C2×A4) |
| unambiguous semidirect product | (C23×D25)⋊C3 |
| Fitting | C23×C25 ⋊ C2×C3 |
| derived | C22×C25 ⋊ C22×C3 |
| Hall | C23×D25 ⋊ C3 |
| Sylow | C25 ⋊ C22×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×D25 |
| commutator, cosocle, hypocenter | C22×C25 | C22×C3 |
| Frattini | C5 | C2×D5×A4 |
| Fitting | C23×C25 | C2×C3 |
| socle | C23×C5 | C3×D5 |
| LCS | G ▷ C22×C25 | |
| UCS | C1 ◁ C2 | |
117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 199);