Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4⋊D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | C2×A4⋊D25 |
| unambiguous semidirect product | (C2×A4)⋊D25 |
| unambiguous semidirect product | (C2×C25)⋊S4 |
| Fitting | C23×C25 ⋊ D3 |
| derived | A4×C25 ⋊ C22 |
| Sylow | C25 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4⋊D25 |
| commutator, cosocle, hypocenter | A4×C25 | C22 |
| Frattini | C5 | C2×C5⋊S4 |
| Fitting | C23×C25 | D3 |
| socle | C23×C5 | D15 |
| LCS | G ▷ A4×C25 | |
| UCS | C1 ◁ C2 | |
99 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 198);