Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | A4×#1039 |
| derived | C22×C52 ⋊ C3×C4 |
| Hall | C22×#1039 ⋊ C3 |
| Sylow | C52 ⋊ C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×C5⋊D5 |
| commutator, hypocenter | C22×C52 | C3×C4 |
| Fitting, socle, cosocle | C23×C52 | C2×C3 |
| prime radical | C2×C52×A4 | C2 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C2 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 698);