Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of A4×C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | A4×C52⋊C3 |
| unambiguous semidirect product | (C22×C52⋊C3)⋊C3 |
| unambiguous semidirect product | (C52×A4)⋊C3 |
| unambiguous semidirect product | (C22⋊(C52⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C22×C52 ⋊ C32 |
| Sylow | C52 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C52 | C32 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 98);