Finite Group DatabasebetaFinite Group Databasebeta| order | 636 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C53 · Schur multiplier (H2) = C2 |
| direct product | A4×C53 |
| unambiguous semidirect product | C22⋊(C3×C53) |
| unambiguous semidirect product | (C22×C53)⋊C3 |
| Fitting, socle, Hall | C22×C53 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C53 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 212 |
212 conjugacy classes — view the full character table.
| derived subgroup of | A4⋊D53 |
| maximal subgroup of | S4×C53, A4⋊D53, A4×D53, … |
| maximal normal subgroup of | S4×C53, A4⋊D53, A4×D53, … |
| maximal quotient of | SL(2,𝔽3)×C53, C2×A4×C53, C22⋊C9×C53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(636, 8);