Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C292 · Schur multiplier (H2) = C2×C29 |
| direct product | A4×C292 |
| unambiguous semidirect product | C22⋊(C3×C292) |
| unambiguous semidirect product | (C22×C29)⋊(C3×C29) |
| Fitting, socle, Hall | C22×C292 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C292 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C292 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C292 |
| Frattini | C1 | G |
| Fitting, socle | C22×C292 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C292 | |
160 conjugacy classes of subgroups.
3364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C292⋊C3, C3×A4×C292 |
| maximal normal subgroup of | A4×C292⋊C3, C3×A4×C292 |
| maximal quotient of | C292×C22⋊C9, C3×A4×C292 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 42);