Finite Group DatabasebetaFinite Group Databasebeta| order | 1092 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C13 · Schur multiplier (H2) = C2 |
| direct product | C7×A4×C13 |
| unambiguous semidirect product | C22⋊(C3×C7×C13) |
| Fitting, socle, Hall | C22×C7×C13 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C7×C13 |
| Hall | C22×C13 ⋊ C3×C7 |
| Hall | C22×C7 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C13 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C7×C13 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 364 |
364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×A4×C13⋊C3, A4×C13×ΓL(1,𝔽8), A4×#63270, … |
| maximal normal subgroup of | C7×A4×C13⋊C3, A4×C13×ΓL(1,𝔽8), A4×#63270, … |
| maximal quotient of | C7×C13×C22⋊C9, C3×C7×A4×C13, C7×C11×A4×C13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1092, 65);