Finite Group DatabasebetaFinite Group Databasebeta| order | 28749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C1369⋊C3 |
| unambiguous semidirect product | C1369⋊(C3×C7) |
| Fitting, Hall | C7×C1369 ⋊ C3 |
| derived, Sylow | C1369 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C1369⋊C3 |
| commutator, cosocle, hypocenter | C1369 | C3×C7 |
| Frattini | C37 | C7×C37⋊C3 |
| Fitting | C7×C1369 | C3 |
| socle | C7×C37 | C37⋊C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9583 |
3213 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28749, 3);