Finite Group DatabasebetaFinite Group Databasebeta| order | 28749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C1369 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C1369 |
| unambiguous semidirect product | C7⋊(C3×C1369) |
| Fitting, Hall | C7×C1369 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C1369 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1369 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C3×C1369 |
| Frattini | C37 | ΓL(1,𝔽8)×C37 |
| Fitting | C7×C1369 | C3 |
| socle, cosocle | C7×C37 | C3×C37 |
| prime radical | ΓL(1,𝔽8)×C37 | C37 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C1369 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9583 |
6845 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28749, 2);