Finite Group DatabasebetaFinite Group Databasebeta| order | 28749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#11715912 |
| Fitting, socle, Hall | C7×C372 ⋊ C3 |
| derived | C7×C37 ⋊ C3×C37 |
| Sylow | C372 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C37×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #11715912 |
| commutator, cosocle, hypocenter | C7×C37 | C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C372 | C3 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C37 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 777 |
3293 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28749, 12);