Finite Group DatabasebetaFinite Group Databasebeta| order | 28665 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×#14274254 |
| Fitting | C3×C5×C13×C49 ⋊ C3 |
| derived, Hall | C13×C49 ⋊ C32×C5 |
| Hall | C5×C13×C49 ⋊ C32 |
| Hall | C5×C49 ⋊ C3×C13⋊C3 |
| Hall | C5×C13 ⋊ C3×C49⋊C3 |
| Sylow | C49 ⋊ C3×C5×C13⋊C3 |
| Sylow | C13 ⋊ C3×C5×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #14274254 |
| commutator, cosocle, hypocenter | C13×C49 | C32×C5 |
| Frattini | C7 | C3×C5×#63270 |
| Fitting | C3×C5×C13×C49 | C3 |
| socle | C3×C5×C7×C13 | ΓL(1,𝔽8) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C3×C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9555 |
3225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28665, 8);