Finite Group DatabasebetaFinite Group Databasebeta| order | 28650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2865 |
| unambiguous semidirect product | C3⋊(C5×D955) |
| unambiguous semidirect product | C5⋊(C5×D573) |
| Fitting, socle, Hall | C3×C52×C191 ⋊ C2 |
| derived | C3×C5×C191 ⋊ C2×C5 |
| Hall | C52×C191 ⋊ D3 |
| Hall | C3×C191 ⋊ C5×D5 |
| Sylow | C191 ⋊ C5×D15 |
| Hall | C3×C52 ⋊ D191 |
| Sylow | C52 ⋊ D573 |
| Sylow | C3 ⋊ C5×D955 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2865 |
| commutator, cosocle, hypocenter | C3×C5×C191 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C191 | C2 |
| LCS | G ▷ C3×C5×C191 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5730 |
7170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28650, 36);