Finite Group DatabasebetaFinite Group Databasebeta| order | 25815 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C1721⋊C5 |
| unambiguous semidirect product | C1721⋊(C3×C5) |
| unambiguous semidirect product | (C3×C1721)⋊C5 |
| Fitting, socle, Hall | C3×C1721 ⋊ C5 |
| derived, Sylow | C1721 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C1721⋊C5 |
| commutator, cosocle, hypocenter | C1721 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1721 | C5 |
| LCS | G ▷ C1721 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5163 |
1047 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25815, 1);