Finite Group DatabasebetaFinite Group Databasebeta| order | 25675 |
| automorphism | ? |
| homology | Abelianization (H1) = C13×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C79⋊C13 |
| unambiguous semidirect product | C79⋊(C13×C25) |
| unambiguous semidirect product | (C25×C79)⋊C13 |
| Fitting, Hall | C25×C79 ⋊ C13 |
| derived, Sylow | C79 ⋊ C13×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C79⋊C13 |
| commutator, hypocenter | C79 | C13×C25 |
| Frattini | C5 | C5×C79⋊C13 |
| Fitting | C25×C79 | C13 |
| socle, cosocle | C5×C79 | C5×C13 |
| prime radical | C5×C79⋊C13 | C5 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1975 |
475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25675, 2);