Finite Group DatabasebetaFinite Group Databasebeta| order | 25900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×(C5⋊D5)⋊D37 |
| unambiguous semidirect product | (C5⋊D5)⋊(C7×D37) |
| unambiguous semidirect product | D185⋊(C7×D5) |
| Fitting, socle, Hall | C52×C7×C37 ⋊ C22 |
| derived, Hall | C52×C37 ⋊ C22×C7 |
| Hall | C7×C37 ⋊ D52 |
| Hall | C52×C7 ⋊ C2×D37 |
| Sylow | C37 ⋊ C7×D52 |
| Sylow | C52 ⋊ C2×C7×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C5⋊D5)⋊D37 |
| commutator, cosocle, hypocenter | C52×C37 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C37 | C22 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C7 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2590 |
1876 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25900, 78);