Finite Group DatabasebetaFinite Group Databasebeta| order | 25900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C7⋊#10625193 |
| unambiguous semidirect product | C7⋊(C5×#10625193) |
| Fitting, socle, Hall | C52×C7×C37 ⋊ C4 |
| derived | C5×C7×C37 ⋊ C4×C5 |
| Hall | C52×C37 ⋊ Dic7 |
| Hall | C7×C37 ⋊ C5×AGL(1,𝔽5) |
| Hall | C52×C7 ⋊ Dic37 |
| Sylow | C37 ⋊ C5×C7⋊AGL(1,𝔽5) |
| Sylow | C52 ⋊ Dic259 |
| Sylow | C7 ⋊ C5×#10625193 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C7⋊#10625193 |
| commutator, hypocenter | C5×C7×C37 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C37 | C4 |
| prime radical | C5×C7×D5×C37 | C2 |
| cosocle | C7×D5×C37 | C2×C5 |
| LCS | G ▷ C5×C7×C37 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5180 |
2605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25900, 67);