Finite Group DatabasebetaFinite Group Databasebeta| order | 25802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×D133 |
| unambiguous semidirect product | C7⋊(D19×C97) |
| unambiguous semidirect product | C19⋊(D7×C97) |
| Fitting, socle, Hall | C7×C19×C97 ⋊ C2 |
| derived, Hall | C7×C19 ⋊ C2×C97 |
| Hall | C19×C97 ⋊ D7 |
| Hall | C7×C97 ⋊ D19 |
| Sylow | C19 ⋊ D7×C97 |
| Sylow | C7 ⋊ D19×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D133 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C97 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C97 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C97 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12901 |
6596 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25802, 7);