Finite Group DatabasebetaFinite Group Databasebeta| order | 25886 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D301 |
| unambiguous semidirect product | C7⋊(C43×D43) |
| unambiguous semidirect product | C43⋊(D7×C43) |
| Fitting, socle, Hall | C7×C432 ⋊ C2 |
| derived | C7×C43 ⋊ C2×C43 |
| Sylow | C432 ⋊ D7 |
| Sylow | C7 ⋊ C43×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D301 |
| commutator, cosocle, hypocenter | C7×C43 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C7×C432 | C2 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C43 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 602 |
6536 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25886, 30);