Finite Group DatabasebetaFinite Group Databasebeta| order | 19292 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C7⋊#6157 |
| unambiguous semidirect product | C7⋊(C13×#6157) |
| Fitting, socle, Hall | C7×C13×C53 ⋊ C4 |
| derived, Hall | C7×C53 ⋊ C4×C13 |
| Hall | C13×C53 ⋊ Dic7 |
| Hall | C7×C13 ⋊ #6157 |
| Sylow | C53 ⋊ C13×Dic7 |
| Sylow | C7 ⋊ C13×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C7⋊#6157 |
| commutator, hypocenter | C7×C53 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C53 | C4 |
| prime radical | C7×C13×D53 | C2 |
| cosocle | C7×D53 | C2×C13 |
| LCS | G ▷ C7×C53 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4823 |
1313 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19292, 28);