Finite Group DatabasebetaFinite Group Databasebeta| order | 19292 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×AGL(1,𝔽53) |
| unambiguous semidirect product | #6157⋊(C7×C13) |
| unambiguous semidirect product | (C7×#6157)⋊C13 |
| Fitting, socle, Hall | C7×C53 ⋊ C4×C13 |
| derived, Sylow | C53 ⋊ C4×C7×C13 |
| Hall | C7×C53⋊C13 ⋊ C4 |
| Hall | C7×#6157 ⋊ C13 |
| Hall | C53⋊C13 ⋊ C4×C7 |
| Hall | #6157 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | AGL(1,𝔽53) |
| commutator, hypocenter | C53 | C4×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C53 | C4×C13 |
| prime radical | C7×D53⋊C13 | C2 |
| cosocle | D53 | C2×C7×C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 371 |
371 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19292, 14);