Finite Group DatabasebetaFinite Group Databasebeta| order | 19292 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊AGL(1,𝔽53) |
| unambiguous semidirect product | (C7⋊#6157)⋊C13 |
| Fitting, socle, derived, Hall | C7×C53 ⋊ C4×C13 |
| Hall | C7×C53⋊C13 ⋊ C4 |
| Hall | C7⋊#6157 ⋊ C13 |
| Hall | C53⋊C13 ⋊ Dic7 |
| Sylow | C53 ⋊ C13×Dic7 |
| Sylow | C7 ⋊ AGL(1,𝔽53) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C53 | C4×C13 |
| prime radical | C7×D53⋊C13 | C2 |
| cosocle | C7×D53 | C2×C13 |
| LCS | G ▷ C7×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 371 |
Polycyclic presentation:
2,13,2,7,53|a^2=c,d^a=d^6,e^a=e^30,e^b=e^16,e^c=e^52137 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19292, 15);