Finite Group DatabasebetaFinite Group Databasebeta| order | 19292 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(Dic53⋊C13) |
| unambiguous semidirect product | Dic371⋊C13 |
| derived, Hall | C7×C53 ⋊ C4×C13 |
| Hall | C7×C53⋊C13 ⋊ C4 |
| Hall | Dic371 ⋊ C13 |
| Hall | C53⋊C13 ⋊ Dic7 |
| Sylow | C53 ⋊ C13×Dic7 |
| Sylow | C7 ⋊ Dic53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(D53⋊C13) |
| commutator, hypocenter | C7×C53 | C4×C13 |
| Fitting, socle, cosocle | C2×C7×C53 | C2×C13 |
| prime radical | C2×C7×C53⋊C13 | C2 |
| LCS | G ▷ C7×C53 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1484 |
Polycyclic presentation:
2,7,13,53,2|a^2=e,b^a=b^6,d^a=d^52,d^c=d^16158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19292, 12);