Finite Group DatabasebetaFinite Group Databasebeta| order | 19812 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#19097153 |
| Fitting, socle, derived, Hall | C22×C13×C127 ⋊ C3 |
| Hall | C13×C127 ⋊ A4 |
| Hall | C22×C127 ⋊ C13⋊C3 |
| Sylow | C127 ⋊ C22⋊(C13⋊C3) |
| Hall | C22×C13 ⋊ C127⋊C3 |
| Sylow | C13 ⋊ C22⋊(C127⋊C3) |
| Sylow | C22 ⋊ #19097153 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C13×C127 | C3 |
| LCS | G ▷ C22×C13×C127 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6604 |
Polycyclic presentation:
3,2^2,13,127|b^a=c,c^a=bc,d^a=d^3,e^a=e^192204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19812, 62);