Finite Group DatabasebetaFinite Group Databasebeta| order | 28158 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | D13⋊#11762246 |
| Fitting, socle, derived, Hall | C13×C192 ⋊ C2×C3 |
| Hall | C13⋊#11762246 ⋊ C2 |
| Hall | C192×D13 ⋊ C3 |
| Sylow | C192 ⋊ D13⋊C3 |
| Hall | D13 ⋊ #11762246 |
| Sylow | C13 ⋊ C2×#11762246 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C192 | C2×C3 |
| LCS | G ▷ C13×C192 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 741 |
Polycyclic presentation:
2,3,13,19^2|c^a=c^12,c^b=c^3,d^b=d^7,e^b=e^11968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28158, 50);