Finite Group DatabasebetaFinite Group Databasebeta| order | 23028 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊#87938 |
| unambiguous semidirect product | (C19⋊#87938)⋊C3 |
| Fitting, socle, derived, Hall | C19×C101 ⋊ C3×C4 |
| Hall | C19⋊#87938 ⋊ C3 |
| Hall | C19⋊C3×C101 ⋊ C4 |
| Sylow | C101 ⋊ (C19⋊C3)⋊C4 |
| Hall | C19⋊C3 ⋊ #87938 |
| Sylow | C19 ⋊ C3×#87938 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C101 | C3×C4 |
| prime radical | C19⋊C3×D101 | C2 |
| cosocle | C19×D101 | C2×C3 |
| LCS | G ▷ C19×C101 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1919 |
Polycyclic presentation:
2,3,2,19,101|a^2=c,d^a=d^18,e^a=e^10,d^b=d^7,e^c=e^100243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23028, 14);