Finite Group DatabasebetaFinite Group Databasebeta| order | 874 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D19 |
| unambiguous semidirect product | C19⋊(C2×C23) |
| Fitting, socle, Hall | C19×C23 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C19×C23 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C23 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 437 |
253 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D23, C2×C23×D19, C3×C23×D19, … |
| maximal normal subgroup of | D19×D23, C2×C23×D19, C3×C23×D19, … |
| maximal quotient of | C23×Dic19, C2×C23×D19, C3×C23×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(874, 1);