Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×(C19⋊C3)⋊C4 |
| derived, Sylow | C19 ⋊ C22×C3×C4 |
| Hall | C22×Dic19 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D19⋊C3 |
| commutator, hypocenter | C19 | C22×C3×C4 |
| Frattini | C2 | C22×D19⋊C3 |
| Fitting, socle | C23×C19 | C2×C3 |
| prime radical | C23×C19⋊C3 | C2 |
| cosocle | C2×C19 | C23×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C23 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 128);