Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×C42⋊C3 |
| unambiguous semidirect product | C42⋊(C3×C19) |
| Fitting, Hall | C42×C19 ⋊ C3 |
| derived, Sylow | C42 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C42⋊C3 |
| commutator, cosocle, hypocenter | C42 | C3×C19 |
| Frattini | C22 | A4×C19 |
| Fitting | C42×C19 | C3 |
| socle | C22×C19 | A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C19 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
152 conjugacy classes — view the full character table.
| derived subgroup of | C19⋊#857 |
| maximal subgroup of | C19×#857, C19⋊#857, D19×C42⋊C3, … |
| maximal normal subgroup of | C19×#857, C19⋊#857, D19×C42⋊C3, … |
| maximal quotient of | C19×#95⋊C3, C2×C19×C42⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 56);