Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of C42⋊(C19⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C42⋊(C19⋊C3) |
| unambiguous semidirect product | C19⋊(C42⋊C3) |
| Fitting, derived, Hall | C42×C19 ⋊ C3 |
| Sylow | C19 ⋊ C42⋊C3 |
| Sylow | C42 ⋊ C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C42×C19 | C3 |
| Frattini | C22 | C22⋊(C19⋊C3) |
| socle | C22×C19 | A4 |
| LCS | G ▷ C42×C19 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
Polycyclic presentation:
3,2^2,19,2^2|b^2=e,c^2=f,b^a=ce,c^a=bc,d^a=d^7,e^a=f,f^a=ef104 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊(C42⋊C3), #14269153, #14269154, … |
| maximal normal subgroup of | D19⋊(C42⋊C3), #14269153, #14269154, … |
| maximal quotient of | C19⋊(#95⋊C3), C2×C42⋊(C19⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 57);