Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| isoclinism | isoclinic class of D19⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | D19⋊(C42⋊C3) |
| Fitting, derived | C42×C19 ⋊ C2×C3 |
| Hall | C42×D19 ⋊ C3 |
| Sylow | C19 ⋊ C2×C42⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C42×C19 | C2×C3 |
| Frattini | C22 | D19⋊A4 |
| socle | C22×C19 | C2×A4 |
| LCS | G ▷ C42×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
Polycyclic presentation:
2,3,2^2,19,2^2|c^2=f,d^2=fg,e^a=e^18,c^b=cd,d^b=cfg,e^b=e^11,f^b=g,g^b=fg64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 379);