Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊C16 |
| unambiguous semidirect product | (C19⋊C16)⋊C3 |
| derived, Sylow | C19 ⋊ C3×C16 |
| Hall | C19⋊C16 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D19⋊C3 |
| commutator, hypocenter | C19 | C3×C16 |
| Fitting, cosocle | C8×C19 | C2×C3 |
| socle | C2×C19 | C3×C8 |
| prime radical | C2×C19⋊C3 | C8 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C8 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2,3,2^3,19|a^2=c,c^2=d,d^2=e,f^a=f^18,f^b=f^772 conjugacy classes — view the full character table.
| maximal subgroup of | C16×D19⋊C3, #10597255⋊C3, C2×(C19⋊C3)⋊C16, … |
| maximal normal subgroup of | C16×D19⋊C3, #10597255⋊C3, C2×(C19⋊C3)⋊C16, … |
| maximal quotient of | (C19⋊C3)⋊C32, C2×(C19⋊C3)⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 1);