Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×C8) |
| unambiguous semidirect product | (C8×D19)⋊C3 |
| Fitting | C8×C19 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C8 |
| Hall | C8×D19 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C3×C8 |
| Frattini | C4 | C2×D19⋊C3 |
| Fitting | C8×C19 | C2×C3 |
| socle | C2×C19 | C2×C3×C4 |
| prime radical | C2×D19⋊C3 | C4 |
| cosocle | C4×C19 | C22×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C16×D19⋊C3, #10597255⋊C3, C2×C8×D19⋊C3, … |
| maximal normal subgroup of | C16×D19⋊C3, #10597255⋊C3, C2×C8×D19⋊C3, … |
| maximal quotient of | C16×D19⋊C3, #10597255⋊C3, C8×(C19⋊C3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 7);