Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(C19⋊C16) |
| unambiguous semidirect product | (C2×C3)⋊(C19⋊C16) |
| unambiguous semidirect product | (C2×C19)⋊(C3⋊C16) |
| derived, Hall | C3×C19 ⋊ C2×C16 |
| Sylow | C19 ⋊ C2×C3⋊C16 |
| Sylow | C3 ⋊ C2×C19⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D57 |
| commutator, hypocenter | C3×C19 | C2×C16 |
| Frattini | C8 | C2×D57 |
| Fitting | C2×C3×C8×C19 | C2 |
| socle, prime radical | C22×C3×C19 | C8 |
| cosocle | C3×C8×C19 | C22 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1824 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 232);