Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×D57 |
| Fitting | C2×C3×C8×C19 ⋊ C2 |
| derived, Hall | C3×C19 ⋊ C22×C8 |
| Sylow | C19 ⋊ C2×D3×C8 |
| Sylow | C3 ⋊ C2×C8×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D57 |
| commutator, hypocenter | C3×C19 | C22×C8 |
| Frattini | C4 | C22×D57 |
| Fitting | C2×C3×C8×C19 | C2 |
| socle | C22×C3×C19 | C2×C4 |
| prime radical | C22×D57 | C4 |
| cosocle | C3×C4×C19 | C23 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C8 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 912 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 964);