Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C92 · Schur multiplier (H2) = C23×C9 |
| direct product | C22×D3×C92 |
| unambiguous semidirect product | C3⋊(C23×C92) |
| unambiguous semidirect product | (C2×C3)⋊(C22×C92) |
| Fitting | C22×C3×C92 ⋊ C2 |
| derived | C3 ⋊ C23×C92 |
| Sylow | C3×C92 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C92 | D3 |
| commutator, hypocenter | C3 | C23×C92 |
| Frattini | C32 | C22×C32×D3 |
| Fitting | C22×C3×C92 | C2 |
| socle | C22×C33 | C2×C32 |
| prime radical | C22×C32×D3 | C32 |
| cosocle | C33 | C23×C32 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C92 | |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
972 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D3×#6900, C22×D3×C9⋊D9, D3×C9×#611 |
| maximal normal subgroup of | C22×D3×#6900, C22×D3×C9⋊D9, D3×C9×#611 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2848);