Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D243 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D243 |
| unambiguous semidirect product | C243⋊C23 |
| unambiguous semidirect product | (C2×C243)⋊C22 |
| Fitting | C22×C243 ⋊ C2 |
| derived, Sylow | C243 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D243 |
| commutator, cosocle, hypocenter | C243 | C23 |
| Frattini | C81 | C22×D3 |
| Fitting | C22×C243 | C2 |
| socle | C22×C3 | D81 |
| LCS | G ▷ C243 | |
| UCS | C1 ◁ C22 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 972 |
492 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 102);