Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×#622 |
| derived | C32 ⋊ C8×C27 |
| Sylow | C32×C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C27 | #157 |
| commutator, hypocenter | C32 | C8×C27 |
| Frattini | C2×C9 | C3×#157 |
| Fitting | C2×C32×C27 | C4 |
| socle, prime radical | C2×C33 | C4×C9 |
| cosocle | C9×C3⋊Dic3 | C2×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C27 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1122);