Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#6294 |
| derived | C33 ⋊ C2×C4×C9 |
| Sylow | C33×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | #1113 |
| commutator, hypocenter | C33 | C2×C4×C9 |
| Frattini | C2×C3 | C3×#1113 |
| Fitting | C2×C33×C9 | C22 |
| socle, cosocle | C2×C34 | C22×C3 |
| prime radical | C2×C32×C3⋊D3 | C2×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C9 | |
522 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3120);