Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #6295 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#6296 |
| Sylow | C33×C9 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | #1113 |
| commutator | C2×C33 | C22×C9 |
| Frattini | C2×C3 | C3×#1113 |
| Fitting | C2×C33×C9 | C22 |
| socle, prime radical, cosocle | C2×C34 | C22×C3 |
| hypocenter | C33 | Q8×C9 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C9 | |
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3122);