Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92333 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#11757637 |
| derived | #732 ⋊ C2×C3×C4 |
| Sylow | #6911 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92333 |
| commutator, hypocenter | #732 | C2×C3×C4 |
| Frattini | C2×C32 | C2×C3×C3⋊D3 |
| Fitting, prime radical | C22×#6911 | C2 |
| socle | C22×C3 | C3×#272 |
| cosocle | C2×#732 | C22×C3 |
| LCS | G ▷ #732 | |
| UCS | C1 ◁ C22 | |
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2109);