Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #10619756 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#10619756 |
| derived | #66361 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10619756 |
| commutator, cosocle, hypocenter | #66361 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | #272 |
| LCS | G ▷ #66361 | |
| UCS | C1 ◁ C3 | |
270 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2453);