Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D32×#272 |
| Fitting, derived, Sylow | C32×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D32×C3⋊D3 |
| commutator, Fitting, cosocle, hypocenter | C32×H(3,𝔽3) | C23 |
| socle | C33 | C22×C3⋊D3 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
1211 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 1211 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3571);