Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊Dic3×#272 |
| derived, Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C3⋊D32 |
| commutator, hypocenter | C32×H(3,𝔽3) | C2×C4 |
| Fitting, cosocle | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3⋊D3 |
| prime radical | C2×C32×#272 | C2 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
1120 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3193);