Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D92 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#10619528 |
| derived | C92 ⋊ C2×C3×C4 |
| Sylow | C3×C92 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D92 |
| commutator, hypocenter | C92 | C2×C3×C4 |
| Frattini | C2×C32 | C3×D32 |
| Fitting | C2×C3×C92 | C22 |
| socle | C2×C33 | D32 |
| prime radical | C2×C3×C9⋊D9 | C2 |
| cosocle | C2×C92 | C22×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2×C3 | |
278 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14516827, D3×#10619528, C3×#13047160, … |
| maximal normal subgroup of | C3×#14516827, D3×#10619528, C3×#13047160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1131);