Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92265⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#92265⋊C2 |
| unambiguous semidirect product | #92265⋊C22 |
| unambiguous semidirect product | #92314⋊C22 |
| Fitting | C2×#6900 ⋊ C22 |
| derived | C92 ⋊ C23×C3 |
| Sylow | #6900 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92265⋊C2 |
| commutator, cosocle, hypocenter | C92 | C23×C3 |
| Frattini | C32 | C2×C3×D32 |
| Fitting | C2×#6900 | C22 |
| socle | C2×C32 | C3×D32 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
394 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72213202, D3×#92265⋊C2, #72219879, … |
| maximal normal subgroup of | #72213202, #72219879, C22×#92265⋊C2, … |
| maximal quotient of | #72213202, D3×#92265⋊C2, #72219874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2687);